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Operations with Complex Numbers

9-1

Operations with Complex Numbers

The HP 35s can use complex numbers in the form

 







It has operations for complex arithmetic (+, –,

), complex trigonometry (sin, cos,

tan), and the mathematics functions –

, 1/

, and

. (where z

and z

are complex numbers).

The form, x+yi, is only available in ALG mode.

To enter a complex number:

Form:

 

Type the real part.

Press



Type the

imaginary

part.

Form:



Type the real part.

Press



Type the

imaginary

part.

Press



Form:





Type the value of r.

Press



Type the

value of

The examples in this chapter all utilize RPN mode unless otherwise noted.

Summary of Contents for 35s

Page 1: ...HP 35s scientific calculator user s guide H Edition 1 HP part number F2215AA 90001 ...

Page 2: ...E HEWLETT PACKARD CO SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING PERFORMANCE OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN 1988 1990 1991 2003 2007 Hewlett Packard Development Company L P Reproduction adaptation or translation of this manual is prohibited without prior written permission of Hewlett Packard Company except ...

Page 3: ...pacing and Clearing 1 4 Using Menus 1 6 Exiting Menus 1 8 RPN and ALG Modes 1 9 Undo key 1 11 The Display and Annunciators 1 12 Keying in Numbers 1 15 Making Numbers Negative 1 15 Exponents of Ten 1 15 Understanding Entry Cursor 1 17 Range of Numbers and OVERFLOW 1 17 Performing Arithmetic Calculations 1 18 Single Argument or Unary Operations 1 18 Two Argument or Binary Operations 1 19 Controlling...

Page 4: ...isplay 2 3 Clearing the X Register 2 3 Reviewing the Stack 2 3 Exchanging the X and Y Registers in the Stack 2 4 Arithmetic How the Stack Does It 2 5 How ENTER Works 2 6 How to Clear the Stack 2 7 The LAST X Register 2 8 Correcting Mistakes with LAST X 2 9 Reusing Numbers with LAST X 2 10 Chain Calculations in RPN Mode 2 12 Work from the Parentheses Out 2 12 Exercises 2 14 Order of Calculation 2 1...

Page 5: ...c Functions 4 1 Quotient and Remainder of Division 4 2 Power Functions 4 2 Trigonometry 4 3 Entering π 4 3 Setting the Angular Mode 4 4 Trigonometric Functions 4 4 Hyperbolic Functions 4 6 Percentage Functions 4 6 Physics Constants 4 8 Conversion Functions 4 10 Rectangular Polar Conversions 4 10 Time Conversions 4 13 Angle Conversions 4 13 Unit Conversions 4 14 Probability Functions 4 15 Factorial...

Page 6: ...rograms 5 10 6 Entering and Evaluating Equations 6 1 How You Can Use Equations 6 1 Summary of Equation Operations 6 3 Entering Equations into the Equation List 6 4 Variables in Equations 6 4 Numbers in Equations 6 5 Functions in Equations 6 5 Parentheses in Equations 6 6 Displaying and Selecting Equations 6 6 Editing and Clearing Equations 6 8 Types of Equations 6 9 Evaluating Equations 6 10 Using...

Page 7: ...ng Initial Guesses for SOLVE 7 8 For More Information 7 12 8 Integrating Equations 8 1 Integrating Equations FN 8 2 Accuracy of Integration 8 6 Specifying Accuracy 8 6 Interpreting Accuracy 8 6 For More Information 8 8 9 Operations with Complex Numbers 9 1 The Complex Stack 9 2 Complex Operations 9 2 Using Complex Numbers in Polar Notation 9 5 Complex Numbers in Equations 9 7 Complex Number in Pro...

Page 8: ...dows for Long Binary Numbers 11 8 Using base in program and equations 11 8 12 Statistical Operations 12 1 Entering Statistical Data 12 1 Entering One Variable Data 12 2 Entering Two Variable Data 12 2 Correcting Errors in Data Entry 12 2 Statistical Calculations 12 4 Mean 12 4 Sample Standard Deviation 12 6 Population Standard Deviation 12 7 Linear Regression 12 7 Limitations on Precision of Data ...

Page 9: ...am 13 10 Executing a Program XEQ 13 10 Testing a Program 13 11 Entering and Displaying Data 13 12 Using INPUT for Entering Data 13 13 Using VIEW for Displaying Data 13 15 Using Equations to Display Messages 13 16 Displaying Information without Stopping 13 18 Stopping or Interrupting a Program 13 19 Programming a Stop or Pause STOP PSE 13 19 Interrupting a Running Program 13 19 Error Stops 13 19 Ed...

Page 10: ...grams 14 1 Calling Subroutines XEQ RTN 14 1 Nested Subroutines 14 2 Branching GTO 14 4 A Programmed GTO Instruction 14 5 Using GTO from the Keyboard 14 5 Conditional Instructions 14 6 Tests of Comparison x y x 0 14 7 Flags 14 9 Loops 14 16 Conditional Loops GTO 14 17 Loops with Counters DSE ISG 14 18 Indirectly Addressing Variables and Labels 14 20 The Variables I and J 14 20 The Indirect Address ...

Page 11: ...tions 16 11 Grouped Standard Deviation 16 18 17 Miscellaneous Programs and Equations 17 1 Time Value of Money 17 1 Prime Number Generator 17 7 Cross Product in Vectors 17 11 Part 3 Appendixes and Reference A Support Batteries and Service A 1 Calculator Support A 1 Answers to Common Questions A 1 Environmental Limits A 2 Changing the Batteries A 3 Testing Calculator Operation A 4 The Self Test A 5 ...

Page 12: ... Two argument Arithmetic in ALG C 2 Simple Arithmetic C 2 Power Functions C 3 Percentage Calculations C 3 Permutations and Combinations C 4 Quotient and Remainder Of Division C 4 Parentheses Calculations C 4 Exponential and Logarithmic Functions C 5 Trigonometric Functions C 6 Hyperbolic functions C 6 Parts of numbers C 7 Reviewing the Stack C 7 Integrating an Equation C 8 Operations with Complex ...

Page 13: ...lts D 3 When SOLVE Cannot Find a Root D 8 Round Off Error D 13 E More about Integration E 1 How the Integral Is Evaluated E 1 Conditions That Could Cause Incorrect Results E 2 Conditions That Prolong Calculation Time E 7 F Messages F 1 G Operation Index G 1 ...

Page 14: ...12 Contents ...

Page 15: ...Part 1 Basic Operation ...

Page 16: ......

Page 17: ...stored To conserve energy the calculator turns itself off after 10 minutes of inactivity If you see the low power indicator in the display replace the batteries as soon as possible See appendix A for instructions Adjusting Display Contrast Display contrast depends on lighting viewing angle and the contrast setting To increase or decrease the contrast hold down the key and press or Watch for this s...

Page 18: ...e a left shifted function yellow and a right shifted function blue The shifted function names are printed in yellow above and in blue on the bottom of each key Press the appropriate shift key or before pressing the key for the desired function For example to turn the calculator off press and release the shift key then press ...

Page 19: ...their bottom right corner as shown above Whenever you need to type a letter for example a variable or a program label the A Z annunciator appears in the display indicating that the alpha keys are active Variables are covered in chapter 3 labels are covered in chapter 13 Cursor Keys Each of the four cursor direction keys is marked with an arrow In this text we will use the graphics Õ Ö and Ø to ref...

Page 20: ...en the calculator is in program entry and equation entry modes as discussed below Equation entry mode If an equation is in the process of being entered or edited erases the character immediately to the left of the insert cursor otherwise if the equation has been entered no insert cursor present deletes the entire equation Program entry mode If a program line is in the process of being entered or e...

Page 21: ...ed by If you press a new menu is displayed so you can verify your decision before erasing all your programs During equation entry is replaced by If you press the menu is displayed so you can verify your decision before erasing all your equations When you select the command is pasted into the command line with three placeholders You must enter a 3 digit number in the placeholder blanks Then all the...

Page 22: ...ssion curve fitting and linear estimation 12 Arithmetic mean of statistical x and y values weighted mean of statistical x values 12 s σ σ σ Sample standard deviation population standard deviation 12 CONST Menu to access the values of 41 physics constants refer to Physics constants on page 4 8 4 SUMS Statistical data summations 12 BASE Base conversions decimal hexadecimal octal and binary 12 INTG S...

Page 23: ...n tests of the X and Y registers 14 x 0 Comparison tests of the X register and zero 14 Other functions MEM Memory status bytes of memory available catalog of variables catalog of programs program labels 1 3 12 MODE Angular modes and operation mode 4 1 DISPLAY Fixed scientific engineering full floating point numerical display formats radix symbol options or complex number display format in RPN mode...

Page 24: ...DISPLAY menu to return to full floating point display of numbers Menus help you execute dozens of functions by guiding you to them You don t have to remember the names of all the functions built into the calculator nor search through the functions printed on the keyboard Exiting Menus Whenever you execute a menu function the menu automatically disappears as in the above example If you want to leav...

Page 25: ... arithmetic operations in either RPN Reverse Polish Notation or ALG Algebraic mode In Reverse Polish Notation RPN mode the intermediate results of calculations are stored automatically hence you do not have to use parentheses In Algebraic mode ALG you perform arithmetic operations using the standard order of operations To select RPN mode Press 9 to set the calculator to RPN mode When the calculato...

Page 26: ...u enter the first number press enter the second number and finally press the key In ALG mode the results and the calculations are displayed In RPN mode only the results are displayed not the calculations RPN mode ALG mode 1 2 1 2 Note You can choose either ALG Algebraic or RPN Reverse Polish Notation mode for your calculations Throughout the manual the v in the margin indicates that the examples o...

Page 27: ...hile in program mode In addition you can use Undo to recover the value of a register just cleared using the CLEAR menu The Undo operation must immediately follow the delete operation any intervening operations will keep Undo from retrieving the deleted object In addition to retrieving an entire entry after its deletion Undo can also be used while editing an entry Press while editing to recover a d...

Page 28: ...e entry is displayed in the first line in ALG mode and the second line in RPN mode Every calculation is displayed in up to 14 digits including an sign exponent and exponent value up to three digits The symbols on the display shown in the above figure are called annunciators Each one has a special significance when it appears in the display First Line Second Line Annunciators ...

Page 29: ... of the fraction is being displayed 5 Left shift is active 1 Right shift is active 1 RPN Reverse Polish Notation mode is active 1 2 ALG Algebraic mode is active 1 C PRGM Program entry is active 13 EQN Equation entry mode is active or the calculator is evaluating an expression or executing an equation 6 0 1 2 3 4 Indicates which flags are set flags 5 through 11 have no annunciator 14 RAD or GRAD Ra...

Page 30: ...n line 1 with missing characters will show an ellipsis to indicate missing characters In RPN mode use the Õ and Ö keys to scroll through an entry and see the leading and trailing characters In ALG mode use Õ and Ö to see the rest of the characters 1 6 The Ø and keys are active for stepping through an equation list a catalog of variables lines of a program menu pages or programs in the program cata...

Page 31: ...ill result in an error message clearing the error message returns you to the previous entry for correction Making Numbers Negative The key changes the sign of a number To key in a negative number type the number then press In ALG mode you may press key before or after typing the number To change the sign of a number that was entered previously just press If the number has an exponent affects only ...

Page 32: ...ample Suppose you want to enter Planck s constant 6 6261 10 34 For a power of ten without a multiplier as in the example of one million above press the key followed by the desired exponent of ten Keys Display Description _ Shows number being entered Rounds number to fit the display format Automatically uses scientific notation because otherwise no significant digits would appear Keys Display Descr...

Page 33: ...rminates entry To separate two numbers key in the first number press to terminate entry and then key in the second number If entry is not terminated if the cursor is present backspaces to erase the last digit If entry is terminated no cursor acts like and clears the entire number Try it Range of Numbers and OVERFLOW The smallest number available on the calculator is 9 99999999999 10499 while the l...

Page 34: ...ns are entered differently depending on whether the calculator is in RPN or ALG mode In RPN mode the number is entered first and then the operation is applied If the key is pressed after the number is entered then the number appears in line 1 and the result is shown in line 2 Otherwise just the result is displayed in line 2 and line 1 is unchanged In ALG mode the operator is pressed first and the ...

Page 35: ...e though the differences are similar to the case for single argument operators In RPN mode the first number is entered then the second number is placed in the x register and the two argument operation is invoked In ALG mode there are two cases one using traditional infix notation and another taking a more function oriented approach The following examples illustrate the differences Keys Display Des...

Page 36: ...mode press In ALG mode the equivalent operation is keyed in as Õ As with the single argument operations some of the two argument operations display differently in RPN mode than in ALG mode These differences are summarized in the table below Keys Display Description 9 Switch to RPN mode if necessary _ Enter 2 then place 3 in the x register Note the flashing cursor after the 3 don t press Enter Pres...

Page 37: ... four options FIX SCI ENG and ALL control the number of digits in the display of numbers During some complicated internal calculations the calculator uses 15 digit precision for intermediate results The displayed number is rounded according to the display format Fixed Decimal Format FIX format displays a number with up to 11 decimal places 11 digits to the right of the or radix mark if they fit Af...

Page 38: ... Engineering Format ENG format displays a number in a manner similar to scientific notation except that the exponent is a multiple of three there can be up to three digits before the or radix mark This format is most useful for scientific and engineering calculations that use units specified in multiples of 103 such as micro milli and kilo units After the prompt _ type in the number of digits you ...

Page 39: ...omatically displayed in scientific format Periods and Commas in Numbers The HP 35s uses both periods and commas to make numbers easier to read You can select either the period or the comma as the decimal point radix In addition you can choose whether or not to separate digits into groups of three using thousand separators The following example illustrates the options Keys Display Description 8 _ C...

Page 40: ...number of formats and although is only available in ALG mode In the example below the complex number 3 4i is displayed in all three ways Keys Display Description 8 Select full floating point precision ALL format The default format uses the comma as the thousand separator and the period as the radix 8 Change to use the comma for the radix Note that the thousand separator automatically changes to th...

Page 41: ...mode is set to FIX 4 but the last six digits 632019 are present internally in the calculator To temporarily display a number in full precision press Î This shows you the mantissa but no exponent of the number for as long as you hold down Î Keys Display Description 9 Enable ALG mode 6 Enter the complex number It displays as 3i4 the default format 8 Change to x yi format 8 or 8 Õ θ Change to rθa for...

Page 42: ...rst separates the integer part of the number from its fractional part 2 Key in the fraction numerator and press again The second separates the numerator from the denominator 3 Key in the denominator then press or a function key to terminate digit entry The number or result is formatted according to the current display format The a b c symbol under the key is a reminder that the key is used twice f...

Page 43: ...essage press or in RPN mode you will return to the stack as it was before the error In ALG mode you will return to the last expression with the edit cursor at the position of the error so that you can correct it Keys Display Description The decimal point is interpreted in the normal way _ When is pressed the 2nd time the display switches to fraction mode Upon entry the number is displayed using th...

Page 44: ...n which you can store any combination of data variables equations or program lines Checking Available Memory Pressing displays the following menu Where is the amount of used indirect variables is the number of bytes of memory available Pressing the displays the catalog of direct variables see Reviewing Variables in the VAR Catalog in chapter 3 Pressing the displays the catalog of programs 1 To ent...

Page 45: ...ations and programs you ve stored It does not affect mode and format settings To clear settings as well as data see Clearing Memory in appendix B To clear all of memory 1 Press You will then see the confirmation prompt which safeguards against the unintentional clearing of memory 2 Press Ö ...

Page 46: ...1 30 Getting Started ...

Page 47: ... to automatic storage is the automatic RPN memory stack HP s operating logic is based on an unambiguous parentheses free mathematical logic known as Polish Notation developed by the Polish logician Jan Łukasiewicz 1878 1956 While conventional algebraic notation places the operators between the relevant numbers or variables Łukasiewicz s notation places them before the numbers or variables For opti...

Page 48: ...art 1 and part 2 part 3 will be null in this case A 3 D vector will occupy part 1 part 2 and part 3 In programming the stack is used to perform calculations to temporarily store intermediate results to pass stored data variables among programs and subroutines to accept input and to deliver output T P a r t 3 O l d e s t n u m b e r P a r t 2 P a r t 1 0 0 0 0 0 Z P a r t 3 P a r t 2 P a r t 1 0 0 ...

Page 49: ...program this instruction The key in contrast is context sensitive It either clears or cancels the current display depending on the situation it acts like 1 only when the X register is displayed also acts like when the X register is displayed and digit entry is terminated no cursor present Reviewing the Stack R Roll Down The roll down key lets you review the entire contents of the stack by rolling ...

Page 50: ... into the X register and so on Exchanging the X and Y Registers in the Stack Another key that manipulates the stack contents is x exchange y This key swaps the contents of the X and Y registers without affecting the rest of the stack Pressing twice restores the original order of the X and Y register contents The function is used primarily to swap the order of numbers in a calculation For example o...

Page 51: ...ents The T top register replicates its contents 2 The stack lifts its contents The T register s contents are lost 3 The stack drops Notice that when the stack lifts it replaces the contents of the T top register with the contents of the Z register and that the former contents of the T register are lost You can see therefore that the stack s memory is limited to four numbers Because of the automati...

Page 52: ... contents of the X register into the Y register The next number you key in or recall writes over the copy of the first number left in the X register The effect is simply to separate two sequentially entered numbers You can use the replicating effect of to clear the stack quickly press 0 All stack registers now contain zero Note however that you don t need to clear the stack before doing calculatio...

Page 53: ... after 1 day 4 Calculates the population after 2 days 5 Calculates the population after 3 days How to Clear the Stack Clearing the X register puts a zero in the X register The next number you key in or recall writes over this zero There are four ways to clear the contents of the X register that is to clear x 1 Press 2 Press 3 Press Mainly used during program entry 4 Press to clear the X Y Z and T ...

Page 54: ...ds the number that was in the X register before the last numeric function was executed A numeric function is an operation that produces a result from another number or numbers such as Pressing returns this value into the X register This ability to retrieve the last x has two main uses 1 Correcting errors 2 Reusing a number in a calculation See appendix B for a comprehensive list of the functions t...

Page 55: ...ess Mistakes with Two Argument Functions If you make a mistake with a two argument operation such as or x you can correct it by using and the inverse of the two argument operation 1 Press to recover the second number x just before the operation 2 Execute the inverse operation This returns the number that was originally first The second number is still in the LAST X register Then If you had used th...

Page 56: ... can use to reuse a number such as a constant in a calculation Remember to enter the constant second just before executing the arithmetic operation so that the constant is the last number in the X register and therefore can be saved and retrieved with Example Calculate Wrong Calculation Mistake Correction Wrong function Ù Wrong first number Wrong second number 3947 52 3947 52 704 96 ...

Page 57: ... Sirius 8 7 light years away Use c the speed of light 9 5 1015 meters per year to convert the distances from the Earth to these stars into meters To Rigel Centaurus 4 3 yr 9 5 1015 m yr To Sirius 8 7 yr 9 5 1015 m yr Keys Display Description Enters first number Intermediate result Brings back display from before Final result ...

Page 58: ...er you would first calculate the intermediate result of 12 3 12 3 15 then you would multiply the intermediate result by 7 15 7 105 Evaluate the expression in the same way on the HP 35s starting inside the parentheses You don t need to press to save this intermediate result before proceeding since it is a calculated result it is saved automatically Keys Display Description Light years to Rigel Cent...

Page 59: ...ample to solve 3 4 5 6 on paper you would first calculate the quantity 3 4 Then you would calculate 5 6 Finally you would multiply the two intermediate results to get the answer Work through the problem the same way with the HP 35s except that you don t have to write down intermediate answers the calculator remembers them for you Keys Display Description Pressing the function key produces the answ...

Page 60: ...f Calculation We recommend solving chain calculations by working from the innermost parentheses outward However you can also choose to work problems in a left to right order For example you have already calculated Then multiplies the intermediate answers together for the final answer 0000 181 05 0 5 3805 16 x 5743 21 9 8 7 6 5 4 3 2 ...

Page 61: ...nds for noncommutative functions and However the first method starting with the innermost parentheses is often preferred because It takes fewer keystrokes It requires fewer registers in the stack The above example when solved left to right needed all registers in the stack at one point Note When using the left to right method be sure that no more than four intermediate numbers or results will be n...

Page 62: ...working through the following problems Calculate 14 12 18 12 9 7 78 0000 A Solution Calculate 23 2 13 9 1 7 412 1429 A Solution Calculate Solution or Calculate Intermediate result Final result 5961 0 7 0 5 12 8 0 4 5 3 5728 4 01 2 71 1 75 2 15 3 3 4 32 0 46 7 33 8 2 5 4 33 8 ...

Page 63: ...RPN The Automatic Memory Stack 2 17 A Solution ...

Page 64: ...2 18 RPN The Automatic Memory Stack ...

Page 65: ...lance and C for the speed of light Example This example shows you how to store the value 3 in the variable A first in RPN mode and then in ALG mode Keys Display Description 9 Switch to RPN mode if necessary _ Enter the value 3 _ The Store command prompts for a letter note the A Z annunciator A The value 3 is stored in A and returned to the stack 9 Switch to ALG mode if necessary A _ Again the Stor...

Page 66: ...register and T register in the stack Storing and Recalling Numbers Numbers and vectors are stored into and recalled from lettered variables by means of the Store and Recall commands Numbers may be real or complex decimal or fraction base 10 or other as supported by the HP 35s To store a copy of a displayed number X register to a direct variable Press letter key To recall a copy of a number from a ...

Page 67: ...de Recall can be used to paste a variable into an expression in the command line Suppose we wish to evaluate 15 2 G with G 1 75 from above We now proceed to switch to RPN mode and recall the value of G Keys Display Description _ Avogadro s number A _ prompts for variable Stores a copy of Avogadro s number in A This also terminates digit entry _ Clears the number in the display A Z The A Z annuncia...

Page 68: ...ut affecting the stack Using the MEM Catalog The MEMORY catalog u provides information about the amount of available memory The catalog display has the following format where mm mmm is the number of bytes of available memory and nnn is the amount of used indirect variables For more information on indirect variables see Chapter 14 The VAR catalog By default all direct variables from A to Z contain ...

Page 69: ...lustrating how to navigate the VAR catalog While we are in the VAR catalog let s extend this example to show you how to clear the value of a variable to zero effectively deleting the current value We ll delete E Suppose now that you wish to copy the value of C to the stack Keys Display Description Clear all direct variables C D E Store 3 in C 4 in D and 5 in E u Enter the VAR catalog Ø Scroll down...

Page 70: ...rithmetic with Stored Variables Storage arithmetic and recall arithmetic allow you to do calculations with a number stored in a variable without recalling the variable into the stack A calculation uses one number from the X register and one number from the specified variable Storage Arithmetic Storage arithmetic uses or to do arithmetic in the variable itself and to store the result there It uses ...

Page 71: ...lt replaces the value in the x register New x Previous x Variable For example suppose you want to divide the number in the X register 3 displayed by the value in A 12 Press A Now x 0 25 while 12 is still in A Recall arithmetic saves memory in programs using A one instruction uses half as much memory as A two instructions A 15 A 12 Result 15 3 that is A x T t T t Z z Z z Y y Y y X 3 A X 3 A 12 A 12...

Page 72: ... and add F to the result Exchanging x with Any Variable The key allows you to exchange the contents of x the displayed X register with the contents of any variable Executing this function does not affect the Y Z or T registers Keys Display Description D E F Stores the assumed values into the variable D E F Adds1 to D E and F D Displays the current value of D E F Clears the VIEW display displays X ...

Page 73: ...including the statistical registers using the I and J commands I is found on the key while J is on the key This is a programming technique called indirect addressing that is covered under Indirectly Addressing Variables and Labels in chapter 14 Keys Display Description A Stores 12 in variable A _ Displays x A Exchanges contents of the X register and variable A A Exchanges contents of the X registe...

Page 74: ...3 10 Storing Data into Variables ...

Page 75: ...onometric functions Hyperbolic functions Percentage functions Physics constants Conversion functions for coordinates angles and units Probability functions Parts of numbers number altering functions Arithmetic functions and calculations were covered in chapters 1 and 2 Advanced numeric operations root finding integrating complex numbers base conversions and statistics are described in later chapte...

Page 76: ...y in the second number Do not press 4 Press the function key Example To display the quotient and remainder produced by 58 9 Power Functions In RPN mode to calculate a number y raised to a power x key in y x then press For y 0 x can be any number for y 0 x must be positive To Calculate Press Natural logarithm base e Common logarithm base 10 Natural exponential Common exponential antilogarithm Keys ...

Page 77: ... the first 12 digits of π into the X register The number displayed depends on the display format Because is a function that returns an approximation of π to the stack it is not necessary to press Note that the calculator cannot exactly represent π since π is a transcendental number To Calculate Press Result 152 106 54 2 1 4 1 4 3 To Calculate Press Result 196 3 125 4 625 4 1 37893 ...

Page 78: ...unctions With x in the display Option Description Annunciator Sets degree mode which uses decimal degrees rather than hexagesimal degrees degrees minutes seconds none Sets radian mode RAD Sets gradient mode GRAD To Calculate Press Sine of x Cosine of x Tangent of x Arc sine of x Arc cosine of x Arc tangent of x Note Calculations with the irrational number π cannot be expressed exactly by the 15 di...

Page 79: ...using inverse trigonometric functions to determine an angle θ often look something like this θ arctan y x If x 0 then y x is undefined resulting in the error Keys Display Description 9 Sets Radians mode RAD annunciator on 5 7 in decimal format Cos 5 7 π 9 Switches to Degrees mode no annunciator Calculates cos 128 57 which is the same as cos 5 7 π ...

Page 80: ...rry out subsequent calculations using both the base number and the result without reentering the base number Example Find the sales tax at 6 and the total cost of a 15 76 item Use FIX 2 display format so the costs are rounded appropriately To Calculate Press Hyperbolic sine of x SINH Hyperbolic cosine of x COSH Hyperbolic tangent of x TANH Hyperbolic arc sine of x ASINH Hyperbolic arc cosine of x ...

Page 81: ...y Description 8 Rounds display to two decimal places Calculates 6 tax Total cost base price 6 tax Keys Display Description This year s price dropped about 2 2 from last year s price 8 Restores FIX 4 format Note The order of the two numbers is important for the CHG function The order affects whether the percentage change is considered positive or negative ...

Page 82: ...roton mass 1 67262158 10 27 kg Neutron mass 1 67492716 10 27 kg Muon mass 1 88353109 10 28 kg Boltzmann constant 1 3806503 10 23 J K 1 Planck constant 6 62606876 10 34 J s Planck constant over 2 pi 1 054571596 10 34 J s Magnetic flux quantum 2 067833636 10 15 Wb Bohr radius 5 291772083 10 11 m ε Electric constant 8 854187817 10 12 F m 1 Molar gas constant 8 314472 J mol 1 k 1 Faraday constant 9648...

Page 83: ... 730313461 Ω λ Compton wavelength 2 426310215 10 12 m λ Neutron Compton wavelength 1 319590898 10 15 m λ Proton Compton wavelength 1 321409847 10 15 m α Fine structure constant 7 297352533 10 3 σ Stefan Boltzmann constant 5 6704 10 8 W m 2 K 4 Celsius temperature 273 15 a Standard atmosphere 101325 Pa γ Proton gyromagnetic ratio 267522212 s 1 T 1 First radiation constant 374177107 10 16 W m2 Secon...

Page 84: ...ght blue shift of the same key converts the other way For each conversion of this type the number you entered is assumed to be measured using the other unit For example when using to convert a number to Fahrenheit degrees the number you enter is assumed to be a temperature measured in Celsius degrees The examples in this chapter utilize RPN mode In ALG mode enter the function first then the number...

Page 85: ...eps required to set a complex number format 1 Press 8 and then choose either or in RPN mode in ALG mode you may also choose 2 Input your desired coordinate value x 6 y x y 6 or r a 3 press Example Polar to Rectangular Conversion In the following right triangles find sides x and y in the triangle on the left and hypotenuse r and angle θ in the triangle on the right Keys Display Description 9 8 Sets...

Page 86: ...pedance equal to the polar magnitude r and voltage lag equal to the angle θ in degrees When the values are converted to rectangular coordinates the x value yields R in ohms the y value yields XC in ohms 8 θ Sets complex coordinate mode 6 θ Convert xiy rectangular to rθ a polar Keys Display Description 9 8 Sets Degrees and complex coordinate mode θ Enters θ degrees of voltage lag Enters r ohms of t...

Page 87: ... seconds and ss is the fractional part of the number of seconds To convert between decimal format and hours minutes and seconds 1 Enter the number you wish to convert 2 Press to convert to hours degrees minutes and seconds or press 5 to convert back to decimal format Example Converting Time Formats How many minutes and seconds are there in 1 7 of an hour Use FIX 6 display format Angle Conversions ...

Page 88: ...onversion functions on the keyboard kg lb ºC ºF cm in l gal MILE KM Keys Display Description _ Enter the angle in degrees µ Convert to radians Read the result as 0 5236 a decimal approximation of π 6 To Convert To Press Displayed Results 1 lb kg kilograms 1 kg lb pounds 32 ºF ºC C 100 ºC ºF F 1 in cm centimeters 100 cm in inches 1 gal l liters 1 l gal gallons 1 MILE KM KMS 1 KM MILE MILES ...

Page 89: ...e in a set and different orders of the same r items are not counted separately Permutations To calculate the number of possible arrangements of n items taken r at a time enter n first then r nonnegative integers only No item occurs more than once in an arrangement and different orders of the same r items are counted separately Seed To store the number in x as a new seed for the random number gener...

Page 90: ...son safety committee How many different combinations of people are possible If employees are chosen at random what is the probability that the committee will contain six women To find the probability of an event divide the number of combinations for that event by the total number of combinations Keys Display Description _ Twenty four people grouped six at a time x Total number of combinations poss...

Page 91: ...Absolute value To replace a number in the x register with its absolute value press For complex numbers and vectors the absolute value of 1 a complex number in rθa format is r 2 a complex number in xiy format is 3 a vector A1 A2 A3 An is Argument value To extract the argument of a complex number use The argument of a complex number 1 in rθa format is a 2 in xiy format is Atan y x Sign value To indi...

Page 92: ... of numbers The RND function rounds x internally to the number of digits specified by the display format The internal number is represented by 12 digits Refer to chapter 5 for the behavior of RND in Fraction display mode To calculate Press Display The integer part of 2 47 The fractional part of 2 47 The absolute value of 7 The sign value of 9 The greatest integer equal to or less than 5 3 ...

Page 93: ...action display mode is turned off the display reverts to the previous display format set via the Display menu Choosing another format via this menu also turns off Fraction display mode if active Functions work the same with fractions as they do with decimal numbers except for RND which is discussed later in this chapter The examples in this chapter all utilize RPN mode unless otherwise noted Enter...

Page 94: ...digit decimal value Most statistics registers are exceptions they re always shown as decimal numbers Display Rules The fraction you see may differ from the one you enter In its default condition the calculator displays a fractional number according to the following rules To change the rules see Changing the Fraction Display later in this chapter The number has an integer part and if necessary a pr...

Page 95: ...is no more than 0 5 below the displayed numerator If is lit the fractional part of the internal 12 digit value is slightly greater than the displayed fraction the exact numerator is no more than 0 5 above the displayed numerator This diagram shows how the displayed fraction relates to nearby values means the exact numerator is a little above the displayed numerator and means the exact numerator is...

Page 96: ...an integer part its fractional part contains less than 12 digits and it can t exactly match a fraction that uses all 12 digits Changing the Fraction Display In its default condition the calculator displays a fractional number according to certain rules However you can change the rules according to how you want fractions displayed You can set the maximum denominator that s used You can select one o...

Page 97: ... register If the displayed fraction is too long to fit in the display the annunciator will appear you can then use Ö and Õ to scroll page by page to see the rest of the fraction To see the number s decimal representation press and then hold Example This example illustrates the steps required to set the maximum denominator to 3125 and then show a fraction that is too long for the display Notes 1 In...

Page 98: ...ave only denominators that are factors of the c value and they re reduced as much as possible For example if you re calculating stock prices you might want to see and c value is 8 Or if the c value is 12 possible denominators are 2 3 4 6 and 12 Fixed denominator Fractions always use the c value as the denominator they re not reduced For example if you re working with time measurements you might wa...

Page 99: ...r to clear the or response Example This example illustrates the display of fractions in the three formats using the number π This example assumes fraction display format is active and that Flag 8 is in its default state cleared To Get This Fraction Format Change These Flags 8 9 Most precise Clear Factors of denominator Set Clear Fixed denominator Set Set Keys Display Description Sets the maximum c...

Page 100: ...curacy indicatior turns off if the fraction matches the decimal representation exactly Otherwise the accuracy indicatior stays on See Accuracy Indicators earlier in this chapter In an equation or program the RND function does fractional rounding if Fraction display mode is active Fraction Format How 2 77 Is Displayed c 4095 c 16 Most Precise 2 77 100 2 7700 2 10 13 2 7692 Factors of Denominator 2 ...

Page 101: ...e is available for operations involving equations When you re evaluating an equation and you re prompted for variable values you may enter fractions values are displayed using the current display format See chapter 6 for information about working with equations Keys Display Description Sets Flag 8 Sets up fraction format for 1 16 inch increments Flags 8 and 9 should be the same as for the previous...

Page 102: ...ues are shown using Fraction display mode if it s active If you re prompted for values by INPUT instructions you may enter fractions The program s result is displayed using the current display format A program can control the fraction display using the c function and by setting and clearing flags 7 8 and 9 See Flags in chapter 14 See chapters 13 and 14 for information about working with programs ...

Page 103: ...on Suppose you frequently need to determine the volume of a straight section of pipe The equation is V 25 π d2 l where d is the inside diameter of the pipe and l is its length You could key in the calculation over and over for example calculates the volume of 16 inches of 2 1 2 inch diameter pipe 78 5398 cubic inches However by storing the equation you get the HP 35s to remember the relationship b...

Page 104: ...ator Begins a new equation turns on the A Z annunciator so you can enter a variable name _ types _ Digit entry uses the _ entry cursor π _ ends the number D π _ types π _ π Terminates and displays the equation Shows the checksum and length for the equation so you can check your keystrokes Keys Display Description value Prompts for variables on the right hand side of the equation Prompts for D firs...

Page 105: ...e left hand side If the equation is an equality or expression calculates its value like See Types of Equations later in this chapter Evaluates the displayed equation Calculates its value replacing with if an is present Solves the displayed equation for the unknown variable you specify See chapter 7 Integrates the displayed equation with respect to the variable you specify See chapter 8 Deletes the...

Page 106: ...you re entering the previous equation isn t affected If you make a mistake press or as required 4 Press to terminate the equation and see it in the display The equation is automatically saved in the equation list right after the entry that was displayed when you started typing If you press instead the equation is saved but Equation mode is turned off Equations can contain variables numbers vectors...

Page 107: ...tions later in this chapter Appendix G Operation Index also gives this information When you enter an equation you enter functions in about the same way you put them in ordinary algebraic equations In an equation certain functions are normally shown between their arguments such as and For such infix operators enter them in an equation in the same order Other functions normally have one or more argu...

Page 108: ...ecting Equations The equation list contains two built in equations 2 2 lin solve and 3 3 lin Solve and the equations you ve entered You can display the equations and select one to work with Keys Display Description π Shows the last equation used in the equation list _ Starts a new equation with variable R _ Enters a number _ Enters infix operators 4 Enters a prefix function with a left parenthesis...

Page 109: ...dicates more characters to the right 2 Press Õ to begin editing the equation at the beginning or press Ö to begin editing the equation at the end Then press Ö or Õ repeatedly to move the cursor through the equation one character at a time and display when there are more characters to the left or right 3 Press Ö or Õ to scroll the long equations in line 2 by a screen To select an equation Display t...

Page 110: ...ses the empty equation line to be deleted The display then shows the previous entry in the equation list 3 Press or to save the equation in the equation list To edit a saved equation 1 Display the desired equation press Õ to activate the cursor at the beginning of the equation or press Ö to activate the cursor at the end of the equation See Displaying and Selecting Equations above 2 When the curso...

Page 111: ...s of Equations The HP 35s works with three types of equations Equalities The equation contains an and the left side contains more than just a single variable For example x 2 y 2 r 2 is an equality Assignments The equation contains an and the left side contains just a single variable For example A 0 5 b h is an assignment Keys Display Description Shows the current equation in the equation list Ö _ ...

Page 112: ...bles you to solve and integrate equations as described in chapters 7 and 8 Because many equations have two sides separated by the basic value of an equation is the difference between the values of the two sides For this calculation in an equation is essentially treated as The value is a measure of how well the equation balances The HP 35s has two keys for evaluating equations and Their actions dif...

Page 113: ...ter in this chapter To halt a calculation press or The message is shown in line 2 The evaluation of an equation takes no values from the stack it uses only numbers in the equation and variable values The value of the equation is returned to the X register Using ENTER for Evaluation If an equation is displayed in the equation list you can press to evaluate the equation If you re in the process of t...

Page 114: ...ind the volume of a 35 mm diameter pipe that s 20 meters long Using XEQ for Evaluation If an equation is displayed in the equation list you can press to evaluate the equation The entire equation is evaluated regardless of the type of equation The result is returned to the X register Keys Display Description as required π Displays the desired equation Starts evaluating the assignment equation so th...

Page 115: ...for each variable that s needed The prompt gives the variable name and its current value such as If the unnamed indirect variable I or J is in an equation you will not be prompted to for its value as the current value stored in the unnamed indirect variable will be used automatically See chapter 14 To leave the number unchanged just press Keys Display Description Displays the desired equation Star...

Page 116: ...ster and displays in right side of the line two If you press during digit entry it clears the number to zero Press again to cancel the prompt To display digits hidden by the prompt press In RPN mode each prompt puts the variable value in the X register and disables stack lift If you type a number at the prompt it replaces the value in the X register When you press stack lift is enabled so the valu...

Page 117: ...nside parentheses are performed before operations outside the parentheses Examples Order Operation Example 1 Parentheses 2 Functions 3 Power 4 Unary Minus 5 Multiply and Divide 6 Add and Subtract 7 Equality Equations Meaning a b3 c a b 3 c a b c 12 a b c 12 CHG t 12 a 6 2 ...

Page 118: ... with a comma In an equation the XROOT function takes its arguments in the opposite order from RPN usage For example 8 3 to is equivalent to All other two argument functions take their arguments in the Y X order used for RPN For example 28 4 x is equivalent to For two argument functions be careful if the second argument is negative These are valid equations LN LOG EXP ALOG SQ SQRT INV IP FP RND AB...

Page 119: ... Perimeter of a Trapezoid The following equation calculates the perimeter of a trapezoid This is how the equation might appear in a book Perimeter a b h The following equation obeys the syntax rules for HP 35s equations RPN Operation Equation function x2 SQ SQRT ex EXP 10x ALOG 1 x INV XROOT yx INT IDIV x X y φ θ sin 1 sin 1 b a h φ θ ...

Page 120: ...de the INV function INV is typed by Example Area of a Polygon The equation for area of a regular polygon with n sides of length d is Area You can specify this equation as π π Notice how the operators and functions combine to give the desired equation Parentheses used to group items Single letter name Optional explicit multiplication Division is done before addition n sin cos 4 1 π π n n d 2 d 2 n ...

Page 121: ...in chapter 13 Verifying Equations When you re viewing an equation not while you re typing an equation you can press to show you two things about the equation the equation s checksum and its length Hold the key to keep the values in the display The checksum is a four digit hexadecimal value that uniquely identifies this equation If you enter the equation incorrectly it will not have this checksum T...

Page 122: ...20 Entering and Evaluating Equations Keys Display Description as required π Displays the desired equation hold Display equation s checksum and length release π Redisplays the equation Leaves Equation mode ...

Page 123: ...blems just as well Markup Cost Price If you know any two of these variables then SOLVE can calculate the value of the third When the equation has only one variable or when known values are supplied for all variables except one then to solve for x is to find a root of the equation A root of an equation occurs where an equality or assignment equation balances exactly or where an expression equation ...

Page 124: ...Zero and the Z register contains the value of the root D value which should be zero For some complicated mathematical conditions a definitive solution cannot be found and the calculator displays See Verifying the Result later in this chapter and Interpreting Results and When SOLVE Cannot Find a Root in appendix D For certain equations it helps to provide one or two initial guesses for the unknown ...

Page 125: ...the display you can start solving for D Try another calculation using the same equation how long does it take an object to fall 500 meters from rest Keys Display Description Ö Clears memory Selects Equation mode _ Starts the equation G _ Terminates the equation and displays the left end Checksum and length Keys Display Description _ Prompts for unknown variable value Selects D prompts for V value ...

Page 126: ...N is the number of moles of gas R is the universal gas constant 0 0821 liter atm mole K or 8 314 J mole K and T is temperature Kelvins K C 273 1 Enter the equation Keys Display Description Displays the equation Solves for T prompts for D Stores 500 in D prompts for V Retains 0 in V prompts for G Retains 9 8 in G solves for T Keys Display Description P _ Selects Equation mode and starts the equatio...

Page 127: ...heres when the temperature is 18 C Calculate the density of the gas N 28 V where 28 is the molecular weight of nitrogen Keys Display Description P value Solves for P prompts for V value Stores 2 in V prompts for N value Stores 005 in N prompts for R value Stores 0821 in R prompts for T Calculates T Kelvins Stores 297 1 in T solves for P in atmospheres Keys Display Description Displays the equation...

Page 128: ...ion system or x y and z for a 3 3 linear equation system The result will be saved in variables x y and z The calculator can detect cases with infinitely many solutions or no solutions Example solve the x y in simultaneous equations Stores 291 1 in T solves for N Calculates mass in grams N 28 Calculates density in grams per liter Keys Display Description Enters equation mode Ø Displays the built in...

Page 129: ... as P V N R T This ensures that an equality or assignment equation balances at the root and that an expression equation equals zero at the root Some equations are more difficult to solve than others In some cases you need to enter initial guesses in order to find a solution See Choosing Initial Guesses for SOLVE below If SOLVE is unable to find a solution the calculator displays See appendix D for...

Page 130: ... clear the message The values in the X and Y registers bracket the interval that was last searched to find the root The Z register contains the value of the equation at the final estimate of the root If the X and Y register values aren t close together or the Z register value isn t close to zero the estimate from the X register probably isn t a root If the X and Y register values are close togethe...

Page 131: ...ure to the desired answer or range of answers For example the equation of linear motion d v0 t 1 2 gt 2 can have two solutions for t You can direct the answer to the required solution by entering appropriate guesses The example using this equation earlier in this chapter didn t require you to enter guesses before solving for T because in the first part of that example you stored a value for T and ...

Page 132: ... amount to be folded up along each of the four sides that gives the specified volume A taller box is preferred to a shorter one If H is the height then the length of the box is 80 2H and the width is 40 2H The volume V is V 80 2H 40 2H H which you can simplify and enter as V 40 H 20 H 4 H Type in the equation Keys Display Description _ Selects Equation mode and starts the equation 4 HÕ _ 40 80 40_...

Page 133: ...urned an exact root by looking at the value of the previous estimate of the root in the Y register and the value of the equation at the root in the Z register 4 H Õ _ H _ Terminates and displays the equation Checksum and length Keys Display Description Leaves Equation mode H _ Stores lower and upper limit guesses Displays current equation H value Solves for H prompts for V Stores 7500 in V solves ...

Page 134: ...quation and press at the prompt for x enter the x coordinate and then obtain the corresponding value of the equation the y coordinate For the problem above you would always set V 7500 and vary the value of H to produce different values for the equation Remember that the value for this equation is the difference between the left and right sides of the equation The plot of the value of this equation...

Page 135: ... then the integral can be expressed mathematically as The quantity I can be interpreted geometrically as the area of a region bounded by the graph of the function f x the x axis and the limits x a and x b provided that f x is nonnegative throughout the interval of integration The operation FN integrates the current equation with respect to a specified variable d_ The function may have more than on...

Page 136: ...egration calculation by pressing or and the message will be shown in line 2 but the integration cannot be resumed However no information about the integration is available until the calculation finishes normally The display format setting affects the level of accuracy assumed for your function and used for the result The integration is more precise but takes much longer in the and higher and setti...

Page 137: ... Now integrate this function with respect to t from zero to π x 2 Keys Display Description Ö Clears memory Selects Equation mode X Types the equation ÕÕ _ Terminates the expression and displays its left end Checksum and length Leaves Equation mode Keys Display Description 9 Selects Radians mode Enters the limits of integration lower limit first Displays the function _ Prompts for the variable of i...

Page 138: ...ough idealized networks require calculating an integral sometimes called the sine integral of the form Find Si 2 value Prompts for value of X x 2 Starts integrating calculates result for The final result for J0 2 Keys Display Description Enters the limits of integration lower limit first Displays the current equation _ Prompts for the variable of integration Prompts for value of X x 3 Starts integ...

Page 139: ...rval of integration are extremely close together or the number of sample points is extremely large Now integrate this function with respect to x that is X from zero to 2 t 2 Keys Display Description Selects Equation mode X Starts the equation Õ _ The closing right parenthesis is required in this case X _ Terminates the equation Checksum and length Leaves Equation mode Keys Display Description 9 Se...

Page 140: ...tion calculation the greater the number of digits displayed the greater the precision of the calculated integral and the greater the time required to calculate it The fewer the number of digits displayed the faster the calculation but the calculator will presume that the function is accurate to the only number of digits specified To specify the accuracy of the integration set the display format so...

Page 141: ...that f x is still calculated accurately to the number of digits shown in the display In general the uncertainty of an integration calculation decreases by a factor of ten for each additional digit specified in the display format Example Changing the Accuracy For the integral of Si 2 just calculated specify that the result be accurate to four decimal places instead of only two Keys Display Descript...

Page 142: ...nge of applications Appendix E contains more detailed information about how the algorithm for integration works conditions that could cause incorrect results and conditions that prolong calculation time and obtaining the current approximation to an integral Keys Display Description 8 Specifies accuracy to four decimal places The uncertainty from the last example is still in the display Rolls down ...

Page 143: ...ics functions z 1 z ln z and e z where z1 and z2 are complex numbers The form x yi is only available in ALG mode To enter a complex number Form 1 Type the real part 2 Press 6 3 Type the imaginary part Form 1 Type the real part 2 Press 3 Type the imaginary part 4 Press 6 Form 1 Type the value of r 2 Press 3 Type the value of θ The examples in this chapter all utilize RPN mode unless otherwise noted...

Page 144: ...2 of the Y register is displayed in line 1 Complex Operations Use the complex operations as you do real operations in ALG and RPN mode To do an operation with one complex number 1 Enter the complex number z as described before 2 Select the complex function T Part3 Part2 Part1 Z Part3 Part2 Part1 Y Part3 Display in line 1 X1iY1 Y 1 o r a 1 or X 1 o r r 1 r1θ a1 X P a r t 3 Display in line 2 X 2 i Y...

Page 145: ...Enter the second complex number z2 as described before 3 Select the arithmetic operation Arithmetic With Two Complex Numbers z1 and z2 To Calculate Press Change sign z Inverse 1 z Natural log ln z Natural antilog ez Sin z Cos z Tan z Absolute value ABS z Argument value ARG z To Calculate Press Addition z1 z2 Subtraction z1 z2 Multiplication z1 z2 Division z1 z2 Power function 2 1 z z ...

Page 146: ...sion z 1 z2 z3 where z1 23 i 13 z2 2i1 z3 4 i 3 Perform the calculation as Evaluate 4 i 2 5 3 i 2 3 Keys Display Description 8 Sets display format 6 Result is 9 1545 i 4 1689 Keys Display Description 8 Sets display format 6 ENTER z1 6 ENTER z2 6 z2 z3 Result is 2 i 2 z 1 z2 z3 Result is 2 5 i 9 Keys Display Description 8 Sets display format 6 Enters 4i 2 5 ...

Page 147: ...orms use pairs of numbers as do complex numbers so you can do arithmetic with these numbers by using the complex operations Example Vector Addition Add the following three loads 6 Enters 3i 2 3 Result is 11 7333i 3 8667 Keys Display Description 6 ENTER 1i1Intermediate result of Z 2 result is 0i 5 Final result is 0 8776 i 0 4794 2 z e r real a b imaginary θ imaginary real ...

Page 148: ...erent however the result form is dependent on the setting in 8menu Keys Display Description 9 Sets Degrees mode 8 Sets complex mode θ θ Enters L1 θ θ Enters L2 θ θ Enters L3 and adds L2 L3 θ Adds L1 L2 L3 Õ Scrolls the screen to see the rest of the answer y 185 lb 62 o 100 lb 261 o 170 lb 143 o L 1 L 2 L 3 x ...

Page 149: ...valuate an equation and are prompted for variable values you may enter complex numbers The values and format of the result are controlled by the display setting This is the same as calculating in ALG mode Equations that contain complex numbers can be solved and integrated Keys Display Description 9 Sets Degrees mode 8 Sets complex mode 6 θ θ Enters 1i1 θ θ Enters 3θ 10 θ θ Enters 5θ 30 and adds 3θ...

Page 150: ...0 in program is When you are running a program and are prompted for values by INPUT instructions you can enter complex numbers The values and format of the result are controlled by the display setting The program that contains the complex number can also be solved and integrated Program lines ALG mode Description Begins the program ...

Page 151: ...ocity and acceleration etc To enter a vector 1 Press 3 2 Enter the first number for the vector 3 Press and enter a second number for a 2 D or 3 D vector 4 Press and enter a third number for a 3 D vector The HP 35s cannot handle vectors with more than 3 dimensions Vector operations Addition and subtraction The addition and subtraction of vectors require that two vector operands have the same length...

Page 152: ...y a scalar 1 Enter a vector 2 Enter a scalar 3 Press for multiplication or for division Keys Display Description 9 Switches to RPN mode if necessary 3 Enters 1 5 2 2 3 Enters 1 5 2 2 Adds two vectors Keys Display Description 9 Switches to ALG mode 3 Õ _ Enters 3 4 4 5 3 Enters 2 3 1 4 Subtracts two vectors ...

Page 153: ...vector A A1 A2 An the magnitude is defined as 1 Press 2 Enter a vector 3 Press For example Absolute value of vector 5 12 3 The answer is 13 In RPN mode 9 3 Keys Display Description 9 Switches to RPN mode 3 Enters 3 4 _ Enters 5 as a scalar Performs multiplication Keys Display Description 9 Switches to ALG mode 3 Õ _ Enters 2 4 Enters 5 as a scalar Performs division A 2 2 2 2 1 n A A A ...

Page 154: ...x D X x Y 1 Enter the first Vector 2 Press 3 Enter the second vector 4 Press Note The sign here means dot product instead of cross product For cross product see chapter 17 Calculate the dot product of two vectors 1 2 and 3 4 Calculate the dot product of two vectors 9 5 and 2 2 Keys Display Description 9 Switches to ALG mode 3 Õ _ Enters the first vector 1 2 3 Executes for dot product and enters th...

Page 155: ...t of two vectors is 28 Keys Display Description 9 Switches to ALG mode 9 Sets Degrees mode Arc cosine function 3 Õ Enters vector A 1 0 3 Õ Enters vector B 0 1 for dot product of A and B 3 Õ Finds the magnitude of vector A 1 0 3 Finds the magnitude of vector B 0 1 The angle between two vectors is 90 Keys Display Description 9 Switches to RPN mode 9 Sets Degrees mode 3 3 Finds the dot product of two...

Page 156: ...uations containing vectors can be solved however the solver has limited ability if the unknown is a vector Equations containing vectors can be integrated however the result of the equation must be a real or a 1 D vector or a vector with 0 as the 2nd and 3rd elements 3 Finds the magnitude of vector 0 5 Multiplies two vectors Divides two values The angle between two vectors is 36 8699 ...

Page 157: ... in the same way as real and complex numbers For example 5 6 2 x 7 8 x 9 10 in a program is A vector can be entered when prompted for a value for a variable Programs that contain vectors can be used for solving and integrating Program lines Description Begins the program 5 6 ...

Page 158: ...t that the d key must be pressed first followed by pressing 3 To enter an element containing the value stored in a lettered variable press h and the variable letter To enter an element from a stack register press the key and use the Õ or Ö keys to move the underline symbol so that it is under the stack register to be used and press To enter an element indirectly indicated by the value in the I or ...

Page 159: ... keys and act as shortcut to enter the digits A to F In ALG mode press A B C D E or F to enter the digits A to F Octal mode The OCT annunciator is displayed when this mode is active Numbers are displayed in Octal format Binary mode The BIN annunciator is displayed when this mode is active Numbers are displayed in Binary format If a number has more than 12 digits the Õ and Ö keys allow to view the ...

Page 160: ...ed that erase them and will be displayed if the decimal base is selected Convert 24FF16 to binary base The binary number will be more than 14 digits the maximum display long placed at the end of a number means that this number is an octal number To enter an octal number type the number followed by placed at the end of a number means that this number is a binary number To enter a binary number type...

Page 161: ...or will automatically add a current base sign b o h following the result to represent base 2 8 16 number in line 2 4 To edit expression again press Ö or Õ In RPN mode When you enter a number in line 2 press and then change the base mode the calculator will convert the base of the numbers in line 1 and line 2 and the sign b o h will be added following the number to represent base 2 8 16 To view the...

Page 162: ...orm and uses integers only If a number has a fractional part only the integer part is used for an arithmetic calculation Menu label Description Logical bit by bit AND of two arguments For example AND 1100b 1010b 1000b Logical bit by bit XOR of two arguments For example XOR 1101b 1011b 110b Logical bit by bit OR of two arguments For example OR 1100b 1010b 1110b Returns the one s complement of the a...

Page 163: ...egister If the result of an operation cannot be represented in valid bits the display shows and then shows the largest positive or negative number possible Example Here are some examples of arithmetic in Hexadecimal Octal and Binary modes 12F16 E9A16 77608 43268 1008 58 5A016 10011002 Keys Display Description Sets base 16 HEX annunciator on Result Sets base 8 OCT annunciator on Converts displayed ...

Page 164: ...e the binary representation of 12510 is displayed as 1111101b which is the same as these 36 digits 000000000000000000000000000001111101b Negative Numbers The leftmost most significant or highest bit of a number s binary representation is the sign bit it is set 1 for negative numbers If there are undisplayed leading zeros then the sign bit is 0 positive A negative number is the 2 s complement of it...

Page 165: ...is range can not be entered when a non decimal base is selected 2 s complement sign changed Binary version indicates more digits The number is negative since the highest bit is 1 Õ Displays the rest of the number by scrolling one screen Õ Displays the rightmost window Negative decimal number Base Positive Integer of Largest Magnitude Negative Integer of Largest Magnitude Hexadecimal 7FFFFFFFFh 800...

Page 166: ...s called a window When a binary number is larger than the 14 digits the or annunciator or both appears indicating in which direction the additional digits lie Press the indicated key Ö or Õ to view the obscured window Using base in program and equations Equations and program are affected by the base setting and binary octal and hexadecimal numbers can be entered in equation and in program as well ...

Page 167: ...imation and Weighted mean x weighted by y Summation statistics n Σx Σy Σx2 Σy2 and Σxy Entering Statistical Data One and two variable statistical data are entered or deleted in similar fashion using the or key Data values are accumulated as summation statistics in six statistics registers 27 through 32 whose names are displayed in the SUMS menu Press and see Note Always clear the statistics regist...

Page 168: ...play immediately after it has been entered press Entering Two Variable Data If the data is a pair of variables enter first the dependent variable the 2nd variable of the pair and press and then enter the independent variable the first variable of the pair and press 1 Press to clear existing statistical data 2 Key in the y value first and press 3 Key in the corresponding x value and press 4 The dis...

Page 169: ...d in the LAST X register After deleting the incorrect statistical data calculator will display the value of Y register in line 1 and value of n in line 2 Example Key in the x y values on the left then make the corrections shown on the right Initial x y Corrected x y 20 4 20 5 400 6 40 6 Keys Display Description Clears existing statistical data Enters the first new data pair Display shows n the num...

Page 170: ...he y values as weights or frequencies The weights can be integers or non integers Reenters the first data pair There is still a total of two data pairs in the statistics registers Menu Key Description L R The linear regression menu linear estimation and curve fitting See Linear Regression later in this chapter The mean menu See Mean below s σ The standard deviation menu σ σ See Sample Standard Dev...

Page 171: ...cturing company purchases a certain part four times a year Last year s purchases were Find the average price weighted for the purchase quantity for this part Remember to enter y the weight frequency before x the price 15 5 9 25 10 0 12 5 12 0 8 5 Keys Display Description Clears the statistics registers Enters the first time Enters the remaining data six data points accumulated Calculates the mean ...

Page 172: ...are described in the next section Population Standard Deviation Example Sample Standard Deviation Using the same process times as in the above mean example May Kitt now wants to determine the standard deviation time sx of the process Calculate the standard deviation of the times Treat all the data as x values Four data pairs accumulated ÕÕ Calculates the mean price weighted for the quantity purcha...

Page 173: ...ation of the y values Example Population Standard Deviation Grandma Hinkle has four grown sons with heights of 170 173 174 and 180 cm Find the population standard deviation of their heights Linear Regression Linear regression L R also called linear estimation is a statistical method for finding a straight line that best fits a set of x y data Keys Display Description Clears the statistics register...

Page 174: ... intercept Menu Key Description Estimates predicts x for a given hypothetical value of y based on the line calculated to fit the data Estimates predicts y for a given hypothetical value of x based on the line calculated to fit the data Correlation coefficient for the x y data The correlation coefficient is a number in the range 1 through 1 that measures how closely the calculated line fits the dat...

Page 175: ...splays n Five data pairs entered ÕÕ Displays linear regression menu Correlation coefficient data closely approximate a straight line Õ Slope of the line Õ y intercept x 0 20 40 60 80 8 50 7 50 6 50 5 50 4 50 r 0 9880 m 0 0387 b 4 8560 70 y y X ...

Page 176: ...hen be added back to the calculation of and and and b must also be adjusted For example if your x values were 7776999 7777000 and 7777001 you should enter the data as 1 0 and 1 then add 7777000 back to and For b add back 7777000 m To calculate be sure to supply an x value that is less 7777000 Similar inaccuracies can result if your x and y values have greatly different magnitudes Again scaling the...

Page 177: ...sums of the squares and the sum of the products of the x and y values that are of interest when performing other statistical calculations in addition to those provided by the calculator If you ve entered statistical data you can see the contents of the statistics registers Press then use and Ø to view the statistics registers Example Viewing the Statistics Registers Use to store data pairs 1 2 and...

Page 178: ...equations and programs Statistics Registers Views Σy2 register Views Σx2 register Views Σy register Views Σx register Views n register Leaves VAR catalog Register Number Description n 27 Number of accumulated data pairs Σx 28 Sum of accumulated x values Σy 29 Sum of accumulated y values Σx2 30 Sum of squares of accumulated x values Σy2 31 Sum of squares of accumulated y values Σxy 32 Sum of produc...

Page 179: ... you want in I or J and then storing the summation value 7 or A Similarly you can press 7 or A or 7 or A to view or recall a register value the display is labeled with the register name The SUMS menu contains functions for recalling the register values See Indirectly Addressing Variables and Labels in chapter 14 for more information ...

Page 180: ...12 14 Statistical Operations ...

Page 181: ...Part 2 Programming ...

Page 182: ......

Page 183: ...ogic A program lets you repeat operations and calculations in the precise manner you want In this chapter you will learn how to program a series of operations In the next chapter Programming Techniques you will learn about subroutines and conditional instructions Example A Simple Program To find the area of a circle with a radius of 5 you would use the formula A π r2 and press RPN mode 5 ALG mode ...

Page 184: ...d the area of a circle with a radius of 5 In ALG mode to enter this program into program memory do the following RPN mode ALG mode π π Keys In RPN mode Display Description Ö Clears memory Activates Program entry mode PRGM annunciator on Resets program pointer to PRGM TOP Radius 2 π Area πx2 Exits Program entry mode Keys In RPN mode Display Description This sets the program to its beginning 5 The a...

Page 185: ...at you put in a program affects how it appears when you view it and how it works when you run it Selecting a Mode Programs created and saved in RPN mode should be edited and executed in RPN mode and programs or steps created and saved in ALG mode should be edited and executed in ALG mode If not the result may be incorrect Resets program pointer to PRGM TOP XÕ π Area πx2 Exits Program entry mode Ke...

Page 186: ...or variables as discussed in chapter 3 You cannot assign the same label more than once this causes the message but a label can use the same letter that a variable uses It is possible to have one program the top one in memory without any label However adjacent programs need a label between them to keep them distinct Programs can not have more than 999 lines Program Returns Programs and subroutines ...

Page 187: ...valuation in an equation is essentially treated as There s no programmable equivalent to for an assignment equation other than writing the equation as an expression then using STO to store the value in a variable For both types of calculations you can include RPN instructions to control input output and program flow Data Input and Output For programs that need more than one input or return more th...

Page 188: ...vate Program entry mode 2 Press to display This sets the program pointer to a known spot before any other programs As you enter program lines they are inserted before all other program lines If you don t need any other programs that might be in memory clear program memory by pressing To confirm that you want all programs deleted press Ö after the message 3 Give the program a label a single letter ...

Page 189: ... and display its left end The equation does not become part of the equation list After you ve entered an equation you can press to see its checksum and length Hold the key to keep the values in the display For a long equation the and annunciators show that scrolling is active for this program line You can use Ö and Õ to scroll the display Clear functions and backspace key Note these special condit...

Page 190: ...Example Entering a Labeled Program The following keystrokes delete the previous program for the area of a circle and enter a new one that includes a label and a return instruction If you make a mistake during entry press to delete the current program line then reenter the line correctly Keys In RPN mode Display Description Activates Program entry mode PRGM on Ö Clears all of program memory A Label...

Page 191: ... like the previous program Cancels program entry PRGM annunciator off Keys In RPN mode Display Description Activates Program entry mode sets pointer to top of memory E Labels this program routine E for equation R Stores radius in variable R R π Selects Equation entry mode enters the equation returns to Program entry mode Ends the program 2 Displays label E and the length of the program in bytes Ch...

Page 192: ...label Line number for example If there is only one program in memory you can also execute it after moving pointer to the top of the program line and pressing run stop key The PRGM annunciator displays and the annunciator turns on while the program is running If necessary enter the data before executing the program Example Run the programs labeled A and E to find the areas of three different circle...

Page 193: ...ithout starting execution 3 Press and hold Ø This displays the current program line When you release Ø the line is executed The result of that execution is then displayed it is in the X register To move to the preceding line you can press No execution occurs 4 The program pointer moves to the next line Repeat step 3 until you find an error an incorrect result occurs or reach the end of the program...

Page 194: ... From variables that already have values stored From automatic equation prompting if enabled by flag 11 set This is also handy if you re using equations In a program you can display information in these ways With a VIEW instruction which shows the name and value of a variable This is the most handy technique On the stack only the values in the X and Y registers are visible You can use PSE for a 1 ...

Page 195: ...variable Press run stop to resume the program The value you keyed in then writes over the contents of the X register and is stored in the given variable If you have not changed the displayed value then that value is retained in the X register The area of a circle program with an INPUT instruction looks like this To use the INPUT function in a program 1 Decide which data values you will need and as...

Page 196: ... to be done by the program Thus the program should not assume that the X Y and Zñregisters contents will be the same before and after the INPUT instruction If you collect all the data in the beginning and then recall them when needed for calculation then this prevents the stack s contents from being altered just before a calculation To respond to a prompt When you run the program it will stop at e...

Page 197: ...uch as binary complex vector numbers pressing Ö and Õ displays the rest Pressing or erases the VIEW display and shows the X register Pressing clears the contents of the displayed variable Press to continue the program If you don t want the program to stop see Displaying Information without Stopping below For example see the program for Normal and Inverse Normal Distributions in chapter 16 Lines T0...

Page 198: ...tail in chapter 14 When the message is displayed the program stops press to resume execution If the displayed message is longer than 14 characters the annunciator turns on when the message is displayed You can then use Õ and Ö to scroll the display If you don t want the program to stop see Displaying Information without Stopping below Example INPUT VIEW and Messages in a Program Write an equation ...

Page 199: ... H π Calculates the surface area Checksum and length of equation S Stores the surface area in S Sets flag 10 to display equations V O L A R E A Displays message in equations Clears flag 10 V Displays volume S Displays surface area Ends program Displays label C and the length of the program in bytes Checksum and length of program Cancels program entry ...

Page 200: ...ntains a PSE pause instruction the information is displayed and execution continues after a 1 second pause In this case no scrolling or keyboard input is allowed The display is cleared by other display operations and by the RND operation if flag 7 is set rounding to a fraction Press to enter PSE in a program The VIEW and PSE lines or the equation and PSE lines are treated as one operation when you...

Page 201: ... equation that s displayed flag 10 set the variable or equation is displayed instead and the display remains after the 1 second pause Interrupting a Running Program You can interrupt a running program at any time by pressing or The program completes its current instruction before stopping Press run stop to resume the program If you interrupt a program and then press or you cannot resume the progra...

Page 202: ...ted 4 Exit program entry or To insert a program line 1 Locate and display the program line that is before the spot where you would like to insert a line 2 Key in the new instruction it is inserted after the currently displayed line For example if you wanted to insert a new line between lines A004 and A005 of a program you would first display line A004 then key in the instruction or instructions Su...

Page 203: ...tion it is used to validate a program line 5 An equation can be editing in any mode no matter which mode it was entered in Program Memory Viewing Program Memory Pressing toggles the calculator into and out of program entry PRGM annunciator on program lines displayed When Program entry mode is active the contents of program memory are displayed Program memory starts at The list of program lines is ...

Page 204: ...w or Managing Calculator Memory in appendix B The Catalog of Programs MEM The catalog of programs is a list of all program labels with the number of bytes of memory used by each label and the lines associated with it Press 2 to display the catalog and press Ø or to move within the list You can use this catalog to Review the labels in program memory and the memory cost of each labeled program or ro...

Page 205: ...to cancel program entry Clearing all of memory also clears all programs The Checksum The checksum is a unique hexadecimal value given to each program label and its associated lines until the next label This number is useful for comparison with a known checksum for an existing program that you have keyed into program memory If the known checksum and the one shown by your calculator are the same the...

Page 206: ... verify the accuracy of your program entry In addition each equation in a program has a checksum See To enter an equation in a program line earlier in this chapter Nonprogrammable Functions The following functions of the HP 35s are not programmable Programming with BASE You can program instructions to change the base mode using These settings work in programs just as they do as functions executed ...

Page 207: ...l revert to Decimal mode when the program is done An instruction in a program to change the base mode will determine how input is interpreted and how output looks during and after program execution but it does not affect the program lines as you enter them Numbers Entered in Program Lines Before starting program entry set the base mode The current setting for the base mode determines the result of...

Page 208: ...ble several times for their solution For example the expression Ax4 Bx3 Cx2 Dx E uses the variable x four different times A program to calculate such an expression using RPN operations could repeatedly recall a stored copy of x from a variable Example Write a program using RPN operations for 5x4 2x3 then evaluate it for x 7 ...

Page 209: ... this polynomial for x 7 Keys In RPN mode Display Description A X 5 X x4 5x4 X x3 2x3 5x4 2x3 Displays label A which takes 46 bytes Checksum and length Cancels program entry Keys In RPN mode Display Description A value Prompts for x Result ...

Page 210: ...13 28 Simple Programming A more general form of this program for any equation Ax4 Bx3 Cx2 Dx E would be Checksum and length 9E5E 51 ...

Page 211: ... with counters to execute a set of instructions a certain number of times Using indirect addressing to access different variables using the same program instruction Routines in Programs A program is composed of one or more routines A routine is a functional unit that accomplishes something specific Complicated programs need routines to group and separate tasks This makes a program easier to write ...

Page 212: ...Subroutine E ends with a RTN instruction that sends program execution back to routine D to store and display the result at line D004 See the flow diagrams below Nested Subroutines A subroutine can call another subroutine and that subroutine can call yet another subroutine This nesting of subroutines the calling of a subroutine within another subroutine is limited to a stack of subroutines 20 level...

Page 213: ...ted Subroutine The following subroutine labeled S calculates the value of the expression as part of a larger calculation in a larger program The subroutine calls upon another subroutine a nested subroutine labeled Q to do the repetitive squaring and addition This saves memory by keeping the program shorter than it would be without the subroutine 2 2 2 2 d c b a ...

Page 214: ...the next line This is called branching Unconditional branching uses the GTO go to instruction to branch to a specific program line label and line number Starts subroutine here Enters A Enters B Enters C Enters D Recalls the data A2 1 A2 B2 2 3 A2 B2 C2 4 5 A2 B2 C2 D2 6 Returns to main routine 135 Nested subroutine Adds x2 246 Returns to subroutine S 2 2 2 2 D C B A ...

Page 215: ...used for subroutines For example consider the Curve Fitting program in chapter 16 The instruction branches execution from any one of three independent initializing routines to LBL Z the routine that is the common entry point into the heart of the program Using GTO from the Keyboard You can use to move the program pointer to a specified label line number without starting program execution Can start...

Page 216: ...n line A005 is that is is x equal to zero then the program compares the contents of the X register with zero If the X register does contain zero then the program goes on to the next line If the X register does not contain zero then the program skips the next line thereby branching to line A007 This rule is commonly known as Do if true The above example points out a common technique used with condi...

Page 217: ...and y x 0 for tests comparing x and 0 Remember that x refers to the number in the X register and y refers to the number in the Y register These do not compare the variables X and Y You can use x y and x 0 to compare two numbers if one of these isn t real number it will return an error message Select the category of comparison then press the menu key for the conditional instruction you want The Tes...

Page 218: ...s less than 0 0001 Do If True the program executes line T014 if the value is equal to or greater than 0 0001 the program skips to line T015 Keys Display In RPN mode ÕÕ In ALG mode ÕÕ Program Lines In RPN mode Description Calculates the correction for X guess Adds the correction to yield a new X guess Tests to see if the correction is significant Goes back to start of loop if correction is signific...

Page 219: ... program displaying and An overflow occurs when a result exceeds the largest number that the calculator can handle The largest possible number is substituted for the overflow result If flag 5 is clear a program with an overflow is not interrupted though is displayed briefly when the program eventually stops Flag 6 is automatically set by the calculator any time an overflow occurs although you can ...

Page 220: ...y off display real numbers in the current display format Fraction denominators not greater than the c value Reduce fractions to smallest form Set Fraction display on display real numbers as fractions Fraction denominators are factors of the c Value No reduction of fractions Used only if flag 8 is set ...

Page 221: ...fect automatic prompting during keyboard execution When flag 11 is clear the default state evaluation SOLVE and FN of equations in programs proceed without interruption The current value of each variable in the equation is automatically recalled each time the variable is encountered INPUT prompting is not affected When flag 11 is set each variable is prompted for when it is first encountered in th...

Page 222: ...menu After selecting the function you want you will be prompted for the flag number 0 11 For example press to set flag 0 press to set flag 10 press to set flag 11 FLAGS Menu A flag test is a conditional test that affects program execution just as the comparison tests do The FS n instruction tests whether the given flag is set If it is then the next line in the program is executed If it is not then...

Page 223: ...ve the flags 0 and 1 are cleared so lines S006 and S010 do not take the natural logarithms of the X and Y inputs If you replace lines S002 and S003 by SF 0 and CF 1 then flag 0 is set so line S006 takes the natural log of the X input If you replace lines S002 and S003 by CF 0 and SF1 then flag 1 is set so line S010 takes the natural log of the Y input Program Lines In RPN mode Description Clears f...

Page 224: ... a fractional number and a denominator the c value The program also contains examples of how the three fraction display flags 7 8 and 9 and the message display flag 10 are used Messages in this program are listed as MESSAGE and are entered as equations 1 Set Equation entry mode by pressing the EQN annunciator turns on 2 Press letter for each alpha character in the message press for each space char...

Page 225: ...ts decimal base Prompts for a number Prompts for denominator 2 4095 Displays message then shows the decimal number Sets c value and sets flag 7 Displays message then shows the fraction Sets flag 8 Displays message then shows the fraction Sets flag 9 Displays message then shows the fraction Goes to beginning of program Checksum and length BE54 123 ...

Page 226: ...el F prompts for a fractional number V value Stores 2 53 in V prompts for denominator D Stores 16 as the c value Displays message then the decimal number Message indicates the fraction format denominator is no greater than 16 then shows the fraction indicates that the numerator is a little below 8 Message indicates the fraction format denominator is factor of 16 then shows the fraction Message ind...

Page 227: ...t but you don t know how many times the loop needs to repeat itself you can create a loop with a conditional test and a GTO instruction For example the following routine uses a loop to diminish a value A by a constant amount B until the resulting A is less than or equal to B Program lines In RPN mode Description It is easier to recall A than to remember where it is in the stack Calculates A B Repl...

Page 228: ...e For a count up loop use variable These functions accomplish the same thing as a FOR NEXT loop in BASIC variable initial value final value increment variable A DSE instruction is like a FOR NEXT loop with a negative increment After pressing a shifted key for ISG or DSE or you will be prompted for a variable that will contain the loop control number described below The Loop Control Number The spec...

Page 229: ...mpares the new ccccccc with fff and makes program execution skip the next program line if this ccccccc fff For example the loop control number 0 050 for ISG means start counting at zero count up to 50 and increase the number by 1 each loop If the loop control number is a complex number or vector it will use the real part or first part to control the loop The following program uses ISG to loop 10 t...

Page 230: ... contents can refer to another variable It holds a number just like any other variable A through Z I and J are programming functions that directs Use the number in I or J to determine which variable or label to address This is an indirect address A through Z are direct addresses Both 0 and 7 are used together to create an indirect address and this applies to both 1 and A as well By itself I or J i...

Page 231: ...labels can use I or J to refer to A through Z variables or labels or statistics registers indirectly The function I or J uses the value in variable I to J to determine which variable label or register to address The following table shows how STO I INPUT I DSE I RCL I VIEW I ISG I STO I FN d I x I RCL I SOLVE I ...

Page 232: ... as STO VIEW and INPUT The functions listed below can use I or J as an address For FN I or J refers to a label for all other functions I or J refers to a variable or register If I J contains Then I J will address 1 variable A or label A 26 variable Z or label Z 27 n register 28 Σx register 29 Σy register 30 Σx2 register 31 Σy2 register 32 Σxy register 0 Unnamed Indirect variables start 800 The Max...

Page 233: ...useful for counting and controlling loops The variable I or J serves as an index holding the address of the variable that contains the loop control number for the functions DSE and ISG Equations with I J You can use I or J in an equation to specify a variable indirectly Notice that or means the variable specified by the number in variable I or J an indirect reference but that I or J and or where t...

Page 234: ...es after using them in order to release the memory Each allocated indirect register uses 37 bytes of program memory 3 There is a maximum of 800 variables Program Lines In RPN mode Description Defined the storage address range 0 100 and saved 12345 into address 100 Saves 67890 into address 150 The defined indirect storage range is now 0 150 Stores 0 into indirect register 100 The defined range is s...

Page 235: ...hat defines the function See To write a program for SOLVE below 2 Select the program to solve press label You can skip this step if you re re solving the same program 3 Solve for the unknown variable press variable Notice that FN is required if you re solving a programmed function but not if you re solving an equation from the equation list To halt a calculation press or and the message will appea...

Page 236: ... must be in the form of an expression that goes to zero at the solution If your equation is f x g x your program should calculate f x g x 0 is implied A function programmed as an equation can be any type of equation equality assignment or expression The equation is evaluated by the program and its value goes to zero at the solution If you want the equation to prompt for variable values instead of ...

Page 237: ... ALG mode Display Description Sets Program mode Program Lines In ALG mode Description Identifies the programmed function Stores P for pressure Stores V for volume Stores N for number of moles of gas Stores R for gas constant Stores T for temp Press Pressure volume Moles gas constant temp Ends the program Checksum and length F425 33 Keys In ALG mode Display Description G Selects G the program SOLVE...

Page 238: ...Stores 005 in N prompts for R value Stores 0821 in R prompts for T Calculates T Stores 297 1 in T solves for P Pressure is 0 0610 atm Keys In RPN mode Display Description Selects Program entry mode Moves program pointer to top of the list of programs H Labels the program 1 Enables equation prompting P V N R T Evaluates the equation clearing flag 11 Checksum and length EDC8 9 Ends the program Cance...

Page 239: ...ogram H P Selects variable P prompts for V Retains 2 in V prompts for N Retains 005 in N prompts for R Retains 0821 in R prompts for T Calculates new T Stores 287 1 in T solves for new P L Calculates pressure change of the gas when temperature drops from 297 1 K to 287 1 K negative result indicates drop in pressure ...

Page 240: ...ue since this might not be the significant output for your program that is you might want to do further calculations with this number before displaying it If you do want this result displayed add a VIEW variable instruction after the SOLVE instruction If no solution is found for the unknown variable then the next program line is skipped in accordance with the Do if True rule explained in chapter 1...

Page 241: ...r certain conditions or if it requires repeated calculations To integrate a programmed function 1 Enter a program that defines the integrand s function See To write a program for FN below Program Lines In RPN mode Description Setup for X Index for X Branches to main routine Checksum and length 62A0 11 Setup for Y Index for Y Branches to main routine Checksum and length 221E 11 Main routine Stores ...

Page 242: ...ncel the operation In this case you should start again from the beginning To write a program for FN The program can use equations ALG or RPN operations in whatever combination is most convenient 1 Begin the program with a label This label identifies the function that you want to integrate label 2 Include an INPUT instruction for each variable including the variable of integration INPUT instruction...

Page 243: ...ng Equation The sine integral function in the example in chapter 8 is This function can be evaluated by integrating a program that defines the integrand Enter this program and integrate the sine integral function with respect to x from 0 to 2 t 2 Defines the function The function as an expression Checksum and length 0EE0 8 Ends the subroutine Checksum and length of program D57E 17 Keys In RPN mode...

Page 244: ...yed add a PSE or STOP instruction to display the result in the X register after the FN instruction If the PSE instruction immediately follows an equation that is displayed Flag 10 set during each iteration of integrating or solving the equation will be displayed for 1 second and execution will continue until the end of each iteration During the display of the equation no scrolling or keyboard inpu...

Page 245: ...a routine that contains an label instruction if attempted a or error will be returned SOLVE cannot call a routine that contains an FN instruction produces a error just as FN cannot call a routine that contains a SOLVE instruction produces an error The SOLVE variable and FN d variable instructions in a program use one of the 20 pending subroutine returns in the calculator Refer to Nested Subroutine...

Page 246: ...15 12 Solving and Integrating Programs ...

Page 247: ...e The program accepts two or more x y data pairs and then calculates the correlation coefficient r and the two regression coefficients m and b The program includes a routine to calculate the estimates and For definitions of these values see Linear Regression in chapter 12 Samples of the curves and the relevant equations are shown below The internal regression functions of the HP 35s are used to co...

Page 248: ... will occur if a negative number is entered for these cases Data values of large magnitude but relatively small differences can incur problems of precision as can data values of greatly different magnitudes Refer to Limitations in Precision of Data in chapter 12 y x y B Mx Straight Line Fit S y x y BeMx Exponential Curve Fit E y x y B MIn x Logarithmic Curve Fit L y x y BxM Power Curve Fit P ...

Page 249: ...status for the exponential model Clears flag 0 the indicator for ln X Sets flag 1 the indicator for ln Y Branches to common entry point Z Checksum and length D6F1 12 This routine sets the status for the power model Sets flag 0 the indicator for ln X Sets flag 1 the indicator for ln Y Checksum and length 3800 9 Defines common entry point for all models Clears the statistics registers Press 4Σ Sets ...

Page 250: ...tine Recalls the most recent data pair Deletes this pair from the statistical accumulation Loops for another X Y pair Checksum and length A79F 15 Defines the start of the output routine Calculates the correlation coefficient Stores it in R Displays the correlation coefficient Calculates the coefficient b If flag 1 is set takes the natural antilog of b Stores b in B Displays value Calculates coeffi...

Page 251: ... loop Loops for another estimate Checksum and length C3B7 36 This subroutine calculates for the straight line model Calculates MX B Returns to the calling routine Checksum and length 9688 15 This subroutine calculates for the straight line model Calculates Y B M Returns to the calling routine Checksum and length 9C0F 15 This subroutine calculates for the logarithmic model Calculates M In X B Retur...

Page 252: ...es for the exponential model Calculates BeMX Branches to M005 Checksum and length 9327 18 This subroutine calculates for the exponential model Calculates ln Y B M Goes to N005 Checksum and length 7219 18 This subroutine calculates for the power model Calculates Y B XM Goes to K005 Checksum and length 11B3 18 This subroutine calculates for the power model Program Lines In RPN mode Description x x y...

Page 253: ...ermines if C001 or A001 should be run If flag 1 is set Executes C001 Executes A001 Goes to Y006 Checksum and length 1C4D 15 Determines if J001 or H001 should be run If flag 1 is set Executes J001 Executes H001 Goes to Y011 Checksum and length 0AA5 15 Determines if I001 or G001 should be run If flag 1 is set Executes I001 Executes G001 Goes to Y011 Checksum and length 666D 15 Program Lines In RPN m...

Page 254: ...pair If you discover that you have made an error after you have pressed in step 3 with the value prompt still visible press again displaying the value prompt and press U to undo remove the last data pair If you discover that you made an error after step 4 press U In either case continue at step 3 6 After all data are keyed in press R to see the correlation coefficient R 7 Press to see the regressi...

Page 255: ...ssion coefficient slope of a straight line R Correlation coefficient also used for scratch X The x value of a data pair when entering data the hypothetical x when projecting or x estimate when given a hypothetical y Y The y value of a data pair when entering data the hypothetical y when projecting or y estimate when given a hypothetical x Statistics registers Statistical accumulation and computati...

Page 256: ...RPN mode Display Description Enters wrong x value of data pair Retrieves prompt U Deletes the last pair Now proceed with the correct data entry Enters correct x value of data pair Enters y value of data pair Enters x value of data pair Enters y value of data pair Enters x value of data pair Enters y value of data pair Enters x value of data pair Enters y value of data pair R Calculates the correla...

Page 257: ...ion is symmetric about the mean M with a standard deviation S and approximates the shape of the bell shaped curve shown below Given a value x this program calculates the probability that a random selection from the sample data will have a higher value This is known as the upper tail area Q x This program also provides the inverse given a value Q x the program calculates the corresponding value x C...

Page 258: ...ion feature of the HP 35s to integrate the equation of the normal frequency curve The inverse is obtained using Newton s method to iteratively search for a value of x which yields the given probability Q x x y Upper tail area x Q x x x x x dx e x Q 2 2 2 1 5 0 σ π σ ...

Page 259: ...sum and length 70BF 26 This routine calculates Q X given X Prompts for and stores X Calculates upper tail area Stores value in Q so VIEW function can display it Displays Q X Loops to calculate another Q X Checksum and length 042A 18 This routine calculates X given Q X Prompts for and stores Q X Recalls the mean Stores the mean as the guess for X called Xguess Checksum and length A970 12 This label...

Page 260: ...upper tail area Q x Recalls the lower limit of integration Recalls the upper limit of integration Selects the function defined by LBL F for integration Integrates the normal function using the dummy variable D π Calculates S Stores result temporarily for inverse routine Adds half the area under the curve since we integrated using the mean as the lower limit Returns to the calling routine Checksum ...

Page 261: ...mputation time is significantly less with a lower number of displayed digits In routine Q the constant 0 5 may be replaced by 2 and You do not need to key in the inverse routine in routines I and T if you are not interested in the inverse capability Program Instructions 1 Key in the program routines press when done 2 Press S 3 After the prompt for M key in the population mean and press If the mean...

Page 262: ... 1 Your good friend informs you that your blind date has 3σ intelligence You interpret this to mean that this person is more intelligent than the local population except for people more than three standard deviations above the mean Suppose that you intuit that the local population contains 10 000 possible blind dates How many people fall into the 3σ band Since this problem is stated in terms of st...

Page 263: ...would be expected to have surpassed What would be the score that only 20 percent of the students would have failed to achieve Accepts the default value of zero for M Accepts the default value of 1 for S D value Starts the distribution program and prompts for X Enters 3 for X and starts computation of Q X Displays the ratio of the population smarter than everyone within three standard deviations of...

Page 264: ...ies f1 f2 fn Keys In RPN mode Display Description S Starts the initialization routine Stores 55 for the mean Stores 15 3 for the standard deviation D value Starts the distribution program and prompts for X Enters 90 for X and calculates Q X Keys In RPN mode Display Description I Starts the inverse routine Stores 0 1 10 percent in Q X and calculates X Resumes the inverse routine Stores 0 8 100 perc...

Page 265: ...ogram Clears statistics registers 27 through 32 Clears the count N Checksum and length E5BC 13 Input statistical data points Stores data point in X Stores data point frequency in F Enters increment for N Recalls data point frequency fi Checksum and length 3387 19 Accumulate summations Stores index for register 27 Updates in register 27 Stores index for register 28 Updates in register 28 Stores ind...

Page 266: ...lculates statistics for grouped data Grouped standard deviation Displays grouped standard deviation Weighted mean Displays weighted mean Goes back for more points Checksum and length DAF2 24 Undo data entry error Enters decrement for N Recalls last data frequency input Changes sign of fi Adjusts count and summations Checksum and length 03F4 23 Program Lines In ALG mode Description i i f x 2 ...

Page 267: ...back to step 3 to enter the correct data 7 When the last data pair has been input press G to calculate and display the grouped standard deviation 8 Press to display the weighted mean of the grouped data 9 To add additional data points press and continue at step 3 To start a new problem start at step 2 Variables Used Example Enter the following data and calculate the grouped standard deviation X Da...

Page 268: ...ts for the first xi value Stores 5 in X prompts for first fi Stores 17 in F displays the counter Prompts for the second xi Prompts for second fi Displays the counter Prompts for the third xi Prompts for the third fi Displays the counter U Removes the erroneous data displays the revised counter Prompts for new third xi Prompts for the new third fi Displays the counter Prompts for the fourth xi Prom...

Page 269: ...e fifth xi Prompts for the fifth fi Displays the counter Prompts for the sixth xi Prompts for the sixth fi Displays the counter G Calculates and displays the grouped standard deviation sx of the six data points Calculates and displays weighted mean Clears VIEW x ...

Page 270: ...16 24 Statistics Programs ...

Page 271: ... as consumer and home loans and savings accounts The TVM equation is The signs of the cash values balance B payment P and future balance F correspond to the direction of the cash flow Money that you receive has a positive sign while money that you pay has a negative sign Note that any problem can be viewed from two perspectives The lender and the borrower view the same problem with reversed signs ...

Page 272: ... non zero to avoid a error If you re solving for I and aren t sure of its current value press I before you begin the SOLVE calculation I Keys In RPN mode Display Description or current equation Selects Equation mode P _ Starts entering equation 4 4 I Õ NÕ _ I F _ 4 I Õ _ N _ B _ Terminates the equation hold Checksum and length ...

Page 273: ...riodic interest For monthly payments the result returned for I is the monthly interest rate i press 12 to see the annual interest rate c Press B to calculate initial balance of a loan or savings account d Press P to calculate periodic payment e Press F to calculate future value or balance of a loan 4 Key in the values of the four known variables as they are prompted for press after each value 5 Wh...

Page 274: ... is 15 and there are 12 payments per year the periodic interest rate i is 15 12 1 25 B The initial balance of loan or savings account P The periodic payment F The future value of a savings account or balance of a loan Keys In RPN mode Display Description 8 Selects FIX 2 display format Ø as needed Displays the leftmost part of the TVM equation P value Selects P prompts for I Converts your annual in...

Page 275: ...he loan has been viewed from the borrower s perspective Money received by the borrower the beginning balance is positive while money paid out is negative value Stores 0 in F prompts for B Calculates B the beginning loan balance Stores 5750 in B calculates monthly payment P ...

Page 276: ...ro so you won t get a error when you calculate the new I Keys In RPN mode Display Description Displays the leftmost hart of the TVM equation I Selects I prompts for P Rounds the payment to two decimal places Calculates new payment Stores 176 89 in P prompts for N Retains 36 in N prompts for F Retains 0 in F prompts for B Retains 5750 in B calculates monthly interest rate Calculates annual interest...

Page 277: ...the first prime number larger than the input The program identifies non prime numbers by exhaustively trying all possible factors If a number is not prime the program adds 2 assuring that the value is still odd and tests to see if it has found a prime This process continues until a prime number is found Retains 0 56 in I prompts for N Stores 24 in N prompts for B Retains 5750 in B calculates F the...

Page 278: ...17 8 Miscellaneous Programs and Equations LBL Y VIEW Prime LBL Z P 2 x LBL P x P 3 D LBL X x 0 yes no Start no yes Note x is the value in the X register ...

Page 279: ...even input Increments P if input an even number Stores 3 in test divisor D Checksum and length EA89 47 This routine tests P to see if it is prime Finds the fractional part of P D Tests for a remainder of zero not prime If the number is not prime tries next possibility Tests to see whether all possible factors have been tried If all factors have been tried branches to the display routine Branches t...

Page 280: ... be displayed 4 To see the next prime number press Variables Used Remarks No test is made to ensure that the input is greater than 3 Example What is the first prime number after 789 What is the next prime number P Prime value and potential prime values D Divisor used to test the current value of P Keys In ALG mode Display Description P Calculates next prime number after 789 Calculates next prime n...

Page 281: ... v2 U i V j W k Program Lines In RPN mode Description Defines the beginning of the rectangular input display routine Displays or accepts input of X Displays or accepts input of Y Displays or accepts input of Z Goes to R001 to input vectors Checksum and length D82E 15 Defines the beginning of the vector enter routine Copies values in X Y and Z to U V and W respectively Goes to R001 to input vectors...

Page 282: ...i 2j 3k Program Lines In RPN mode Description Defines the beginning of the cross product routine Calculates YW ZV which is the X component Calculates ZU WX which is the Y component Stores XV YU which is the Z component Stores X component Stores Y component Goes to R001 to input vectors Checksum and length 838D 72 ...

Page 283: ...component z Input v2 of y component Input v2 of z component E Run E routine to exchange v2 in U V and W variables Input v1 of x component Input v1 of y component Input v1 of z component C Run C routine to calculate x component of cross product Calculate y component of cross product Calculate z component of cross product ...

Page 284: ...17 14 Miscellaneous Programs and Equations ...

Page 285: ...Part 3 Appendixes and Reference ...

Page 286: ......

Page 287: ... A 8 Answers to Common Questions Q How can I determine if the calculator is operating properly A Refer to page A 5 which describes the diagnostic self test Q My numbers contain commas instead of periods as decimal points How do I restore the periods A Use the 85 5 function page 1 23 Q How do l change the number of decimal places in the display A Use the 8 menu page 1 21 Q How do I clear all or por...

Page 288: ...rrect answers when I use the trigonometric functions A You must make sure the calculator is using the correct angular mode 9 or Q What does an annunciator in the display mean A It indicates something about the status of the calculator See Annunciators in chapter 1 Q Numbers show up as fractions How do I get decimal numbers A Press Environmental Limits To maintain product reliability observe the fo...

Page 289: ...the new batteries readily at hand before you open the battery compartment To install batteries 1 Have two fresh button cell batteries at hand Avoid touching the battery terminals handle batteries only by their edges 2 Make sure the calculator is OFF Do not press ON again until the entire battery changing procedure is completed If the calculator is ON when the batteries are removed the contents of ...

Page 290: ...the calculator after every step to see if its operation has been restored If your calculator requires service refer to page A 8 The calculator won t turn on steps 1 4 or doesn t respond when you press the keys steps 1 3 1 Reset the calculator Hold down the key and press It may be necessary to repeat these reset keystrokes several times 2 Erase memory Press and hold down then press and hold down bo...

Page 291: ...self test described in the next section If the calculator fails the self test it requires service 2 If the calculator passes the self test you may have made a mistake operating the calculator Reread portions of the manual and check Answers to Common Questions page A 1 3 Contact the Calculator Support Department listed on page A 8 The Self Test If the display can be turned on but the calculator doe...

Page 292: ...t Go to step 5 The calculator displays followed by a one digit number if it failed the self test If you received the message because you pressed a key out of order reset the calculator hold down press and do the self test again If you pressed the keys in order but got this message repeat the self test to verify the results If the calculator fails again it requires service see page A 8 Include a co...

Page 293: ...f HP receives notice of such defects during the warranty period HP will replace software media which does not execute its programming instructions due to such defects 3 HP does not warrant that the operation of HP products will be uninterrupted or error free If HP is unable within a reasonable time to repair or replace any product to a condition as warranted you will be entitled to a refund of the...

Page 294: ...D ABOVE IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT SPECIAL INCIDENTAL CONSEQUENTIAL INCLUDING LOST PROFIT OR DATA OR OTHER DAMAGE WHETHER BASED IN CONTRACT TORT OR OTHERWISE Some countries States or provinces do not allow the exclusion or limitation of incidental or consequential damages so the above limitation or exclusion may not apply to you 8 The only warrant...

Page 295: ...nam 65 6100 6682 EMEA Country Telephone numbers Austria 01 360 277 1203 Belgium 02 620 00 86 Belgium 02 620 00 85 Czech Republic 296 335 612 Denmark 82 33 28 44 Finland 09 8171 0281 France 01 4993 9006 Germany 069 9530 7103 Greece 210 969 6421 Netherlands 020 654 5301 Ireland 01 605 0356 Italy 02 754 19 782 Luxembourg 2730 2146 Norway 23500027 Portugal 021 318 0093 Russia 495 228 3050 South Africa...

Page 296: ... 709 7751 British Virgin Islands 1 800 711 2884 Cayman Island 1 800 711 2884 Curacao 001 800 872 2881 800 711 2884 Chile 800 360 999 Colombia 01 8000 51 4746 8368 01 8000 51 HP INVENT Costa Rica 0 800 011 0524 Dominica 1 800 711 2884 Dominican Republic 1 800 711 2884 Ecuador 1 999 119 800 711 2884 Andinatel 1 800 225 528 800 711 2884 Pacifitel El Salvador 800 6160 French Antilles 0 800 990 011 800...

Page 297: ...711 2884 Paraguay 009 800 541 0006 Peru 0 800 10111 Puerto Rico 1 877 232 0589 St Lucia 1 800 478 4602 St Vincent 01 800 711 2884 St Kitts Nevis 1 800 711 2884 St Marteen 1 800 711 2884 Suriname 156 800 711 2884 Trinidad Tobago 1 800 711 2884 Turks Caicos 01 800 711 2884 US Virgin Islands 1 800 711 2884 Uruguay 0004 054 177 Venezuela 0 800 474 68368 0 800 HP INVENT NA Country Telephone numbers Can...

Page 298: ...iving antenna Increase the separation between the equipment and the receiver Connect the equipment into an outlet on a circuit different from that to which the receiver is connected Consult the dealer or an experienced radio or television technician for help Modifications The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved ...

Page 299: ...lowing EU Directives Low Voltage Directive 2006 95 EC EMC Directive 2004 108 EC Compliance with these directives implies conformity to applicable harmonized European standards European Norms which are listed on the EU Declaration of Conformity issued by Hewlett Packard for this product or product family This compliance is indicated by the following conformity marking placed on the product Hewlett ...

Page 300: ...ding it over to a designated collection point for the recycling of waste electrical and electronic equipment The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment For more information about where you can drop off your waste equipment for ...

Page 301: ...m lines SOLVE FN and statistical calculations also require user memory The FN operation is particularly expensive to run All of your stored data is preserved until you explicitly clear it The message means that there is currently not enough memory available for the operation you just attempted You need to clear some or all of user memory For instance you can Clear any or all equations see Editing ...

Page 302: ...in a program 1 Display the program line containing the equation 2 Press to see the checksum and length For example Resetting the Calculator If the calculator doesn t respond to keystrokes or if it is otherwise behaving unusually attempt to reset it Resetting the calculator halts the current calculation and cancels program entry digit entry a running program a SOLVE calculation an FN calculation a ...

Page 303: ...respond to keystrokes and you are unable to restore operation by resetting it or changing the batteries try the following MEMORY CLEAR procedure These keystrokes clear all of memory reset the calculator and restore all format and modes to their original default settings shown below 1 Press and hold down the key 2 Press and hold down 3 Press 6 You will be pressing three keys simultaneously When you...

Page 304: ...EAR ALL MEMORY CLEAR Default Angular mode Unchanged Degrees Base mode Unchanged Decimal Contrast setting Unchanged Medium Decimal point Unchanged Thousand separator Unchanged 1 000 Denominator c value Unchanged 4095 Display format Unchanged FIX 4 Flags Unchanged Cleared Complex mode Unchanged xiy Fraction display mode Unchanged Off Random number seed Unchanged Zero Equation pointer EQN LIST TOP EQ...

Page 305: ...t as it halts a program for prompting so any number then entered writes over the X register but it enables stack lift when the program resumes Neutral Operations The following operations do not affect the status of stack lift DEG RAD GRAD FIX SCI ENG ALL DEC HEX OCT BIN CLVARS PSE SHOW RADIX RADIX CLΣ h and STOP and Ø and 1 2 label nnn EQN FDISP Errors and program entry Switching binary windows Di...

Page 306: ...able stores the recalled number in LASTx In ALG mode the LAST X register is a companion to the stack it holds the number that is the result of last expression It supports using the previous expression result in ALG mode x2 ex 10x LN LOG yx I x INT Rmdr SIN COS TAN ASIN ACOS ATAN SINH COSH TANH ASINH ACOSH ATANH IP FP SGN INTG RND ABS CHG Σ Σ RCL HMS HMS DEG RAD nCr nPr ARG CMPLX CMPLX ex LN yx 1 x...

Page 307: ...ly selected Pressing will place an instruction into a program or equation that recalls the value of the chosen stack register for further use These are displayed as REGX REGY REGZ and REGT For example a program line entered by first pressing d and then entering the instructions REGX x REGY x REGZ x REGT will compute the product of the values in the 4 stack registers and place the result into the X...

Page 308: ...B 8 User Memory and the Stack ...

Page 309: ...16 Entering statistical two variable data Press 9 to set the calculator to ALG mode When the calculator is in ALG mode the ALG annunciator is on In ALG mode operations are performed in the following order 1 Expression in parenthesis 2 Factorial function requires inputting values before you press 3 Functions that require inputting values after pressing the function key for example COS SIN TAN ACOS ...

Page 310: ...ithmetic operations are affected by ALG mode Simple arithmetic Power functions Percentage calculations or Permutations and Combinations x Quotient and Remainder of Division Simple Arithmetic Here are some examples of simple arithmetic In ALG mode you enter the first number press the operator enter the second number and finally press the key To Calculate Press Display 12 3 12 3 12 3 12 3 ...

Page 311: ...Suppose that the 15 76 item cost 16 12 last year What is the percentage change from last year s price to this year s To Calculate Press Display 123 641 3 cube root Õ64 To Calculate Press Display 27 of 200 Õ2 7 200 less 27 Õ27 25 plus 12 Õ12 To Calculate Press x of y y Õ x Percentage change from y to x y 0 y Õx Keys Display Description Õ This year s price dropped about 2 2 from last year s price ...

Page 312: ... or remainder of division operations involving two integers Integer 1 Õ Integer 2 Integer 1 Õ Integer 2 Example To display the quotient and remainder produced by 58 9 Parentheses Calculations Use parentheses when you want to postpone calculating an intermediate result until you entered more numbers For example suppose you want to calculate Keys Display Description x Õ Total number of combinations ...

Page 313: ...esis Implied multiplication is not available in Equation mode For example the expression 2 5 4 can be entered as 4 without the key inserted between 2 and the left parenthesis Exponential and Logarithmic Functions Keys Display Description 4 No calculation is done Õ _ Calculates 85 12 _ Calculates 30 73 Calculates 30 85 12 9 To Calculate Press Display Natural logarithm base e Common logarithm base 1...

Page 314: ...f x Arc cosine of x Arc tangent of x To Calculate Press Hyperbolic sine of x SINH key in a number press Hyperbolic cosine of x COSH key in a number press Hyperbolic tangent of x TANH key in a number press Hyperbolic arc sine of x ASINH key in a number press Hyperbolic arc cosine of x ACOSH key in a number press Hyperbolic arc tangent of x ATANH key in a number press ...

Page 315: ...g the displays the underline on the Y register Pressing displays the following menu value Pressing displays the following menu value You can press and along with Õ or Ö to review the entire contents of the stack and recall them They will appear as or depending on which part of the stacked was recalled and may be used in further calculations To calculate Press Display The integer part of 2 47 The f...

Page 316: ...ter 6 and leave Equation mode 2 Enter the limits of integration key in the lower limit and press then key in the upper limit 3 Display the equation Press and if necessary scroll through the equation list press or Ø to display the desired equation 4 Select the variable of integration Press variable This starts the calculation Operations with Complex Numbers To enter a complex number Form 1 Type the...

Page 317: ...two complex numbers 1 Enter the first complex number z1 2 Select the arithmetic operation 3 Enter the second complex number z2 4 Press to calculate 5 The calculated result will be displayed in Line 2 and the displayed form will be the one that you have set in 9 Here are some examples with complex numbers Examples Evaluate sin 2 3i Examples Evaluate the expression z 1 z2 z3 where z1 23 13 i z2 2 i ...

Page 318: ...re some examples of arithmetic in Hexadecimal Octal and Binary modes Example 12F16 E9A16 Keys Display Description 8Ë Sets display form 4 6 Õ 4 6 6 Result is 2 5000 9 0000 i Keys Display Description 4 6Õ 4 6 Result is 11 7333 i 3 8667 Keys Display Description Sets base 16 HEX annunciator on ...

Page 319: ...at y ends up in the Y register and X in the X register 1 Press 4Σ to clear existing statistical data 2 Key in the y value first and press 3 Key in the corresponding x value and press F E9 A Result Sets base 8 OCT annunciator on Converts displayed number to octal Integer part of result A0 Set base 16 HEX annunciator on Result in hexadecimal base Restores decimal base ...

Page 320: ...statistical data the calculator will display n 0 in line 2 Example After keying in the x y values on the left make the corrections shown on the right Initial x y Corrected x y 20 4 20 5 400 6 40 6 Keys Display Description 4Σ Clears existing statistical data Z 6 Σ Enters the first new data pair Z 6 Σ Display shows n the number of data pairs you entered º Brings back last x value Last y is still in ...

Page 321: ...imation is a statistical method for finding a straight line that best fits a set of x y data To find an estimated value for x or y key in a given hypothetical value for y or x press then press or Õ To find the values that define the line that best fits your data press followed by or ...

Page 322: ...C 14 ALG Summary ...

Page 323: ... of the function f x If any two successive estimates of the function f x have opposite signs then SOLVE presumes that the function f x crosses the x axis in at least one place between the two estimates This interval is systematically narrowed until a root is found For SOLVE to find a root the root has to exist within the range of numbers of the calculator and the function must be mathematically de...

Page 324: ...he calculated root is an accurate estimate of the theoretical infinitely precise root of the equation An ideal solution is one for which f x 0 However a very small non zero value for f x is often acceptable because it might result from approximating numbers with limited 12 digit precision f x x a f x b x f x x c f x x d Function Whose Roots Can Be Found ...

Page 325: ... the 12th digit and the function s value is positive for one estimate and negative for the other Or they are 0 10 499 or 0 10 499 In most cases f x will be relatively close to zero To obtain additional information about the result press see the previous estimate of the root x which was left in the Y register Press again to see the value of f x which was left in the Z register If f x equals zero or...

Page 326: ...ession Keys Display Description Select Equation mode X X X Enters the equation Checksum and length Cancels Equation mode Keys Display Description X _ Initial guesses for the root Selects Equation mode displays the left end of the equation X Solves for X displays the result Final two estimates are the same to four decimal places f x is very small so the approximation is a good root ...

Page 327: ...In this case f x may be relatively large Keys Display Description Selects Equation mode X X Enters the equation Checksum and length Cancels Equation mode Keys Display Description X _ Your initial guesses for the positive root Selects Equation mode displays the equation X Calculates the positive root using guesses 0 and 10 Final two estimates are the same f x 0 X _ Your initial guesses for the nega...

Page 328: ...e possible root However the value for f x will be relatively large If the pole occurs at a value of x that is exactly represented with 12 digits then that value would cause the calculation to halt with an error message Example A Discontinuous Function Find the root of the equation IP x 1 5 Enter the equation Keys Display Description Selects Equation mode XÕ Enter the equation Checksum and length C...

Page 329: ...opposite sign for f x Example Find the root of the equation As x approaches f x becomes a very large positive or negative number Enter the equation as an expression Keys Display Description X _ Your initial guesses for the root Selects Equation mode displays the equation X Finds a root with guesses 0 and 5 Shows root to 11 decimal places The previous estimate is slightly bigger f x is relatively l...

Page 330: ...is working on a horizontal asymptote an area where f x is essentially constant for a wide range of x see figure b below The search is concentrated in a local flat region of the function see figure c below In these cases the values in the stack will be same as the values before executing SOLVE Checksum and length Cancels Equation mode Keys Display Description X _ Your initial guesses for the root S...

Page 331: ...nimum Calculate the root of this parabolic equation x2 6x 13 0 It has a minimum at x 3 Enter the equation as an expression Keys Display Description Selects Equation mode X X Enters the equation f x x a f x x b f x x c Case Where No Root Is Found ...

Page 332: ...ion X _ Your initial guesses for the root Selects Equation mode displays the equation X Search fails with guesses 0 and 10 Keys Display Description Selects Equation mode X Enters the equation Checksum and length Cancels Equation mode X _ Your positive guesses for the root Selects Equation mode displays the equation X Solves for x using guesses 0 005 and 5 Previous estimate is the same f x 0 0 1 10...

Page 333: ...on X Your negative guesses for the root Selects Equation mode displays the equation X Solves for X displays the result Keys Display Description Selects Equation mode X 4 X ÕÕ Enters the equation Checksum and length Cancels Equation mode Keys Display Description X _ Your positive guesses for the root Selects Equation mode displays the left end of the equation X Calculates the root using guesses 0 a...

Page 334: ...a positive denominator but a negative numerator causing a negative square root Example A Local Flat Region Find the root of the function f x x 2 if x 1 f x 1 for 1 x 1 a local flat region f x x 2 if x 1 In RPN mode enter the function as the program Checksum and length 9412 39 Keys Display Description X _ Selects Equation mode displays the left end of the equation X No root found for f x ...

Page 335: ...o However given initial guesses of 1 and 2 SOLVE returns the answer 1 0000 due to round off error Round off error can also cause SOLVE to fail to find a root The equation has a root at However no 12 digit number exactly equals so the calculator can never make the function equal to zero Furthermore the function never changes sign SOLVE returns the message Keys In RPN mode Display Description X _ En...

Page 336: ...D 14 More about Solving ...

Page 337: ...alculated function f x always provide an exact answer Evaluating the function at an infinite number of sample points would take forever However this is not necessary since the maximum accuracy of the calculated integral is limited by the accuracy of the calculated function values Using only a finite number of sample points the algorithm can calculate an integral that is as accurate as is justified...

Page 338: ...mely unlikely to exceed the displayed uncertainty of the approximation In other words the uncertainty estimate in the Y register is an almost certain upper bound on the difference between the approximation and the actual integral Conditions That Could Cause Incorrect Results Although the integration algorithm in the HP 35s is one of the best available in certain situations it like all other algori...

Page 339: ... comes to know the general behavior of the function by sampling the function at more and more points If a fluctuation of the function in one region is not unlike the behavior over the rest of the interval of integration at some iteration the algorithm will likely detect the fluctuation When this happens the number of sample points is increased until successive iterations yield approximations that ...

Page 340: ...1 But the problem is not that was represented by 10499 since the actual integral of this function from zero to 10499 is very close to 1 The reason for the incorrect answer becomes apparent from the graph of f x over the interval of integration Keys Display Description Select equation mode X Enter the equation X End of the equation Checksum and length Cancels Equation mode Keys Display Description ...

Page 341: ...ems such as this see the next topic Conditions That Prolong Calculation Time Fortunately functions exhibiting such aberrations a fluctuation that is uncharacteristic of the behavior of the function elsewhere are unusual enough that you are unlikely to have to integrate one unknowingly A function that could lead to incorrect results can be identified in simple terms by how rapidly it and its low or...

Page 342: ...than if they are confined to only a small fraction of the interval These two situations are shown in the following two illustrations Considering the variations or fluctuation as a type of oscillation in the function the criterion of interest is the ratio of the period of the oscillations to the width of the interval of integration the larger this ratio the more quickly the calculation will finish ...

Page 343: ...equal the sum of the approximations over the subintervals Conditions That Prolong Calculation Time In the preceding example the algorithm gave an incorrect answer because it never detected the spike in the function This happened because the variation in the function was too quick relative to the width of the interval of integration If the width of the interval were smaller you would get the correc...

Page 344: ... with higher densities of sample points until the disparity between successive approximations becomes sufficiently small For a narrow interval in an area where the function is interesting it takes less time to reach this critical density To achieve the same density of sample points the total number of sample points required over the larger interval is much greater than the number required over the...

Page 345: ...of integration includes mostly regions where the function is not interesting Fortunately if you must calculate such an integral you can modify the problem so that the calculation time is considerably reduced Two such techniques are subdividing the interval of integration and transformation of variables These methods enable you to change the function or the limits of integration so that the integra...

Page 346: ...E 10 More about Integration ...

Page 347: ...program variable while another integration calculation was running A running program attempted to solve a program while an integration calculation was running The catalog of variables indicates no values stored You set a wrong guess number like a complex number or vector when SOLVING equation for a variable The calculator is executing a function that might take a while Allow you to verify clearing...

Page 348: ...ns with r n with non integer r or n or with n 1016 Attempted to save a complex number or vector in the statistical data Attempted to save a base n number that contains digits greater than the largest base n number digit allowed Attempted to save an invalid data in the statistical register using operation Attempt to compare complex numbers or vectors Attempted to use a trigonometric or hyperbolic f...

Page 349: ... been erased see page The calculator has insufficient memory available to do the operation See appendix B The condition checked by a test instruction is not true Occurs only when executed from the keyboard Attempted to refer to a nonexistent program label or line number with or Note that the error can mean you explicitly from the keyboard called a program label that does not exist or the program t...

Page 350: ...nning program and leaving the message in the display until you press a key Indicates the top of program memory The memory scheme is circular so is also the line after the last line in program memory The calculator is running an equation or program other than a SOLVE or FN routine Attempted to execute variable or d variable without a selected program label This can happen the first time that you us...

Page 351: ...the error The magnitude of the number is too large to be converted to HEX OCT or BIN base the number must be in the range 34 359 738 368 n 34 359 738 367 A running program attempted an 21st nested label Up to 20 subroutines can be nested Since SOLVE and FN each uses a level they can also generate this error The condition checked by a test instruction is true Occurs only when executed from the keyb...

Page 352: ...F 6 Messages ...

Page 353: ...eceded by arrows for example DEG are alphabetized as if the arrow were not there The last column marked refers to notes at the end of the table Name Keys and Description Page Changes the sign of a number 1 15 1 Addition Returns y x 1 19 1 Subtraction Returns y x 1 19 1 Multiplication Returns y x 1 19 1 Division Returns y x 1 19 1 Power Indicates an exponent 6 16 1 Deletes the last digit keyed in c...

Page 354: ... SUMS menus 1 11 6 4 11 8 Goes to the top line of the equation or the first line of the last label in program mode 6 3 Ø Goes to the last line of the equation or the first line of the next label in program mode 6 3 Separates the two or three arguments of a function 6 5 1 1 x Reciprocal 1 18 1 10x Common exponential Returns 10 raised to the power 4 2 1 Percent Returns y x 100 4 6 1 CHG Percent chan...

Page 355: ...ion standard deviation of y values 12 7 1 FN d variable _ variable Integrates the displayed equation or the program selected by FN using lower limit of the variable of integration in the Y register and upper limit of the variable of integration in the X register 8 2 15 7 4parenthesis press Õ to leave the parenthesis for further calculation 6 6 1 3 A vector symbol for performing vector operations 1...

Page 356: ...ower antilogarithm 6 16 1 ALL 8 Displays all significant digits May have to scroll right Õ to see all of the digits 1 23 AND 1AND Logic operator 11 4 1 ARG Replaces a complex number with its Argument θ 4 17 1 ASIN Arc sine Returns sin 1 x 4 4 1 ASINH Hyperbolic arc sine Returns sinh 1 x 4 6 1 ATAN Arc tangent Returns tan 1 x 4 4 1 ATANH Hyperbolic arc tangent Returns tanh 1 x 4 6 1 b ÕÕÕÕ Returns ...

Page 357: ...isplayed fractions to x If x 1 displays current c value 5 4 C Converts F to C 4 14 1 CF n n Clears flag n n 0 through 11 14 12 Displays menu to clear numbers or parts of memory clears indicated variable or program from a MEM catalog clears displayed equation 1 5 1 28 Clears all stored data equations and programs 1 29 Clears all programs calculator in Program mode 13 23 Clears the displayed equatio...

Page 358: ...11 1 1 DEC Selects Decimal mode 11 1 DEG 9 Selects Degrees angular mode 4 4 DEG Radians to degrees Returns 360 2π x 4 13 1 8 Displays menu to set the display format radix or thousand separator and display format of complex number 1 21 DSE variable variable Decrement Skip if Equal or less For control number ccccccc fffii stored in a variable subtracts ii increment value from ccccccc counter value a...

Page 359: ...fts y into the Z register lifts z into the T register and loses t 2 6 Activates or cancels toggles Equation entry mode 6 3 13 7 ex Natural exponential Returns e raised to the x power 4 1 1 EXP Natural exponential Returns e raised to the specified power 6 16 1 F Converts C to F 4 14 1 Turns on and off Fraction display mode 5 1 FIX n 8 n Selects Fixed display with n decimal places 0 n 11 1 21 Displa...

Page 360: ...16 mode 11 1 Displays the HYP_ prefix for hyperbolic functions 4 6 HMS Hours to hours minutes seconds Converts x from a decimal fraction to hours minutes seconds format 4 13 1 HMS 5 Hours minutes seconds to hours Converts x from hours minutes seconds format to a decimal fraction 4 13 1 6 Used for entering complex numbers 9 2 1 I J 7 A 7 A Value of variable whose letter corresponds to the numeric v...

Page 361: ...ne stores your input in the variable Used only in programs 13 13 INV Reciprocal of argument 6 16 1 IP Integer part of x 4 17 1 ISG variable variable Increment Skip if Greater For control number ccccccc fffii stored in variable adds ii increment value to ccccccc counter value and if the result fff final value skips the next program line 14 18 KG Converts pounds to kilograms 4 14 1 KM Converts miles...

Page 362: ...ession line Σ xi yj Σ xi 2 12 7 1 MILE Converts kilometers to miles 4 14 1 Displays the amount of available memory and the catalog menu 1 28 2 Begins catalog of programs 13 22 1 Begins catalog of variables 3 4 9 Displays menu to set ALG or RPN mode or angular modes 1 7 4 4 n Returns the number of sets of data points 12 11 1 NAND Logic operator 11 4 1 NOR Logic operator 11 4 1 NOT Logic operator 11...

Page 363: ...relation coefficient between the x and y values 12 7 1 rθ a 8 Changes the display of complex numbers 1 25 RAD 9 Selects Radians angular mode 4 4 RAD Degrees to radians Returns 2π 360 x 4 13 1 RADIX 8 6 Selects the comma as the radix mark decimal point 1 23 RADIX 8 Selects the period as the radix mark decimal point 1 23 RANDOM Executes the RANDOM function Returns a random number in the range 0 thro...

Page 364: ...isplayed fraction in Fraction display mode 4 18 5 8 1 9 Activates Reverse Polish notation 1 9 RTN Return Marks the end of a program the program pointer returns to the top or to the calling routine 13 4 14 1 R Roll down Moves t to the Z register z to the Y register y to the X register and x to the T register in RPN mode Displays the X Y Z T menu to review the stack in ALG mode 2 3 C 7 R Roll up Mov...

Page 365: ... x 4 3 1 SINH Hyperbolic sine Returns sinh x 4 6 1 SOLVE variable variable Solves the displayed equation or the program selected by FN using initial estimates in variable and x 7 1 15 1 Inserts a blank space character during equation entry 14 14 1 SQ Square of argument 6 16 1 SQRT Square root of x 6 16 1 STO variable variable Store Copies x into variable 3 2 STO variable variable Stores variable x...

Page 366: ... values 12 6 1 TAN Tangent Returns tan x 4 3 1 TANH Hyperbolic tangent Returns tanh x 4 6 1 VIEW variable variable Displays the labeled contents of variable without recalling the value to the stack 3 4 13 15 Evaluates the displayed equation 6 12 XEQ label label Executes the program identified by label 14 1 x2 Square of x 4 2 1 x Square root of x 4 2 1 The xth root of y 4 2 1 Returns the mean of x ...

Page 367: ... with a variable 3 8 x y x exchange y Moves x to the Y register and y to the X register 2 4 Displays the x y comparison tests menu 14 7 x y If x y executes next program line if x y skips next program line 14 7 x y Õ If x y executes next program line if x y skips next program line 14 7 x y ÕÕ If x y executes next program line if x y skips next program line 14 7 x y ÕÕÕ If x y executes next program ...

Page 368: ... 0 executes next program line if x 0 skips next program line 14 7 x 0 ÕÕÕ If x 0 executes next program line if x 0 skips next program line 14 7 x 0 ÕÕÕÕ If x 0 executes next program line if x 0 skips next program line 14 7 x 0 ÕÕÕÕÕ If x 0 executes next program line if x 0 skips next program line 14 7 XOR Logic operator 11 4 1 xiy 8 Changes display of complex numbers 4 11 x yi 8 Changes display of...

Page 369: ...es 1 Function can be used in equations Õ Given an x value in the X register returns the y estimate based on the regression line m x b 12 11 1 yx Power Returns y raised to the xth power 4 2 1 Name Keys and Description Page y y ...

Page 370: ...G 18 Operation Index ...

Page 371: ...implied units 4 4 A 2 angular mode 4 4 A 2 B 4 annunciators alpha 1 3 battery 1 1 A 3 flags 14 12 list of 1 13 low power 1 1 A 3 shift keys 1 2 answers to questions A 1 arithmetic binary 11 4 general procedure 1 18 hexadecimal 11 4 intermediate results 2 12 long calculations 2 12 octal 11 4 order of calculation 2 14 stack operation 2 5 9 2 assignment equations 6 9 6 11 6 12 7 1 B backspace key can...

Page 372: ...stions about A 1 resetting A 4 B 2 self test A 5 shorting contacts A 5 testing operation A 4 A 5 turning on and off 1 1 cash flows 17 1 catalogs leaving 1 4 program 1 28 13 22 using 1 28 variable 1 28 3 4 chain calculations 2 12 change percentage functions 4 6 changing sign of numbers 1 15 9 3 checksums equations 6 19 13 7 13 24 programs 13 22 CLEAR menu 1 5 clearing equations 6 9 general informat...

Page 373: ... 1 16 E in numbers 1 15 1 22 A 1 ENG format 1 22 See also display format entry cursor backspacing 1 4 meaning 1 17 EQN annunciator in equation list 6 4 6 7 in Program mode 13 7 EQN LIST TOP 6 7 F 2 equality equations 6 9 6 11 7 1 equation list adding to 6 4 displaying 6 6 editing 6 8 EQN annunciator 6 4 in Equation mode 6 3 operation summary 6 3 Equation mode backspacing 1 4 6 8 during program ent...

Page 374: ...actorial function 4 15 financial calculations 17 1 FIX format 1 21 See also display format flags annunciators 14 12 clearing 14 12 default states 14 9 equation evaluation 14 11 equation prompting 14 11 fraction display 14 10 meanings 14 9 operations 14 12 overflow 14 9 setting 14 12 testing 14 9 14 12 unassigned 14 9 flow diagrams 14 2 FN in programs 15 6 15 10 integrating programs 15 8 solving pr...

Page 375: ...VE programs 15 2 responding to 13 14 integer part function 4 17 integration accuracy 8 2 8 6 E 1 difficult functions E 2 E 7 display format 8 2 8 6 8 7 evaluating programs 15 7 how it works E 1 in programs 15 10 limits of 8 2 15 8 C 8 E 7 memory usage 8 2 purpose 8 1 restrictions 15 11 results on stack 8 2 8 6 stopping 8 2 15 8 subintervals E 7 time required 8 6 E 7 transforming variables E 9 unce...

Page 376: ... 21 B 2 size 1 28 B 1 stack 2 1 usage B 1 MEMORY CLEAR A 4 B 3 F 3 MEMORY FULL B 1 F 3 menu keys 1 6 menus example of using 1 8 general operation 1 6 leaving 1 4 1 8 list of 1 6 messages clearing 1 4 displaying 13 16 13 18 in equations 13 16 responding to 1 27 F 1 summary of F 1 minimum of function D 8 modes See angular mode base mode Equation mode Fraction display mode Program entry mode MODES me...

Page 377: ...1 A 3 power curve fitting 16 1 power functions 1 17 4 2 9 3 precedence equation operators 6 14 precision numbers 1 25 D 13 present value See financial calculations PRGM TOP 13 4 13 7 13 21 F 4 prime number generator 17 7 probability functions 4 15 normal distribution 16 11 program catalog 1 28 13 22 program labels branching to 14 2 14 4 14 16 checksums 13 23 clearing 13 6 duplicate 13 6 entering 1...

Page 378: ...g through 13 11 stopping 13 14 13 16 13 19 techniques 14 1 testing 13 11 using integration 15 10 using SOLVE 15 6 variables in 13 12 15 1 15 7 prompts affect stack 6 14 13 14 clearing 1 4 6 14 13 15 equations 6 13 INPUT 13 12 13 14 15 2 15 8 programmed equations 14 11 15 1 15 9 responding to 6 13 13 14 showing hidden digits 6 14 PSE pausing programs 13 19 15 10 preventing program stops 14 11 Q que...

Page 379: ...self test calculator A 5 shift keys 1 3 sign of numbers 1 15 9 3 11 6 sign conventions finance 17 1 Sign value 4 17 sine trig 4 4 9 3 A 2 C 6 single step execution 13 11 slope curve fit 12 8 16 1 SOLVE checking results 7 7 D 3 discontinuity D 5 evaluating equations 7 1 7 7 evaluating programs 15 2 flat regions D 8 how it works 7 7 D 1 in programs 15 6 initial guesses 7 2 7 7 7 8 7 12 15 6 minimum ...

Page 380: ...2 13 12 STO arithmetic 3 6 STOP 13 19 storage arithmetic 3 6 subroutines See routines sums of statistical variables 12 11 syntax equations 6 14 6 19 13 16 T tangent trig 4 4 9 3 A 2 C 6 temperatures converting units 4 14 limits for calculator A 2 test menus 14 7 testing the calculator A 4 A 5 time formats 4 13 time value of money 17 1 T register 2 5 trigonometric functions 4 4 9 3 C 6 troubleshoot...

Page 381: ...ying program data 13 15 13 18 15 6 displaying variables 3 4 no stack effect 13 15 stopping programs 13 15 volume conversions 4 14 W weight conversions 4 14 weighted means 12 4 windows binary numbers 11 8 X evaluating equations 6 10 6 12 running programs 13 10 13 22 X ROOT arguments 6 17 X register affected by prompts 6 14 arithmetic with variables 3 6 clearing 1 5 2 3 2 7 clearing in programs 13 7...

Page 382: ...Index 12 ...

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HP 35s, User Manual

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