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HP 48GII

  Algebraic and RPN Operating Modes 

 

Tip!

 The most important stack commands in RPN are 

DUP

, which copies the number in level 1 to level 2, and 

SWAP

, which swaps 

the numbers in levels 1 and 2. 

DUP

 is done by pressing the 

`

 key, as was described above. 

SWAP

 is needed in many cases, for 

example if you want to divide the number in level 1 by the number in level 2 then you must swap them before pressing the 

/

 key. 

SWAP

 is so important that there is a shortcut key for it, just press the right arrow key 

 in RPN mode when you are not editing 

anything, and it will swap the numbers in levels 1 and 2. 

 

The command line 

 
As you typed the example in Algebraic and in RPN modes, what you typed went into a special line, below the stack, but above the 

menu keys. If you are still in RPN mode, try calculating the price of the carpet again. First type the number 17.32, and the display will 

look like this: 

 

 Figure 

7

 

 
The previous result, 70, is on level 1 of the stack. The new number is between the stack and the menu keys, on a special line called 

the 

Command Line

. Both Algebraic mode and RPN mode use this for numbers and text you are typing or editing. When you press 

`

 the contents of the command line are evaluated and the result is put on the stack. 

 
In RPN you do not need to press 

`

 to put a number on the stack, if you are going to use it at once. In the case above, you can 

press 

`

 to put 17.32 on the stack, and then press 

*

 to multiply 70 by 17.32, but you can skip the 

`

 and just press 

*

 to 

get the answer. You do need to press 

`

 if you are typing two numbers one after another, as in the carpet example. 

 

Example –  a more complicated expression 

 

Here is a more complicated expression to compare Algebraic and RPN modes further. 

 

((3.2*5²)+3!) 

 

In Algebraic mode it is possible to type the expression almost as it stands. The only difference is that the x-squared key 

„º

 

must be pressed before a number, whereas the x-squared symbol is written after the number to be squared. Set Algebraic mode and 

type the following: 
 

R„Ü„Ü3.2*„º5™™+3~…2 

 

 Figure 

8

 

 

The square root comes before the number it works on, the multiplication sign comes between the numbers it uses, and the factorial 
sign comes after the number it works with. The x-squared symbol was written after the number to be squared, but on the calculator it 

had to come before. There are three sets of nested brackets, which have to be treated correctly. Note that when you press 

„º

 in Algebraic mode the brackets are automatically put in for you. To enter the factorial sign you have to use ALPHA mode 

to type the exclamation mark. Even though the calculator makes things easy for you, you still need to take care when typing the 
expression. Now press 

`

to see the result. 

 

hp calculators 

- 6 - 

HP 48GII

  Algebraic and RPN Operating Modes 

Summary of Contents for 48GI

Page 1: ... RPN Operating Modes Calculation Modes A simple example the area of a piece of carpet Setting the mode Algebraic and RPN modes and the stack The command line Example a more complicated expression Example which stepladder The Operating Mode ...

Page 2: ...ong both 5 yards wide So you need to calculate 6 8 5 In algebraic mode you work out the total length first that s 6 yards 8 yards Then you multiply by the width 5 yards So you would type these keys Ü This gives the brackets to put around 6 8 6 8 This gives the 6 8 This moves past the right bracket 5 This multiplies by 5 This tells the calculator that the formula is finished so it can now get the a...

Page 3: ...numbers such as 2 3 will be automatically converted to approximate results such as 0 666666666667 Press H then C below the CAS menu label to select the CAS Modes form Press the down arrow key twice to reach the Approx selection If this already has a check mark by it then you do not need to set it so press the E key below the CANCEL menu label If Approx is not checked then press C below the CHK men...

Page 4: ...what you need then pressing the menu keys These let you edit an expression or view it in textbook mode or echo a copy to the bottom of the stack so you can use it again see Figure 4 Figure 4 If you want to use an earlier answer in another calculation you can also use to access the îfunction which is above the key By default the HP48GII gives you ANS 1 the answer to the calculation you did one step...

Page 5: ...d not use brackets and indeed RPN is designed to work without brackets This makes it somewhat quicker to type than Algebraic mode the carpet example took 6 keystrokes in RPN and 9 in Algebraic mode Polish Notation a mathematical notation without brackets was introduced by the Polish mathematician Jan Lukasiewicz in the 1920s In RPN the operations such as or or S are done after the number is entere...

Page 6: ... press to put a number on the stack if you are going to use it at once In the case above you can press to put 17 32 on the stack and then press to multiply 70 by 17 32 but you can skip the and just press to get the answer You do need to press if you are typing two numbers one after another as in the carpet example Example a more complicated expression Here is a more complicated expression to compa...

Page 7: ...in the Algebraic example above RPN would take 3 less keystrokes If you are willing to work out how to do the calculation RPN saves you any confusion about brackets and works with fewer keystrokes If you are new to HP calculators try using both modes and see if you prefer one or the other or if you want to switch between them as you use the HP48GII Example which stepladder Many people would prefer ...

Page 8: ...t Algebraic mode is less well suited to such step by step calculations especially because î must be used repeatedly to bring back the result of the previous calculation Once all the examples have been completed it may be worth returning the calculator to its normal modes It can also be helpful to clear the stack by pressing The Operating Mode The examples and explanations in this training aid have...

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