hp calculators
HP 48GII
Algebraic and RPN Operating Modes
Figure
6
The HP48GII automatically put ANS(1) in front of the * when you pressed
*
with nothing before it. ANS(1) is now the number
1,212.40, the most recent answer. The number 70.00 is ANS(2). After you press
`
it will become ANS(3).
As you see, the HP48GII provides a range of ways to work in Algebraic mode. You will develop your own favorite ways to work as
you gain experience with the calculator.
Why “Algebraic”?
You can see that the formula to calculate was typed and is displayed the way it looks when it is written down on
paper in algebraic notation. That is why this calculation mode is called Algebraic Mode. Algebraic notation was invented for use with
unknown variables, such as X, but over the centuries it has also developed as a shorthand way of writing things such as “add the
number eight to the number six and multiply the result by the number five”.
To compare the above to RPN mode, switch to RPN, pressing
H
then
W
then
%OK$
. Now type the RPN keys for the carpet
area calculation.
6 `
This puts the 6 in the calculator, ENTER separates it from the next number
8 +
This gives the 8 and adds it
5
*
This gives the 5 and multiplies by it
There is a clear pattern here. You type a number, then you do something with that number. Then you type another number, and do
something again. In this example, you add the 8 to the 6 that you entered before, then you multiply by 5, but RPN works the same
way for other actions too. Just for example, to calculate the square root of 30, you type 30 and then press the
R
key.
At each step, RPN takes one or more numbers it needs, then puts the answer on the stack.
Why “RPN?”
You might have noticed that calculating the carpet area in RPN did 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 entered, not before it,
so this method of calculation is called Reverse Polish Notation, RPN for short. The numbers it uses are on the stack, not inside
brackets, so it is also called “Stack notation”.
The
`
key has a special task in RPN. It puts onto the stack the number you have just typed, without doing anything else to that
number. Then the number is ready for what you want to do next, for example add another number to it. If you press
`
again, it
repeats its action, putting another copy of the number onto the stack. It does the latter in Algebraic mode as well.
As in Algebraic mode, the stack works to help you, but in a different way, suited to RPN calculations. The RPN stack is made up of
numbered levels, with a value in each level. The values are the results of earlier calculations, or numbers you put on the stack with
the
`
key. The formula for the previous calculation is not put on the stack, because each calculation is just one step, but if you
want to bring back what you just did, press
„®
to see the last 4 lines you typed, and select what you want with the arrow
keys, then press
%OK$
.
The numbers on the stack are ready for you to use in further calculations. As with Algebraic mode, the HP48GII has commands to let
you pick numbers off the stack, and there are also commands to move numbers around the stack. In fact RPN uses the stack as a
central tool, and there is a whole set of stack commands. You can find them by pressing
„°
and then selecting the STACK
option.
hp calculators
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HP 48GII
Algebraic and RPN Operating Modes
