Reverse Polish Notation

You need to understand this to use the calculator.

When you do calculations you work with one or two numbers at a time. If you want the square root of nine you are working with one number. If you want to add two and three, well that's two numbers.

One Number Functions

To work out something that depends on one number, you key in the number and press the calculator button for the answer. For example you press 4, 5, then SIN to work out the sine of 45. If the DEG-RAD switch is in DEG (for degrees) the calculator will display "0.71".

Sine 0.71

Internally it calculates the answer with far more precision but you're probably not going to write all that down so it rounds the answer in the display for you. You can tell it to display with greater precision (eg "to four decimal places") if you like. There'll be more on that later.

Two Number Functions

To work out something with two numbers, it works the same way. You key in the first number and the second number and press the calculator button for the answer. How do you tell it you've finished keying in the first number? You use the ENTER key to separate the two. An example: fifty divided by twenty- five. You press 5, 0, ENTER, 2, 5, then the divide button. The calculator will display "2.00".

Enter Divide 2.00

Complicated Equations

Complicated equations are always combinations of one and two number functions. If you had to work out the square root of nine times two and three added together, you'd do the following steps:

work out the square root of nine
work out what two and three added together is, then
multiply the two answers together

The calculator works the same way. You press:

9, square root (the calculator displays "3.00"),
2, ENTER, 3, add (the calculator displays "5.00"),
multiply (the calculator displays "15.00").

Square root 3.00

enter add 5.00

times 15.00

The calculator automatically remembers the earlier answers for you so when you pressed "multiply" it multiplied three and five, the last two answers.

The Hewlett Packard advertising at the time puts it this way: "This ingenious system gives you the problem solving power of an equals key and at least three levels of parentheses, yet is distinguished by its similarity to your natural way of solving mathematical problems. It allows you to approach the solution of every problem in the same natural manner as you would by hand ... through the process of equation simplification. Since there is no need to re-format equations, operation is easy. And, it's made even easier by the fact that you only work with one or two numbers at any one time." - HP-21 ad from 1975.

Functions execute when you press the button. You see every intermediate answer (the "3.00" and "5.00" in the example above). You can check your working as you are working. You don't have the "what happened?" or "is that right?" feeling that you get from other calculators where you press an equals button.

contents