Calculator input methods

A Button-operated calculator is a hardware or software calculator which is operated using buttons - as opposed to a Formula calculator which is operated by entering formulas with a keyboard.

Mode of operations

There are various ways in which the in which a button-operated calculator might interpret key strokes.

Reverse Polish Notation (RPN) (Postfix notation)

Main article: Reverse Polish Notation

In Reverse Polish Notation also known as Postfix notation all operations are entered after the operands on which the operation is performed. Reverse Polish Notation is parenthesis-free which usually leads to less button presses needed to perform a operation. By the use of stack one can enter formulas without the need to rearrange operands.

Examples

Formula	Key strokes	Key stroke count
${\displaystyle 1+2\times 3}$	1 ENTER 2 ENTER 3 × +	7
${\displaystyle \sin 30\times \cos 30}$	3 0 SIN 3 0 COS ×	7

Note example 1 which is one of the few examples where Reverse Polish Notation does not use the fewest button presses - provided one does not rearrange operands. If one would do so then only 5 key strokes would be needed.

Immediate execution

With this mode of operation each binary operation is executed as soon as the next operator is pressed, therefore the order of operations in a mathematical expression is not taken into account, except for models which have buttons for brackets which can take order in to account. Also for unitary operators like √ or x² the number is entered first then the operator.

Examples

Formula	Key strokes	Key stroke count
${\displaystyle 1+2\times 3}$	2 × 3 + 1 =	6
${\displaystyle \sin 30\times \cos 30}$	3 0 SIN × 3 0 COS =	8

From the first example one can see that it is necessary to rearrange operands in order to get the correct result.

Infix notation

Main article: infix notation

With this mode the mathematical order of operations is where honored.

Examples

Formula	Key strokes	Key stroke count
${\displaystyle 1+2\times 3}$	1 + 2 × 3 =	6
${\displaystyle \sin 30\times \cos 30}$	3 0 SIN × 3 0 COS =	8

BASIC notation

Main article: Pocket computer

This mode was used from the 80th to the 90th in BASIC programmable calculators and pocket computers.

In BASIC notation the formula is entered as it would be entered in BASIC PRINT command - the PRINT command itself being optional. On pressing the ENTER the result would be displayed. Typing mistakes in the entered formula could be corrected using the same editor function as available when programming the calculator.

Some BASIC programmable Pocket computers had dedicated trigonometric keys ^[1] hence the keystroke count is given as a range. Some BASIC programmable Pocket computers could also be operate in arithmetic logic.

Examples

Formula	Key strokes	Key stroke count
${\displaystyle 1+2\times 3}$	1 + 2 × 3 ENTER	6
${\displaystyle \sin 30\times \cos 30}$	SIN ( 3 0 ) × COS ( 3 0 ) ENTER	12 .. 16

Mathematical display

Some calculators allow the entering of equations in a way which resembles how they would normally be written.

SHARP calls this method Direct algebraic logic (D.A.L.). Casio calls this method Visually Perfect Algebraic Mode (V.P.A.M).

Examples

Formula	Key strokes	Key stroke count
${\displaystyle 1+2\times 3}$	1 + 2 × 3 ENTER	6
${\displaystyle \sin 30\times \cos 30}$	SIN 3 0 → × COS 3 0 ENTER	9

Note the → in the 2nd example: most of these calculators will automatically insert needed parenthesis and the → key skips over the closing parenthesis from the sin operation. Machines equipped with an alphanumeric display will display SIN(30)×COS(30) before pressing ENTER.

References

1. The picture of the FX-880P show sin, cos and tan keys on the second row right hand side.