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.
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. Some calculators have buttons for brackets and these calculators can take order in to account. Also for unitary operators like √ or x2 the number is entered first then the operator.
Formula | Key strokes | Key stroke count |
---|---|---|
2 × 3 + 1 =
|
6 | |
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.
Reverse Polish Notation (RPN) (Postfix 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.
Formula | Key strokes | Key stroke count |
---|---|---|
1 ENTER 2 ENTER 3 × +
|
7 | |
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.
Infix notation
With this mode the precedence of mathematical operators is taken into account.
Formula | Key strokes | Key stroke count |
---|---|---|
1 + 2 × 3 =
|
6 | |
SIN 3 0 × COS 3 0 =
|
8 |
BASIC notation
This is the same as infix notation except that functions require their parameters to be in brackets.
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.
Formula | Key strokes | Key stroke count |
---|---|---|
|
6 | |
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) on its scientific calculators and Natural textbook display on its 9860 graphic calculators.
Formula | Key strokes | Key stroke count |
---|---|---|
|
6 | |
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
.