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)
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 (without order of operations)
Infix notation without order of operations is used by simple non-scientific calculators. With this mode the mathematical order of operations is not honored and all operations are immediately executed. Also advanced operations like √ or x2 are entered after the operation.
| 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.
infix notation (with order of operations)
Infix notation with order of operations where used by scientific calculators in from the 70th to the 90th. With this mode the mathematical order of operations is where honored but advanced operations like √ or x2 where are still entered after the operation. This mode of operation has been replaced by Direct algebraic logic.
| Formula | Key strokes | Key stroke count |
|---|---|---|
1 + 2 × 3 =
|
6 | |
3 0 SIN × 3 0 COS =
|
8 |
BASIC notation
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.
This mode of operation to has been replaced by Direct algebraic logic.
| Formula | Key strokes | Key stroke count |
|---|---|---|
|
6 | |
SIN ( 3 0 ) × COS ( 3 0 ) ENTER
|
12 .. 16 |
Direct algebraic logic (D.A.L.)
Direct algebraic logic (D.A.L.) is a method for entering equations on scientific calculators which allows symbols and numbers to be entered as they are written. SHARP introduced it in 1992[2]. Today D.A.L. is used almost with every scientific calculator except those which use Reverse Polish Notation.
| Formula | Key strokes | Key stroke count |
|---|---|---|
|
6 | |
SIN 3 0 → × COS 3 0 ENTER
|
9 |
Note the → in the 2nd example: most DAL 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
- ^ The picture of the FX-880P show sin, cos and tan keys on the second row right hand side.
- ^ D.A.L description from Sharp
External links
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