RISC OS 3.7 User Guide

# 32 SciCalc

SciCalc is a scientific calculator providing a range of scientific functions in addition to simple arithmetic ones.

## Starting SciCalc

SciCalc is in the Apps directory on your hard disc or network. To start the application:

  1 Double-click on the !SciCalc application icon. The application icon appears on the icon bar.

  2 Click on the icon bar icon to display the calculator window:

## Entering numbers

There are two ways of entering numbers into the calculator. You can use the mouse to move the pointer over the required key and then click, or you can use the keyboard directly. Clicking in the numeric display turns the title bar a cream colour, indicating that numbers and selected operators may be entered from the keyboard. When the title bar is grey, the keyboard does not affect the state of SciCalc.

If you use the numeric keypad, make sure that the Num Lock key is on. The keys in the numeric keypad are also equivalent to those on the calculator keypad.

## Arithmetic functions

These operate exactly like an ordinary calculator, except that you can enter numbers and operators (+, -, etc) either by clicking on the SciCalc display or by using the numeric keypad on the keyboard. When you enter a number it appears in the calculator's display. When you first load SciCalc it is set for normal decimal arithmetic (to base 10). This is denoted by the word (Dec) in the title bar.

### Rules of precedence

SciCalc treats the calculation you enter as a formula and does not perform the calculation until you click on the Equals button. SciCalc performs the calculation according to the precedence of operators. From highest to lowest; Multiply, Divide, Add and Subtract.

Multiplication takes place before addition so:

2 + 6 x 5 = 32 (not 40)

You can change the order of calculation by using brackets:

(2 + 6) x 5 = 40

### Simple multiplication

To multiply 2 by 5 and view the result, enter the following in this order:

2 x 5 =

The result will appear in the display.

#### Changing the sign

The ± key switches the sign of x.

#### Calculating percentages

The percentage function operates as follows: to increase x by y percent, press:

x + y %

To decrease x by y percent, type - instead of +.

#### Clearing the last entry

Press CE to clear the current display. For example, pressing the following:

2 + 6 x 3 CE 5 =

calculates

2 + 6 x 5 =

and thus gives the result 32.

#### Erase all calculations - Clear

Press C to clear not only the display but also the whole inpu t so far.

## Memory functions

SciCalc has a single memory. To enter the displayed value into the memory, press Min. To display the contents of the memory, press MR. To clear the memory, press MC.

## Advanced functions

#### Calculating roots

To ca lculate the square root of x, press the square root symbol, then x.

To obtain the yth root of x, press y, then the square root symbol, then x, followed by y. For example, to calculate the fourth root of 52, click on the following keys:

52 y x 4 =

which will display the result 2.685349614.

### Calculating squares and powers

To calculate the square of x, click on x2.

To raise x to a power other than 2, click on xy followed by the power you want to take. For example, to raise 52 to the power 4, click on the following keys:

52 xy 4 =

which will display the result 7311616.

For example, to raise 10 to the nth power, press 10x. To raise e to the nth power, press ex. (e is defined as 2.7182818).

### Calculating reciprocals and factorials

For the reciprocal of x, press 1/x.

For x factorial, press x!.

### Calculating logarithms

To obtain the logarithm (base 10) of x, press LOG.

For the natural logarithm (base e), press LN.

### Using brackets

To obtain a bracket, press (). The same key produces a left or right bracket, whichever is appropriate in the context. For example, to calculate (2 + 3) x 5, press

() 2 + 3 () x 5 =

(There is only one level of brackets available.)

### Using pi

To use pi in a calculation, press the pi symbol.

### Calculating exponents

To express x in exponent form, press Exp followed by y, the exponent. For example,

50 Exp 4 =

displays the result 5000 00.

## Trigonometric functions

Among t he more advanced functions available in SciCalc are the standard trigonometric functions:

SIN sine

COS cosine

TAN tangent

ASN arcsine (sine-1)

ACS arccosine (cosine-1)

ATN arctangent (tangent-1)

To obtain hyperbolic trigonometric functions, press Hyp before pressing the function button.

## Changing the number base

As already mentioned, when first loaded SciCalc normally works with decimals. Successive clicks on Base switch it to binary (base 2), octal (base 8) and hexadecimal (base 16) bases. The current base is shown in the Title bar. The calculator layout is modified to provide the input requirements for each base: for bases using fewer than ten characters, some are greyed out, while for hex, some of the function keys are replaced with the necessary letters. In addition, when a function is not available in a base, it is greyed out. For example, in base 8 SciCalc looks like this:

Base provides a handy way of converting a number between bases. Once you have entered a number into the display, clicking on Base converts it successively to the other bases.

### Logic functions in the non-decimal bases

In the non-decimal bases - binary, octal and hexadecimal - the arithmetic functions are augmente d by a MOD function. In addition, the scientific functions are replaced by logic functions: NAND, NOR, NOT, AND, OR, EOR, EQV, rotate, arithmetic shift and logic shift.

## Degrees, radians and gradians

You can switch between degrees, radians and gradians by clicking on the Mode button; the current unit is shown in the Title bar.

Changing from decimal to a non-decimal base rounds the currently displayed value to the nearest integer, but has no effect on previous parts of the current calculation. Rounding also occurs on numbers being recalled from memory in non-decimal bases.

## Keyboard short-cuts

### Calculator functions and their keyboard equivalents

Calculator: Keyboard equivalent (if any): Function:

- 0...9: 0...9: numbers
- +, -, x, /,= : +, -, *, /, = : standard operators
- : Return, Enter : same as =
- ± : # : change sign on number or exponent
- Exp : E : allows entry of exponent
- . : . : decimal point
- 10x, LOG, LN, eX: exponential and logarithmic functions
- xCy : combination
- xPy : permutation
- (): (, ): brackets (one level only)
- Pi : the number Pi
- RND : random number between 0.0 and 1.0
- NOT, AND, OR, EOR : logical functions
- %: % : percentage
- HYP (followed by a trig function): hyperbolic functions
- SIN, COS, TAN : trigonometric functions
- ASN, ACS, ATN : inverse trigonometric functions
- x! : !: factorial
- SQRTx : square root
- ySQRTx : Yth root of X
- x2 : square
- xY : ^: X raised to the power Y
- /x : reciprocal
- C : Delete : clear calculation
- CE : clear current number only
- MC : clear memory
- Min : memory in
- MR : memory recall
- Mode : select radians/degrees/gradians
- Base : select decimal/binary/octal/hexadecimal base

### Keyboard equivalents in non-decimal bases

Calculator: Keyboard equivalent (if any): Function:

- NAND : none: NOT AND
- NOR : none: NOT OR
- EQV : none: NOT EOR (equivalence)
- <O , O> : none: rotate left or right
- <<< , >>> : none: logical shift left or right
- << , >> : none: arithmetic shift left or right
- DIV : none: integer division
- MOD : none: modulus (integer remainder)
- A - F : A - F : hexadecimal base digits

### Operator precedence

Operators are evaluated in the following order of precedence (highest shown first):

  1 unary operators

  2 ySQRTx

  3 xPOWERy
  4 xCy, xPy

  5 *, /, DIV, MOD

  6 +, -

  7 , <<, >>, <<<, >>>

  8 AND, NAND

  9 OR, EOR, NOR, EQV

## Technical notes

SciCalc's accuracy is limited to that of BASIC VI - 64-bit floating point.

### Numeric range

Modes and their Numeric range

- Decimal: Real values: -9.9E99 to 9.9E99 entry

  -9.9E307 to 9.9E307 displayable

- Binary: 32bit signed: 10000000000000000000000000000000 to 11111111111111111111111111111111
- Octal: 32bit signed: 20000000000 to 17777777777
- Hexadecimal: 32bit signed: 80000000 to 7FFFFFFF

### Accuracy

Modes: Their accuracy: Number of digits displayed:

- Binary : Absolute: 32
- Octal: Absolute: 10 - 11
- Hexadecimal: Absolute: 8
- Decimal: 64-bit FP: 10 or 10 + 2 digit exponent

Note: Real number underflow is not trapped.

## Saving features in a Desktop boot file

You m ay wish to change some aspects of the way SciCalc operates. For example, the position of the SciCalc window when it is opened, the number base it uses and the angle mode.

These features are stored by setting up SciCalc as you wish to use it, and then saving the features by creating a Desktop boot file; instructions on how to create a Desktop boot file are given in Configuring applications on page 427.