SLR 10 & 11

N

Natural - Positive integers

Z

Whole - Positive and negative integers

Q

Rational - values that can be represented as ratios, fractions, or decimals - includes recurring numbers

Irrational

cannot be expressed as a fraction - surds and endless decimals

R

Real - rational and irrational numbers - used for measurements

Ordinal

First, second, third

Why is hex used

• shorthand binary

• fewer mistakes

• easier to remember

• takes up less memory

Binary

• Can be 16 bits

• Two types - signed and unsigned

• Signed can be negative (127 to -128)

• Use two's compliment on signed values

Two’s Compliment

• Only use this if the binary number begins with a 1

• Flip the bit - 1 = 0 and 0 = 1

• Add 1 bit

Addition rules

0 + 0 = 0

1 + 0 = 1

1 + 1 = (1) 0

0 + 1 = 1

1 + 1 + 1 = (1) 1

Subtraction

Make the second value negative, then add

Ignore any overflow errors

Multiplication

Double and perform a left shift.

Division

Halve and perform a right shift

Fixed Point

The column headings to the left of the point remain the same, the headings to the right halve

• not all decimals can be represented - rounding error

• limits the number of values, especially if signed

Floating Point

Can store almost any decimal as the point can move

• Mantissa - the main part of the number

• Exponent - moves the floating point

• A positive exponent moves to the right, a negative exponent moves to the left

Normalisation

Standard form for binary - stores a number more efficiently - gets rid of excess 0 or 1

Ignore the exponent - will begin 0.1 (positive) or 1.0 (negative)