Binary number system key terms

Unsigned binary

A binary number system that represents only non-negative values, from 0 up to a maximum determined by the number of bits.

Bit

A binary digit that can have a value of 0 or 1 and contributes a place value when it is 1.

Carry

A value passed into the next column when the sum in a binary column is too large to remain in that column.

Partial product

An intermediate result produced when multiplying the multiplicand by one digit of the binary multiplier, including the appropriate positional shift.

Two’s complement

A binary coding scheme for representing signed integers, including negative integers, by inverting the bits of the positive value and adding 1.

Signed binary

Binary representation in which bit patterns are used to represent both positive and negative integers.

Fixed point

A binary representation where the binary point is placed at a fixed, specified position.

Mantissa

The part of the simplified floating-point representation that contains the significant binary value; it is combined with the exponent to form the number.

Binary fraction

A fractional value represented using binary digits, with each fractional position contributing a binary fraction value.

Rounding error

The inaccuracy introduced when a value that cannot be represented exactly is stored as an approximation.

Absolute error

The magnitude of the difference between an actual value and the value stored or processed by a computer.

Relative error

The absolute error divided by the actual value, often expressed as a decimal or percentage.

Fixed point

A number representation with a binary point at a fixed position, giving a predetermined division between whole-number and fractional bits.

Floating point

A number representation in which the binary point can move, allowing a wider range of values but potentially variable precision and slower calculations.

Normalisation

The process of moving the binary point in a floating point mantissa to its required standard position and adjusting the exponent so that the value remains unchanged.

Mantissa

The part of a floating point representation that contains the significant digits of the number.

Overflow

The condition in which a calculation produces a value greater than the maximum value representable using the available fixed number of bits.

Underflow

The condition in which a calculation produces a value less than the minimum value representable using the available fixed number of bits.