Floating Point Numbers - Yr 2 Only

Floating point numbers are a method of dynamic binary numerical representation, allowing for a customizable range and accuracy using the same number of digits. Floating point consists of 2 parts, a mantissa which contains the binary value of the represented number, and the exponent which shifts the decimal point according to the size of the number. For a floating point number to be normalized and make the best use of available memory, it must begin with "0.1" for a positive number and "1.0" for a negative number. Any deviation with this could be a waste of bits, as the same number could be represented with a smaller mantissa.

For example, the number 32 could be represented by a floating point number with an 8 bit mantissa and a 5 bit exponent.

The mantissa would be as follows: 0.1000000

The exponent must shift the decimal point to shift 1 into the value of 32, it must therefore have a value of 6: 00110