Floating Point Numbers

• Position Values are set by the binary point • To the left they double in size (1,2,4) • to the right of the point they halve in size (0.5, 0.25, 0.125)

set by the software in use, or occasionally the hardware of the processor

The difference between the highest and lowest numbers that can be represented

the smallest possible fraction that can be represented

There is a trade- off between range and precision.

mantissa- the pattern of 1s and 0s exponent - the power of 2 / how much it is to be shifted. • both are stored with two’s complement • bits for each vary depending on the question

an 01 or a 10. The binary point is between the 1 and 0.

Fixed point : Less processing, therefore quicker. Floating point: maximum range and precision.

• the binary point in the (normalised) mantissa is after the first digit • find the value of the exponent. • If it is positive, shift the binary point on the mantissa to the right that many places. • If it is negative, shift it to the left that many places. this will create empty spaces. Fill these with the bit value (1 or 0 ) that the mantissa starts with.

• find the mantissa - the first 01 or 10 of the number, and all the 1s and 0s after it • the point of the mantissa is between the 1 and the 0. • how many hops would it take to move the binary point from that position, to where it belongs in it’s fixed form? • That number is the exponent. (if hopped left, exponent is negative. otherwise, positive)

• remove “spare” 0s or 1s from the front of the mantissa until it starts with 01 or 10. • how many you removed, subtract that number from the exponent.

• find the smaller exponent, make it lager to match the other • how much did you add? add that many 1s or 0s to the start of the mantissa • Now add the mantissas together. The two nums have the same exponent.