Exponent bias

The bias is an offset which is always applied to the exponent of a floating point number, $127$ for single precision and $1023$ for double precision.

We use a bias instead of two’s complement as it allows for the numeric ordering to be the same as the lexicographic ordering which allows fast size comparisons of numbers.

Example: convert single-precision exponent $0111010_2$:

$$0111010_2=122_{10}$$

Subtract the bias to find $122_{10}-127_{10}=-5_{10}$.