Biased Representation
Signed exponents would complicate comparisons
In biased notation the most negative number is 000...02 and the most positive is 111...12
Since the single precision exponent field is 8 bits, allowing 256 different configurations, the bias for sp fp is 127
- +2 is presented as 2+127 = 129 = 1000 0001
- -2 is represented as -2+127 = 125 = 0111 1101
The bias for double precision is 1023
The formula: (-1)sign*(1+mantissa)*2(exponent-bias)
01111111100000000000000000000000 1.0 x 2-1
00000000100000000000000000000000 1.0 x 2+1