Floating Point Numbers (2)
E is usually coded in excess-K two’s complement.
K is called a bias and usually selected to be 2e-1 (e is the number of bits).
So, biased E is:
- -2e-1 £ E £ 2e-1
- 0 £ E + 2e-1 £ 2e
Excess-K form of E is written as: E = (be-1, be-2 ... b0)excess-K (1.16)
where be-1 is the sign bit.
Combining Eqs. (1.14) and (1.16), we have
N = (SMbe-1be-2 ... b0an-1 ... a-m)r (1.17)
representing N = (1.18)
The number 0 is represented by an all-zero word.