Floating Point Numbers (3)
Multiple representations of a given number:
N = M ´ rE (1.19)
= (M ¸ r) ´ rE+1 (1.20)
= (M ´ r) ´ rE-1 (1.21)
Example: M = +(1101.0101)2
M = +(1101.0101)2
= (0.11010101)2 ´ 24 (1.22)
= (0.011010101)2 ´ 25 (1.23)
= (0.0011010101)2 ´ 26 (1.24)
…
Normalization is used for a unique representation: mantissa has a nonzero value in its MSD position.
Eq. 1.22 gives the normalization representation of M.