If the floating-point representation on a certain system has a sign bit, a 3-bit
ID: 3531281 • Letter: I
Question
If the floating-point representation on a certain system has a sign bit, a 3-bit exponent and a 4-bit significand: a) what is the largest positive and the smallest positive number that can be stored on the system if the storage is normalized? (assume no bits are implied, there is no biasing, exponents us 2s complement notation, and exponents of all zeros and all ones are allowed).
I've asked this question before and received the answer of:
Largest Positive =0 011 1111 which is .1111 x 2^(3) = 7.5(decimal)
Smallest Positive: 0.12 x 2^(-4) = .000012 = 1/32 = 0.03125
I understand the answer to the Largest Positive.
But for the smallest positive wouldn't the answer be 0 100 0001 = .0001 x 2^(-4) = 0.00000001 ???
Explanation / Answer
a. Largest Positive: 0.11112 x 23 = 111.12 = 7.5 Smallest Positive: 0.12 x 2?4= .000012 = 1/32 = 0.03125 b. For all non-negative exponents, we would need a bias of 4.