Question

.A floating-point number representation on a certain system has a sign bit, a 4-bit exponent and a 5-bit significand.

Please provide steps taken to get the answer

a) What is the largest positive and the smallest positive number that can be stored on this system if the storage is normalized? (Assume no bits are implied, there is no biasing, exponents use two's complement notation, and exponents of all zeros and all ones are allowed.)

b) What bias should be used in the exponent if we prefer all exponents to be nonnegative? Why would you choose this bias?

Answer 1

Solution

Largest Positive

0.1111₂ * 2⁴

= 0.9375*16

= 15

Largest positive is 15

Smallest Positive

0.1₂ x 2^-5

= .000001₂

= 1/64

= 0.015625

Smallest positive is 0.015625

For all non-negative exponents, we would need a bias of 4

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all the best