Question

1. If the floating-point number storage on a certain system has a sign bit, a 4-bit exponent and a 5-bit significand:

       i) 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.)

       ii) What bias should be used in the exponent if we prefer all exponents to be non-negative? Why would you choose this bias?

Answer 1

1)

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

2)

For a n bit exponent, the bias used is 2^n-1 -1

Here n= 4

So the bias would be 2^4-1-1 = 2³ -1 = 8-1=7

Thus the correct answer is 7.