Question

What is the resolution to cover a range of numbers xmax-xmin with ‘b’ number of bits?

(a) (xmax+xmin)/(2^b-1)

(b) (xmax+xmin)/(2^b+1)

(c) (xmax-xmin)/(2^b-1)

(d) (xmax-xmin)/(2^b+1)

The question was asked during an interview.

Question is taken from Representation of Numbers topic in portion Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct answer is (c) (xmax-xmin)/(2^b-1)

The best explanation: A fixed point representation of numbers allows us to cover a range of numbers, say, xmax-xmin with a resolution

Δ=(xmax-xmin)/(m-1)

where m=2^b is the number of levels and ‘b’ is the number of bits.