Question

What is the range of round-off error for a foxed point representation?

(a) [-0.5(2^-b+2^-bm), 0.5(2^-b+2^-bm)]

(b) [0, (2^-b+2^-bm)]

(c) [0, (2^-b-2^-bm)]

(d) [-0.5(2^-b-2^-bm), 0.5(2^-b-2-bm^-bm)]

The question was asked by my school teacher while I was bunking the class.

Question is from Representation of Numbers in section Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct choice is (d) [-0.5(2^-b-2^-bm), 0.5(2^-b-2-bm^-bm)]

Explanation: The round-off error is independent of the type of fixed point representation. The maximum error that can be introduced through rounding is 0.5(2^-b+2^-bm) and this can be either positive or negative, depending on the value of x. Therefore, the round-off error is symmetric about zero and falls in the range

[-0.5(2^-b-2^-bm), 0.5(2^-b-2-bm^-bm)].