Question

What is the step size or the resolution of an A/D converter?

(a) Δ = (R)/2^(b+1)

(b) Δ = (R)/2^(b-1)

(c) Δ = (R)/3^(b+1)

(d) Δ = (R)/2

I have been asked this question by my college professor while I was bunking the class.

I want to ask this question from Quantization and Coding in division Sampling and Reconstruction of Signals of Digital Signal Processing

Answer 1

The correct choice is (a) Δ = (R)/2^(b+1)

Explanation: The coding process in an A/D converter assigns a unique binary number to each quantization level. If we have L levels, we need at least L different binary numbers. With a word length of b + 1 bits we can represent 2^b+1 distinct binary numbers. Hence we should have 2^(b+1) > L or, equivalently, b + 1 > log2 L. Then the step size or the resolution of the A/D converter is given by

Δ = (R)/2^(b+1), where R is the range of the quantizer.