Question

Discrete samples of an analog signal are uniformly quantized to PCM. If the maximum value of analog sample is to be represented within 0.1% accuracy, then the minimum number of binary digits required per sample is
1. 4
2. 8
3. 10
4. 12
5.

Answer 1

Correct Answer - Option 3 : 10

Calculation:

In PCM, maximum error = Δ/2

Where, Δ = step size

Δ/2 = +0.1 %

Δ = ± 0.2 %

\(\Delta =\pm \frac{2}{1000}\)   …1)

\(\text{ }\!\!\Delta\!\!\text{ }=\frac{2{{V}_{max}}}{{{2}^{n}}}\)   …2)

From 1) and 2)

\(\frac{2}{1000}=\frac{2{{V}_{max}}}{{{2}^{n}}}\)

\(\frac{2}{1000}=\frac{2\left( 1 \right)}{{{2}^{n}}}\)

2n = 1000

2n = 2¹⁰

Taking log on both sides and solving we get n = 13.28 which will be taken as:

n = 10