Question

An analog signal is sampled, quantized and transmitted using a PCM system. If the tolerable error in sampled amplitude is 0.1% of he peak to peak full scale value, then the minimum number of binary digits required to fulfill this requirement is equal to

• A. 7
• B. 8
• C. 9
• D. 6

Answer 1

The correct option is C 9

$\begin{array}{cc}\text{Minimum quantization error}& =\frac{\Delta }{2}\\ \text{where}\Delta & =\frac{V_{p-p}}{L}\\ \frac{V_{pp}}{2L}& \le \frac{0.1}{100}\times V_{pp}\\ \frac{1000}{2}& \le L\\ L& \ge 500\\ 2^n& \ge 500\\ n& \ge 8.9\\ n_{min}& =9\end{array}$