# Number of binary digits in PCM

This is the problem from Shaum Otlines Analog and Digital Communications, Hwei Hsu Problem 5.13.

It asks for number of binary digits in each sample if each sample at the receiving end of the system has to be 0.5 per cent of the peak-to-peak full scale value. First of all, how can i understand term "peak-to-peak full-scale" value? What is that supposed to mean?

Now, in the solution to this problem, it says that the peak error is $$0.005*2m_p$$ where $$2m_p$$ is distance from lower to upper peak of the signal.

However, i am not familiar with term "peak error", what is "peak error"?

And then, PEAK TO PEAK ERROR turns out to be $$2*0.005*m_p$$. What is peak to peak error and what is the difference between peak error and ppeak to peak error? Any help appreciated!

• i think it means that the quantization error of each quantized sample must not exceed 0.005 times the maximum peak-to-peak amplitude of the signal. i think, in particular, this means that you will need at least 200 quantization levels (assuming equally-spaced quantization levels) and so your binary word must have at least 200 possible values. sounds like 8 bits to me. – robert bristow-johnson Apr 12 '19 at 21:35
• @robertbristow-johnson That is correct. – MBaz Apr 12 '19 at 22:32
• @robertbristow-johnson Ok, thanks, but that still doesnt answer my questions what is peak error, peak to peak error and what is difference between these two. – cdummie Apr 13 '19 at 7:11
• well it depends on whether your quantization is rounding to the nearest quantized level or always rounding in the same direction (normally down). – robert bristow-johnson Apr 14 '19 at 2:24
• @robertbristow-johnson Let's say i am rounding in the same direction (down), how would i define those terms in that case? – cdummie Apr 15 '19 at 10:05