The number of quantization levels is increased from 4 to 64. The bandwidth required for the transmission of a PCM signal increases by a factor of 

Concept:

The number of levels for an n-bit PCM system is given by:

L = 2n

We can also state that the number of bits for a given quantization level will be:

n = log2 L

Also, the bandwidth of PCM is given by:

\(BW=n{f_s}\)

n = number of bits to encode

fs = sampling frequency

Calculation:

For L = 4 quantization levels, the number of bits n = log2 4 = 2 bits. The bandwidth is, therefore:

B.W. = 2 fs

Similarly, For L = 64 quantization levels, the number of bits n = log2 64 = 6 bits. The bandwidth is, therefore:

B.W. = 6 fs

Clearly, the Bandwidth is increased by 3 times.