Discussion
The maximum dynamic range for a linear PCM system using 16-bit quantizing :
Answer: A
The maximum dynamic range is 98.08 dB.
For an n-bit linear quantizer with a full-scale sinusoidal input, the signal to quantization noise ratio, which sets the usable dynamic range, is
\[ \begin{aligned} \text{SQNR} &= 1.76 + 6.02n\ \text{dB} \\ &= 1.76 + 6.02 \times 16 \\ &= 1.76 + 96.32 = 98.08\ \text{dB} \end{aligned} \]
Each extra bit adds about 6 dB. The value 49.04 dB is half the answer, 32 dB is twice the number of bits, and 16 dB is the number of bits itself, none of which is a decibel ratio for 16 bits.
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