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The number of bits in a binary $\mathrm{PCM}$ system is increased from $n$ to $n+1$. As a result, the signal to quantization noise ratio will improve by a factor

1. $\frac{n+1}{n}$
2. $2^{(n+1) / n}$
3. $2^{2(n+1) / n}$
4. which is independent of $\mathrm{n}$