GATE 2022 IN Q.26: solution and answer

Official answer: 0.42 to 0.44Source: Official answer key, GATE 2022 IN (IIT Kharagpur)

1. Each voice signal is sampled at $f_s=12\text{kHz}$, so each signal gives $12000$ samples per second.

2. Each sample is coded as an 8-bit word, so one signal needs $12000\times 8=96000\text{bits/s}$.

3. Time-division multiplexing interleaves the 24 signals on one line without latency, so the line carries $R_b=24\times 96000=2.304\times 10^6\text{bits/s}$.

4. The bit duration is the reciprocal of this rate: $$T_b=\frac{1}{R_b}=\frac{1}{2.304\times 10^6\text{bits/s}}\approx 0.434\times 10^{-6}\text{s}.$$

5. In microseconds, $T_b\approx 0.434\mu \text{s}$, which is $0.43\mu \text{s}$ to two decimal places.