Question

Consider 24 voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at 12 kHz and represented by an 8-bit word, the bit-duration (in microseconds) is _________ (round off to two decimal places)

Hint:

The bit-duration is the inverse of the bit rate, which is calculated by multiplying the sampling rate by the number of bits per sample.

Answer 1

Correct Answer: 0.42

The bit-duration for each signal is the reciprocal of the sampling rate multiplied by the number of bits per sample. Given: - Sampling rate = 12 kHz = \( 12 \times 10^3 \) samples per second, - Bits per sample = 8 bits, - Number of signals = 24. The bit rate per signal is: \[ \text{Bit rate} = 12 \times 10^3 \times 8 = 96000 \, \text{bits per second}. \] The bit-duration is the reciprocal of the bit rate: \[ \text{Bit-duration} = \frac{1}{96000} \, \text{seconds}. \] Converting to microseconds: \[ \text{Bit-duration} = \frac{1}{96000} \times 10^6 \, \mu s = 10.42 \, \mu s. \] Thus, the bit-duration is approximately \( 0.44 \, \mu s \).