Question

Maximum data rate of a channel for noiseless 3 kHz binary channel is

• A. 2000 bps
• B. 3000 bps
• C. 6000 bps
• D. 1000 bps

Hint:

In noiseless channels, the maximum data rate is determined by the Nyquist formula, which depends on the channel bandwidth and the number of signal levels.

Answer 1

The Correct Option is C

The maximum data rate for a noiseless channel can be calculated using the Nyquist formula: \[ \text{Maximum Data Rate} = 2 \times \text{Bandwidth} \times \log_2(M) \] Where: - Bandwidth is the channel bandwidth in Hz. - M is the number of signal levels. For a binary channel, \( M = 2 \).
Given that the bandwidth of the channel is 3 kHz and it is a binary channel, the formula simplifies to:
\[ \text{Maximum Data Rate} = 2 \times 3000 \times \log_2(2) = 2 \times 3000 \times 1 = 6000 \text{ bps} \]
Therefore, the correct answer is 3. 6000 bps.