GATE CS 2025 Set 2 Q.34: Sequential Circuits, Counters and Registers

In a 4-bit ripple counter, if the period of the waveform at the last flip-flop is 64 microseconds, then the frequency of the ripple counter in kHz is ________. (Answer in integer)

Your answer

Official answer and solution

Official answer: 250
From: Official GATE 2025 answer key

Solution

Use the frequency-division property of an $n$ -bit ripple counter: $T_{\text{last}} = 2^n T_{\text{clk}}$ .

In a $4$ -bit binary ripple counter, each flip-flop divides the frequency by $2$ (doubles the period), so the period at the output of the $4$ th (last) flip-flop is:

T_4 = 2^4 \cdot T_{\text{clk}} = 16 \, T_{\text{clk}} = 64\text{ }\mu\text{s} \implies T_{\text{clk}} = \frac{64}{16} = 4\text{ }\mu\text{s}

Therefore, the clock frequency of the ripple counter is:

f_{\text{clk}} = \frac{1}{T_{\text{clk}}} = \frac{1}{4 \times 10^{-6}\text{ s}} = 250 \times 10^3\text{ Hz} = 250\text{ kHz}

Final answer

250

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2025 Computer Science and Information Technology - Session 2 (CS2)
Question: 34 of 65
Section: Computer Science and Information Technology

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