GATE CS 2025 Set 2 Q24 — Sequential Circuits

A $4$-bit ripple counter consists of $4$ cascaded flip-flops. Each stage divides the frequency of its input signal by $2$.

For a $4$-bit ripple counter, the frequency of the waveform at the last (fourth) flip-flop, $f_{\text{out}}$, is related to the input clock frequency, $f_{\text{in}}$, by:

In terms of time periods, since $T = \frac{1}{f}$:

Given that the period of the waveform at the last flip-flop is $T_{\text{out}} = 64\ \mu\text{s}$:

The frequency of the ripple counter (which is the input clock frequency $f_{\text{in}}$) is:

Thus, the frequency of the ripple counter is 250 kHz.