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)
Answer
250
Explanation
Each flip-flop in a ripple counter toggles on every active edge it receives, so its output completes one cycle for every two input cycles: each stage halves the frequency. The output of the 4th (last) flip-flop therefore runs at \(f_{clk}/2^{4} = f_{clk}/16\), and its period is 16 clock periods.
\(16\,T_{clk} = 64\ \mu\text{s} \Rightarrow T_{clk} = 4\ \mu\text{s} \Rightarrow f_{clk} = \frac{1}{4\ \mu\text{s}} = 250\ \text{kHz}\).
The counter’s frequency is its input clock frequency. Taking the last stage’s own frequency, \(1/64\ \mu\text{s} \approx 15.6\) kHz, is the usual slip.
Answer: 250