Question

For the circuit shown, the clock frequency is $f_0$ and the duty cycle is 25%. For the signal at the Q output of the Flip-Flop, ________________.

• A. frequency is $f_0/4$ and duty cycle is 50%
• B. frequency is $f_0/4$ and duty cycle is 25%
• C. frequency is $f_0/2$ and duty cycle is 50%
• D. frequency is $f_0$ and duty cycle is 25%

Hint:

In JK flip-flops with $J = K = 1$, the output always toggles, ensuring a perfect 50% duty cycle regardless of input waveform shape.

Answer 1

The Correct Option is A

The circuit includes a 2-bit binary counter driven by a clock of frequency $f_0$ and duty cycle 25%. A 2-bit counter generates: - LSB toggles at: \[ f_0 / 2 \] - MSB toggles at: \[ f_0 / 4 \] The MSB output is applied to a JK flip-flop with $J = 1$ and $K = 1$, meaning it toggles on every positive clock edge. Thus, the output $Q$ toggles at the same rate as MSB: \[ f_Q = f_0 / 4. \] A toggling JK flip-flop always produces a 50% duty cycle, regardless of the input duty cycle (because it changes state only on clock edges). Therefore: \[ f_Q = \frac{f_0}{4}, \qquad \text{duty cycle} = 50%. \] Final Answer: $f_0/4$ and duty cycle 50%