GATE CS 1993 Q6-3 — Sequential Circuits

The given circuit represents a 3-bit Johnson Counter (also known as a twisted ring counter or switch-tail ring counter), which is a type of feedback shift register.

Let the outputs of the three J-K flip-flops be $Q_2, Q_1, Q_0$. In a Johnson counter, the inverted output of the last stage is fed back to the input of the first stage, and the output of each stage is shifted to the next stage on every clock pulse:

• $J_2 = \overline{Q_0}$, $K_2 = Q_0$
• $J_1 = Q_2$, $K_1 = \overline{Q_2}$
• $J_0 = Q_1$, $K_0 = \overline{Q_1}$

Starting with the initial state $Q_2Q_1Q_0 = 000$, the state transitions on successive clock pulses are:

Since the sequence repeats after every $6$ clock pulses, the circuit acts as a Mod-6 Counter. Additionally, because the data shifts through the flip-flops, it is also classified as a Shift Register.