GATE CS 2015 Set 2 Q7 — Sequential Circuits

To find the minimum number of JK flip-flops required, we analyze the period of the given count sequence:

The sequence repeats after every $8$ steps. Thus, the counter has a period (or modulus) of $8$.

For the counter to transition correctly through this sequence, it must distinguish between identical consecutive outputs (for example, distinguishing the first $0$ from the second $0$ so that the next state transitions to $0$ and $1$ respectively). This requires the counter to have at least $8$ unique internal states.

The minimum number of flip-flops $n$ required to represent $N$ distinct internal states is given by:

Substituting $N = 8$:

Therefore, the minimum number of JK flip-flops required is 3.