Discussion
We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is
Answer: D
The minimum number of flip-flops is 3.
The sequence 0-1-0-2-0-3 has six steps, and the state 0 occurs three times with three different successors (1, 2 and 3). A synchronous counter's next state depends only on its present state, so the three 0s must be three distinct internal states that happen to give output 0.
That makes six states in all. Two flip-flops give only four states, so at least three are needed (\(2^{3} = 8 \ge 6\)). Options 0, 1 and 2 cannot hold six distinct states.
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