The minimum number of JK flip-flops required to construct a synchronous counter with the count sequence $(0,0,1,1,2,2,3,3,0,0,\ldots)$ is ______.

The counter cycles through the sequence $(0, 0, 1, 1, 2, 2, 3, 3)$.

Since each output state appears twice, the circuit needs distinct internal states to differentiate the first occurrence from the second occurrence of each number (e.g., $0_a \to 0_b$ and $0_b \to 1_a$).

• Total number of unique states $N = 8$.

• The minimum number of flip-flops $n$ required satisfies:

  $$2^n \ge N \implies 2^n \ge 8 \implies n = 3$$

Therefore, a minimum of 3 JK flip-flops are required.