The minimum number of JK flip-flops required to construct a synchronous…
2015
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,…) is __________ .
Answer: 3 — Answer: 3 JK flip-flops. Reason: There are four distinct count values: 0, 1, 2, 3. To uniquely encode four values you need at least 2 flip-flops (since 2^2 =…
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Correct answer: 3
Answer: 3 JK flip-flops.
Reason:
There are four distinct count values: 0, 1, 2, 3. To uniquely encode four values you need at least 2 flip-flops (since 2^2 = 4).
Each value is repeated twice in the sequence, so the counter must remember whether to hold the same output for one more clock or to advance to the next number. That requires one additional flip-flop as a one-bit memory (for example, a toggle/divide-by-2 stage).
With only 2 flip-flops the next state would be a fixed function of the current 2-bit output, so you could not sometimes stay and sometimes advance from the same binary output without extra memory.
Therefore the minimum number is 2 + 1 = 3 flip-flops.
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