GATE CS 2016 Set 1 — Question 18
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Digital Logic → Sequential Circuits → Counters (Sync, Async)
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Question
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 ________.
Correct answer
3 to 4
Solution
The counter sequence is (repeats).The output sequence has length 6. Notice that the output '0' appears three times, but each time it transitions to a different next state (1, 2, or 3). Therefore, the internal states corresponding to these outputs must be distinct to determine the correct next state.The sequence of unique states required is:
(output 0) (output 1) (output 0) (output 2) (output 0) (output 3) Total number of distinct states in the cycle = 6.
To implement a counter with states, the minimum number of flip-flops required is .Number of flip-flops = .
(output 0) (output 1) (output 0) (output 2) (output 0) (output 3) Total number of distinct states in the cycle = 6.
To implement a counter with states, the minimum number of flip-flops required is .Number of flip-flops = .
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