GATE CS 2015 Set 2 — Question 17
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Digital Logic → Sequential Circuits → Counters (Sync, Async)
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Question
The minimum number of JK flip-flops required to construct a synchronous counter with the count sequence is
Correct answer
3 to 3
Solution
The given count sequence is .Let's list the unique states in this sequence:
.Therefore, a minimum of 3 JK flip-flops are required to construct a synchronous counter with this sequence.
- The number 0 appears twice.
- The number 1 appears twice.
- The number 2 appears twice.
- The number 3 appears twice.
1.0 (first occurrence)
2.0 (second occurrence)
3.1 (first occurrence)
4.1 (second occurrence)
5.2 (first occurrence)
6.2 (second occurrence)
7.3 (first occurrence)
8.3 (second occurrence)
To represent 8 distinct states, we need flip-flops such that ..Therefore, a minimum of 3 JK flip-flops are required to construct a synchronous counter with this sequence.
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