GATE EC 2026 Set 1 — Question 27
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Digital Circuits → Sequential Logic → Ripple & Synchronous Counters
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Question
A binary ripple counter is designed to count to . Which of the following is/are the number of flip-flops required to design the counter?
Correct answer
(B) 7
Solution
A counter that counts from 0 to must have at least distinct states.
In this case, the counter counts from to , which means it requires states.
The number of flip-flops required to represent states must satisfy the inequality:Substituting :If , , which is less than 65 (Insufficient).
If , , which is greater than or equal to 65 (Sufficient).
Therefore, the minimum number of flip-flops required is 7. Among the provided options, only 7 is a valid choice.
In this case, the counter counts from to , which means it requires states.
The number of flip-flops required to represent states must satisfy the inequality:Substituting :If , , which is less than 65 (Insufficient).
If , , which is greater than or equal to 65 (Sufficient).
Therefore, the minimum number of flip-flops required is 7. Among the provided options, only 7 is a valid choice.
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