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GATE 2011 CS (CS1) – Question 61

Digital Logic · Sequential Circuits · 2 marks · Multiple choice

All three flip-flops in the shown counter start zero. How many distinct PQR states are generated?

Diagram for GATE 2011 CS (CS1) question 61
  1. 3
  2. 4
  3. 5
  4. 6

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Show answer and explanation

Correct answer: (B) 4

Explanation

Using $P^+=R$, $Q^+=\overline{P+R}$ and $R^+=Q\bar R$, the state sequence is 000→010→011→100→000. It repeats after four distinct states, so the answer is four, B. The remaining four bit patterns are outside this reset-reachable cycle.

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