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GATE CSE 2021 Set 1 Q38: Next three states of a 3-bit T flip-flop counter

Question

Consider a 3-bit counter, designed using T flip-flops, as shown below:

Assuming the initial state of the counter given by PQR as 000, what are the next three states?

Three T flip-flops P, Q and R sharing a common clock pulse. T_P is fed from R, T_Q from P' (the complement of P), and T_R from Q', with outputs P, Q, R taken from the flip-flops
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Answer: A (official GATE 2021 final answer key)

Concept used: A T flip-flop toggles when T=1T = 1; all flip-flops are clocked together, so evaluate every TT input from the present state.

First step: Read off the wiring: TP=RT_P = R, TQ=P′T_Q = P', TR=Q′T_R = Q'. From 000, find which flip-flops toggle.

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Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

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