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GATE CS 2011 Q51 — Combinational Circuits

Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration.

If all the flip-flops were reset to $0$ at power on, what is the total number of distinct outputs (states) represented by $PQR$ generated by the counter?

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Answer: B

To find the number of distinct states generated by the counter, we analyze the feedback connections of the circuit. The inputs to the three D flip-flops are given by:

$D_P = \overline{P + Q}$ (NOR gate output with inputs $P$ and $Q$ )
$D_Q = P$
$D_R = Q$

Given that all flip-flops are initially reset to $0$ at power-on, the initial state is $PQR = 000$ . We trace the state transitions at each clock pulse:

Clock Pulse	Current State ( $PQR$ )	Next Inputs ( $D_P, D_Q, D_R$ )	Next State ( $PQR$ )
Initial	$000$	$D_P = \overline{0+0} = 1$ , $D_Q = 0$ , $D_R = 0$	$100$
1	$100$	$D_P = \overline{1+0} = 0$ , $D_Q = 1$ , $D_R = 0$	$010$
2	$010$	$D_P = \overline{0+1} = 0$ , $D_Q = 0$ , $D_R = 1$	$001$
3	$001$	$D_P = \overline{0+0} = 1$ , $D_Q = 0$ , $D_R = 0$	$100$
4	$100$	(Repeats the cycle: $100 \rightarrow 010 \rightarrow 001 \rightarrow 100$ )

The distinct states generated by the counter are $000$ , $100$ , $010$ , and $001$ . Thus, the total number of distinct states is 4.

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Published 10 Oct 2026

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