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GATE CS 2006 Q37 — Combinational Circuits

Consider the circuit in the diagram. The $\oplus$ operator represents Ex-OR. The D flip-flops are initialized to zeroes (cleared).

The following data: $100110000$ is supplied to the “data” terminal in nine clock cycles. After that the values of $q_{2}q_{1}q_{0}$ are:

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Answer: C

From the given sequential circuit, we can determine the input equations for each D flip-flop:

$D_2 = \text{data} \oplus q_0$
$D_1 = q_2$
$D_0 = q_1$

The flip-flops are initialized to $q_2 q_1 q_0 = 000$ . The input sequence $100110000$ is processed from left to right (MSB first) over 9 clock cycles:

Clock Cycle	Input (data)	$q_2$	$q_1$	$q_0$
Initial	—	0	0	0
1	1	1	0	0
2	0	0	1	0
3	0	0	0	1
4	1	0	0	0
5	1	1	0	0
6	0	0	1	0
7	0	0	0	1
8	0	1	0	0
9	0	0	1	0

After 9 clock cycles, the state of the flip-flops is $q_2 q_1 q_0 = 010$ .

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Published 10 Oct 2026

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