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GATE CS 2015 Set 1 Q20 — Sequential Circuits

Consider a $4$ -bit Johnson counter with an initial value of $0000.$ The counting sequence of this counter is

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Answer: D

A $4$ -bit Johnson counter (or twisted ring counter) shifts bits at each clock pulse, with the complement of the serial output fed back into the serial input.

Let the state of the counter be represented by $Q_3 Q_2 Q_1 Q_0$ . The feedback equation for a right-shifting Johnson counter is:

D_3 = \overline{Q_0}, \quad D_2 = Q_3, \quad D_1 = Q_2, \quad D_0 = Q_1

Starting with the initial state $0000$ , the sequence of states is calculated as follows:

Clock Pulse	$Q_3 Q_2 Q_1 Q_0$	Decimal Equivalent
Initial	$0000$	$0$
1	$1000$	$8$
2	$1100$	$12$
3	$1110$	$14$
4	$1111$	$15$
5	$0111$	$7$
6	$0011$	$3$
7	$0001$	$1$
8	$0000$	$0$

Thus, the counting sequence is $0, 8, 12, 14, 15, 7, 3, 1, 0$ , which corresponds to Option D.

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Published 10 Oct 2026

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