GATE CS 2015 Set 1 — Question 21

MCQ+1 / -0.33MediumCounters (Sync, Async)Sequential CircuitsDigital Logic

Digital Logic → Sequential Circuits → Counters (Sync, Async)

Last updated 5 September 2026

Question

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

Correct answer (D) 0, 8, 12, 14, 15, 7, 3, 1, 0 Solution A 4-bit Johnson counter (also known as a twisted ring counter) operates by shifting bits and feeding the complement of the last bit back into the first bit. Assuming a right-shift operation: 1. Initial state: 0000 (Decimal 0) 2. Complement of last bit (0) is 1. Shift right and feed 1 to MSB: 1000 (Decimal 8) 3. Complement of last bit (0) is 1. Shift right and feed 1 to MSB: 1100 (Decimal 12) 4. Complement of last bit (0) is 1. Shift right and feed 1 to MSB: 1110 (Decimal 14) 5. Complement of last bit (0) is 1. Shift right and feed 1 to MSB: 1111 (Decimal 15) 6. Complement of last bit (1) is 0. Shift right and feed 0 to MSB: 0111 (Decimal 7) 7. Complement of last bit (1) is 0. Shift right and feed 0 to MSB: 0011 (Decimal 3) 8. Complement of last bit (1) is 0. Shift right and feed 0 to MSB: 0001 (Decimal 1) 9. Complement of last bit (1) is 0. Shift right and feed 0 to MSB: 0000 (Decimal 0) The sequence is 0, 8, 12, 14, 15, 7, 3, 1, 0. This matches option (D). Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (D) 0, 8, 12, 14, 15, 7, 3, 1, 0 Solution A 4-bit Johnson counter (also known as a twisted ring counter) operates by shifting bits and feeding the complement of the last bit back into the first bit. Assuming a right-shift operation: 1. Initial state: 0000 (Decimal 0) 2. Complement of last bit (0) is 1. Shift right and feed 1 to MSB: 1000 (Decimal 8) 3. Complement of last bit (0) is 1. Shift right and feed 1 to MSB: 1100 (Decimal 12) 4. Complement of last bit (0) is 1. Shift right and feed 1 to MSB: 1110 (Decimal 14) 5. Complement of last bit (0) is 1. Shift right and feed 1 to MSB: 1111 (Decimal 15) 6. Complement of last bit (1) is 0. Shift right and feed 0 to MSB: 0111 (Decimal 7) 7. Complement of last bit (1) is 0. Shift right and feed 0 to MSB: 0011 (Decimal 3) 8. Complement of last bit (1) is 0. Shift right and feed 0 to MSB: 0001 (Decimal 1) 9. Complement of last bit (1) is 0. Shift right and feed 0 to MSB: 0000 (Decimal 0) The sequence is 0, 8, 12, 14, 15, 7, 3, 1, 0. This matches option (D).

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