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

2015

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

  1. A.

    0, 1, 3, 7, 15, 14, 12, 8, 0

  2. B.

    0, 1, 3, 5, 7, 9, 11, 13, 15, 0

  3. C.

    0, 2, 4, 6, 8, 10, 12, 14, 0

  4. D.

    0, 8, 12, 14, 15, 7, 3, 1, 0

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Correct answer: D

Key insight: In a Johnson (twisted-ring) counter the inverted output of the last flip-flop is fed back into the first flip-flop and the register shifts by one bit each clock. This produces a block of 1s that grows and then shrinks, giving 2n distinct states for an n-bit counter.

  • State transitions (binary -> decimal): 0000 (0) -> 1000 (8) -> 1100 (12) -> 1110 (14) -> 1111 (15) -> 0111 (7) -> 0011 (3) -> 0001 (1) -> 0000 (0)

Therefore the counting sequence is 0, 8, 12, 14, 15, 7, 3, 1, 0, which matches the provided correct option.

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