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Digital Logic
Combinational & Sequential Circuits
GATE 2015
Medium

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

  • 0, 1, 3, 7, 15, 14, 12, 8, 0
  • B0, 1, 3, 5, 7, 9, 11, 13, 15, 0
  • C0, 2, 4, 6, 8, 10, 12, 14, 0
  • D0, 8, 12, 14, 15, 7, 3, 1, 0

Explanation

A Johnson (twisted-ring) counter shifts in the COMPLEMENT of the last flip-flop's output each cycle. Starting at 0000: shift in 1 → 0001(1); 0011(3); 0111(7); 1111(15); now the last bit is 1, so shift in 0 → 1110(14); 1100(12); 1000(8); 0000(0) — completing the cycle 0,1,3,7,15,14,12,8,0.

Source: GATE CS 2015 (Session 1 / 7th Feb Shift 1) (2015)

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