The GATE Grind

GATE 2015 CS – Question 21

Digital Logic · Sequential Circuits · 1 mark · Multiple choice

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

  1. 0, 1, 3, 7, 15, 14, 12, 8, 0
  2. 0, 1, 3, 5, 7, 9, 11, 13, 15, 0
  3. 0, 2, 4, 6, 8, 10, 12, 14, 0
  4. 0, 8, 12, 14, 15, 7, 3, 1, 0

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Show answer and explanation

Correct answer: (D) 0, 8, 12, 14, 15, 7, 3, 1, 0

Explanation

A Johnson counter shifts right and feeds the complement of the last bit back into the first. Starting from 0000 the states are 0000, 1000, 1100, 1110, 1111, 0111, 0011, 0001 and then back to 0000. In decimal this is 0, 8, 12, 14, 15, 7, 3, 1, 0.