GATE | GATE-CS-2015 (Set 1) | Question 30

Consider a 4 bit Johnson counter with an initial value of 0000. The counting sequence of this counter is:
(A) 0, 1, 3, 7, 15, 14, 12, 8, 0
(B) 0, 1, 3, 5, 7, 9, 11, 13, 15, 0
(C) 0, 2, 4, 6, 8, 10, 12, 14, 0
(D) 0, 8, 12, 14, 15, 7, 3, 1, 0


Answer: (D)

Explanation: Refer http://en.wikipedia.org/wiki/Ring_counter#Johnson_Counter_.284-bits.29

The four bit Johnson’s counter connects the complement of the output of the last shift register to the input of the first register with shift distance=1 i.e 1 bit will shift/cycle

It will work as follows:

0000 //Last 0 complemented and fed as input to first register

1000

1100

1110

1111 //Last 1 complemented and fed as input to first register

0111

0011

0001

0000

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