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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