# GATE | GATE-CS-2006 | Question 37

Consider the circuit in the diagram. The ⊕ operator represents Ex-OR. The D flipflops are initialized to zeroes (cleared). The following data: 100110000 is supplied to the “data” terminal in nine clock cycles. After that the values of q2q1q0 are:
(A) 000
(B) 001
(C) 010
(D) 101

Explanation:
The D flipflops are initialized to zeroes. This implies q0 = 0, q1 = 0 and q2 = 0 initially.

Clock cycle 1 :
q0 = data = 1 , q1 = q0before XOR q2before = 0 XOR 0 = 0 , q2 = q1before = 0

Clock cycle 2 :
q0 = data = 0 , q1 = q0before XOR q2before = 1 XOR 0 = 1 , q2 = q1before = 0

Clock cycle 3 :
q0 = data = 0 , q1 = q0before XOR q2before = 0 XOR 0 = 0 , q2 = q1before = 1

Clock cycle 4 :
q0 = data = 1 , q1 = q0before XOR q2before = 0 XOR 1 = 1 , q2 = q1before = 0

Clock cycle 5 :
q0 = data = 1 , q1 = q0before XOR q2before = 1 XOR 0 = 1 , q2 = q1before = 1

Clock cycle 6 :
q0 = data = 0 , q1 = q0before XOR q2before = 1 XOR 1 = 0 , q2 = q1before = 1

Clock cycle 7 :
q0 = data = 0 , q1 = q0before XOR q2before = 0 XOR 1 = 1 , q2 = q1before = 0

Clock cycle 8 :
q0 = data = 0 , q1 = q0before XOR q2before = 0 XOR 0 = 0 , q2 = q1before = 1

Clock cycle 9 :
q0 = data = 0 , q1 = q0before XOR q2before = 0 XOR 1 = 1 , q2 = q1before = 0

Thus, option (C) is correct.

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