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

Answer: (C)

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 = q0_before XOR q2_before = 0 XOR 0 = 0 , q2 = q1_before = 0 
Clock cycle 2 : q0 = data = 0 , q1 = q0_before XOR q2_before = 1 XOR 0 = 1 , q2 = q1_before = 0 
Clock cycle 3 : q0 = data = 0 , q1 = q0_before XOR q2_before = 0 XOR 0 = 0 , q2 = q1_before = 1 
Clock cycle 4 : q0 = data = 1 , q1 = q0_before XOR q2_before = 0 XOR 1 = 1 , q2 = q1_before = 0 
Clock cycle 5 : q0 = data = 1 , q1 = q0_before XOR q2_before = 1 XOR 0 = 1 , q2 = q1_before = 1 
Clock cycle 6 : q0 = data = 0 , q1 = q0_before XOR q2_before = 1 XOR 1 = 0 , q2 = q1_before = 1 
Clock cycle 7 : q0 = data = 0 , q1 = q0_before XOR q2_before = 0 XOR 1 = 1 , q2 = q1_before = 0 
Clock cycle 8 : q0 = data = 0 , q1 = q0_before XOR q2_before = 0 XOR 0 = 0 , q2 = q1_before = 1 
Clock cycle 9 : q0 = data = 0 , q1 = q0_before XOR q2_before = 0 XOR 1 = 1 , q2 = q1_before = 0 

Thus, option (C) is correct.  

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