Consider the circuit in the diagram. The ⊕ operator represents Ex-OR. The D…
2006
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
Attempted by 20 students.
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Correct answer: C
Key idea: On each clock the register shifts: q2 becomes the previous q1, q1 becomes the previous q0, and q0 becomes data XOR the previous q2.
Initialize: q2 q1 q0 = 000.
After clock 1 (input 1): q0 = 1 XOR 0 = 1 → state = 001
After clock 2 (input 0): q0 = 0 XOR 0 = 0 → state = 010
After clock 3 (input 0): q0 = 0 XOR 0 = 0 → state = 100
After clock 4 (input 1): q0 = 1 XOR 1 = 0 → state = 000
After clock 5 (input 1): q0 = 1 XOR 0 = 1 → state = 001
After clock 6 (input 0): q0 = 0 XOR 0 = 0 → state = 010
After clock 7 (input 0): q0 = 0 XOR 0 = 0 → state = 100
After clock 8 (input 0): q0 = 0 XOR 1 = 1 → state = 001
After clock 9 (input 0): q0 = 0 XOR 0 = 0 → state = 010
Conclusion: After nine clocks the register contains q2 q1 q0 = 010.
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