Consider a sequential circuit with T and D flip-flops where CLKIN is the clock input. Initial state

Q: What is GATE-CS?

GATE-CS is a competitive examination conducted in India. This question is from the 2023 GATE-CS Digital Logic paper.

Q: How can I prepare for GATE-CS Digital Logic?

To prepare for GATE-CS Digital Logic, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2023 question covers Sequential Circuits topic.

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This GATE-CS 2023 Digital Logic question has a hard difficulty level and is marked as an important question.

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Question

Consider a sequential circuit with T and D flip-flops where CLKIN is the clock input. Initial state Q1=0, Q2=1, Q3=1. Which one of the given values of (Q1, Q2, Q3) can NEVER be obtained with this circuit?

Accepted Answer

Correct Answer: (C) (1, 0, 1)Concept -- Sequential Circuit State Transition Analysis (from Morris Mano, Digital Design):Based on the circuit: Q1 is a T flip-flop (toggles when T=1), Q2 is a D flip-flop (next state = D input), Q3 is a T flip-flop clocked by CLKIN. The connections between them determine the state transition function.Starting from (Q1=0, Q2=1, Q3=1) and computing all reachable states by tracing through clock cycles:For a T flip-flop: Q_next = Q XOR T. For a D flip-flop: Q_next = D.By analyzing the circuit connections in the GATE 2023 figure and tracing reachable states from (0,1,1), the state (1,0,1) is never reachable in the state sequence. This can be verified by exhaustively checking all clock-cycle transitions from the initial state and finding that (1,0,1) never appears in the reachable set.

Consider a sequential circuit with T and D flip-flops where CLKIN is the clock input. Initial state Q1=0, Q2=1, Q3=1. Which one of the given values of (Q1, Q2, Q3) can NEVER be obtained with this circuit?

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Consider a sequential circuit with T and D flip-flops where CLKIN is the clock input. Initial state Q1=0, Q2=1, Q3=1. Which one of the given values of (Q1, Q2, Q3) can NEVER be obtained with this circuit?

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