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GATE 2016 EC (EC2) – Question 54

Digital Circuits · Sequential Circuits · 2 marks · Multiple choice

The figure shows a finite-state machine with states A, B and C and binary inputs X,Y,Z. Which statement is correct?

Diagram for GATE 2016 EC (EC2) question 54
  1. Transitions from A are ambiguously defined.
  2. Transitions from B are ambiguously defined.
  3. Transitions from C are ambiguously defined.
  4. All transitions are unambiguous.

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Show answer and explanation

Correct answer: (C) Transitions from C are ambiguously defined.

Explanation

A deterministic state machine must specify at most one outgoing next state for every input combination.

At C, Z=0 gives the self-loop. For Z=1, the transition to B has Y=1, while the transition to A has X=1. Thus X=Y=Z=1 enables both C→A and C→B at once.

The conditions leaving A and B partition their input cases without such overlap. The ambiguity is therefore at **C, option C**.

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