ITPEC FE Subject A October 2025 Question 4

Mealy Machine (State Transition Diagram) — trace input through a finite automaton to produce output.

Given automaton with states S₁, S₂, S₃ and input 0011001110:

Transition table:
- S₁ + 0 → S₁, output 0 | S₁ + 1 → S₂, output 0
- S₂ + 0 → S₁, output 0 | S₂ + 1 → S₃, output 1
- S₃ + 0 → S₁, output 0 | S₃ + 1 → S₃, output 1

Step-by-step trace:
- 0 → S₁→S₁, out 0
- 0 → S₁→S₁, out 0
- 1 → S₁→S₂, out 0
- 1 → S₂→S₃, out 1
- 0 → S₃→S₁, out 0
- 0 → S₁→S₁, out 0
- 1 → S₁→S₂, out 0
- 1 → S₂→S₃, out 1
- 1 → S₃→S₃, out 1
- 0 → S₃→S₁, out 0

Output: 0001000110

Why not others:
- (b) 0001001110 — wrong output at step 9 (assumes S₂→S₃ transition instead of S₃→S₃, but output is the same; actual error is at step 7)
- (c) 0010001000 — misreads the transition from S₁ on input 1 as producing output 1
- (d) 0011111110 — treats the automaton as if output always equals input after first transition

Key rule: In a Mealy machine, output depends on both the current state AND the input (labeled on transitions as input/output). Trace each symbol one at a time, updating state after each step.

AI-generated — may contain errors