The finite state machine shown below has A as the starting state. Each arc…
2002
The finite state machine shown below has A as the starting state. Each arc label is x/y, where x is a 1-bit input and y is a 2-bit output. Which of the following best describes the output?
- A.
Outputs the sum of the present and the previous bits of the input.
- B.
Outputs 01 whenever the input sequence contains 11.
- C.
Outputs 00 whenever the input sequence contains 10.
- D.
None of these
Attempted by 7 students.
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Correct answer: A
In the diagram, A is the starting state and represents the case where the previous input bit is 0. From A, input 0 gives output 00 and input 1 gives output 01, matching previous + current.
When the previous bit is 1 (states B/C), input 0 gives output 01 and input 1 gives output 10. These are exactly 1 + 0 = 1 and 1 + 1 = 2 in 2-bit binary.
Thus each output is the sum of the present input bit and the previous input bit.