For a state machine with the following state diagram the expression for the…
2006
For a state machine with the following state diagram the expression for the next state S+ in terms of the current state S and the input variables x and y is
- A.
S+ = S' . y' + S . x
- B.
S+ =S. x . y' + S' . y . x'
- C.
S+ =x . y'
- D.
S+ =S' . y + S . x'
Attempted by 19 students.
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Correct answer: A
Solution approach: derive the next state for each current state from the transitions and then combine them.
If the current state S = 1: the self-loop labeled x = 1 means the machine stays in state 1 when x = 1, and the arrow to state 0 for x = 0 means it moves to 0 when x = 0. Therefore for S = 1, the next state S+ = x.
If the current state S = 0: the self-loop labeled y = 1 means the machine stays in state 0 when y = 1, and the arrow to state 1 for y = 0 means it moves to 1 when y = 0. Therefore for S = 0, the next state S+ = y'.
Combine the two cases using S and its complement S': when S = 1 use S+ = x, when S = 0 use S+ = y'. This gives
Final expression: S+ = S·x + S'·y'
This matches the expression S'·y' + S·x.