GATE | GATE IT 2006 | Question 37

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’col

Explanation:

For the next state to be S=1 there are two possible cases:

• S=1, x=1
• S=0, y=0

For the next state to be S=0 there are two possible cases:

• S=1, x=0
• S=0, y=1

The above conditions can be tabulated as (where X means that variable has no effect on state transition)

 x y S S+ 1 X 1 1 X 0 0 1 0 X 1 0 X 1 0 0

It is clearly visible that S+ depends on state S and either of the variable x or y. This directly eliminates option (B) and option (C).
Now we can check for the other two options. When S=1 and x=1 option (D) gives S+ as 0 which should otherwise be one hence (D) can also be eliminated.
Option (A) satisfies all, hence the answer.

This solution is contributed by Yashika Arora.

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