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How to solve it ?

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there is only one flipflop, so state diagram have state0 and state1.

state0 means Q=0 and statemeans Q=1

you have only one input that is A.

 

what happens if A=1 on state?

X1=0 and X0=1 due to state0 ==> Y = A.X1 + A' . X0 = 1.0 + 0.1 = 0 ==> S = 0 ==> R=1

if S=0 and R=1 then Q=0

∴ if A=1 on state= state0

 

what happens if A=0 on state?

X1=0 and X0=1 due to state0 ==> Y = A.X1 + A' . X0 = 0.0 + 1.1 = 1 ==> S = 1 ==> R=0

if S=1 and R=0 then Q=1

∴ if A=0 on state= state1

 

what happens if A=1 on state?

X1=1 and X0=0 due to state1 ==> Y = A.X1 + A' . X0 = 1.1 + 0.0 = 1 ==> S = 1 ==> R=0

if S=1 and R=0 then Q=1

∴ if A=1 on state= state1

 

what happens if A=0 on state?

X1=1 and X0=0 due to state1 ==> Y = A.X1 + A' . X0 = 0.1 + 1.0 = 0 ==> S = 0 ==> R=1

if S=0 and R=1 then Q=0

∴ if A=0 on state= state0

Graphical representation is

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