Questions

$(8$ marks$)$ Consider a state machine with states $A,B,C,D,$ a binary input, and a binary output:

If the input is $0,$ the state sequence is $ABCD$Adots;

If the input is $1$ and the state is $A$ or $C,$ then the state sequence is $ACA$Cdots; and

If the input is $1$ and the state is $B$ or $D,$ then state machine remains in the same state.

The output is $1$ in state A and $0$ otherwise.

Sketch the state diagram and design a Moore machine that implements this sequential system.

All expressions should be in fully reduced sum$-$of$-$products form. You do not need to sketch the circuit.