Exercise $1$:

A sequential circuit with two $D$ flip$-$flops A and $B,$ two inputs, $x$ and $y$ ; and one output $z$ is specified by the following next$-$state and output equations:

$A(t+1)=xy+xB$

$B(t+1)=xA+xB$

$z=A$

a$)$ Draw the logic diagram of the circuit.

b$)$ List the state table for the sequential circuit.

c$)$ Draw the corresponding state diagram.