Q$2.(4$ pts$)$ Design a sequential circuit.

A sequential circuit has one D flip$-$flop and one JK$-$flip$-$flop, two inputs $x$ and $y,$ and one output $z.$ A and B are the outputs of each D flip$-$flop, and JK$-$flip$-$flop, respectively. The flip$-$flop input equations and the circuit output are as follows. Here $D_A$ is the $D$ input of the D$-$flip flop of $A,$ and $J_B,K_B$ is the $J$ and $K$ input of the JK$-$flip flop of B$.$

$D_A=xy+yB$

$J_B=xB+xy$

$K_B=yB+xA$

$z=y+xy$

Q$2-1.(1$pt$)$ Draw the logic diagram of the circuit and test it with Logisim. Please attach the circuit image only, $($i$.$e$.,$ capture the circuit image and attach it to your submission file. No need to include $.$circ.$)$

Attach the circuit image here.

Q$2-2.$ Construct a state transition table as well as a state diagram of this circuit. Note that you don't have to simplify states. $(1$pt$)$

$\backslash$table$[[$x$,$Y$,$A$($t$),$B$($t$),$A$($t$+1),$B$($t$+1),$Z$],[0,0,0,0,,,],[0,0,0,1,,,],[0,0,1,0,,,],[0,0,1,1,,,],[0,1,0,0,,,],[0,1,0,1,,,],[0,1,1,0,,,],[0,1,1,1,,,],[1,0,0,0,,,],[1,0,0,1,,,],[1,0,1,0,,,],[1,0,1,1,,,],[1,1,0,0,,,],[1,1,0,1,,,],[1,1,1,0,,,],[1,1,1,1,,,]]$

Attach a state diagram here. $(2$pts$)$