$4-(10)$ Design a two to four bit decoder using only gates.

$5-$ 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:

$A(t+1)=x{y}_{-}+xB$

$B(t+1)=xA+x{B}_{-}$

$z=A$

$($a$)(5)$Draw the logic diagram of the circuit.

$($b$)(10)$List the state table for the sequential circuit.

$($c$)(10)$ Draw the corresponding state diagram.

$6-$ For the following state table