$(24$ points$)$ We would like to analyze the following sequential network. It has two input

bits $x_1$ and $x_0,$ with a single output bit z$.$ Note, that both D Flip$-$flops connect to the

same CLK$,$ not shown in the figure for simplicity.

$($a$)(6$ Points$)$ Write expressions for $z,y_1(t+1)$ and $y_0(t+1)$ in terms of inputs

and $\{$:$x_0)$ and present states and $\{$:$y_0).$

$($b$)(6$ Points$)$ Using the expressions, fill in the table below.

$($c$)$ Draw the state diagram for this system.