$(10\%)$ A sequential circuit has two inputs $($X$1$ and X $2)$ and one output $(Z).$ The output begins as $0$ and remains a constant value unless one of the following input sequences occurs:

$($a$)$ The input sequence $x1x2=11,10$ causes the output to become $0.$

$($b$)$ The input sequence $x1x2=00,10$ causes the output to become $1.$

$($c$)$ The input sequence $x1x2=01,10$ causes the output to toggle.

Derive a Moore state table and state graph.