A sequential circuit has two inputs $x_{\text{I}}$ and $x_2$ and one output $z.$ Whenever an $x_{\text{I}}=1$ is observed, the output becomes $1$ provided $x_2=1$ has been observed exactly twice since the last time $x_{\text{I}}=1$ was observed. The output remains $1$ until $x_{\text{I}}=1$ is observed. From the mentioned specification, analyze it and then draw the state diagram as $($a$)$ a Mealy machine, and $($b$)$ as a Moore machine.