$1.$ There is a system to detect some input pattern. The output of the system is $1$ iff there has been a nonoverlapping input pattern of $1101.$

$$

$9.$a$$ If the system is a Mealy system, show the state diagram for the defined states given below. A sample of input$/$output is shown as follows:

$$

$0010110110111001011011$

$000000010000000000001000$

$(5$ points$)$

$$

State A:$$ nowhere state looking for the first $1$;

State B:$1$ state looking for $1$;

State C:$11$ state looking for $0$;

State D:$110$ state looking for $1.$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$9.$b$$ If the system is a Moore system, show the state diagram for the defined states given below. A sample of input$/$output is as follows:

$$

$0010110110111001011011$

$000000001000000000000100$

$(5$ points$)$

$$

State A:$$ nowhere state looking for the first $1$;

State B:$1$ state looking for $1$;

State C:$11$ state looking for $0$;

State D:$110$ state looking for $1$;

State E:$1101$ state