Design a one$-$input $(x),$ two$-$output $($ Y and Z $)$ synchronous Moore FSM$.$ Y should be $1$ if and only if the most recent two inputs were $01.Z$ should be $1$ if and only if Y was $1$ at some time in the past and the most recent input was $0.$

$[10]$

a$)$ Determine the state diagram.

$[4]$

b$)$ Determine the state table.

$[2]$

c$)$ Design the FSM using D FF$.$ Equations are enough you do not need to draw the gate level diagram.

$[4]$