Mealy Design $[50$ points$]$

A sequential circuit has one input X and three outputs Z$1,$ Z$2,$ and Z$3.$

$$ If a sequence of $3$ ones is received on X$,$ then Z$1=1.$ Else Z$1=0.$

$$ If a sequence of $3$ zeros is received on X$,$ then Z$2=1.$ Else Z$2=0.$

$$ If the last three bits received on X are $101,$ then Z$3=1.$ Else Z$3=0.$

$($a$)$ Draw a state diagram for a Mealy machine implementation of this problem. $[20$

points$]$

$($b$)$ Draw the overall $$block$$ diagram for the circuit, with blocks of combinational

logic and D flip$-$flops. $[10$ points$]$

$($c$)$ Design the combinational logic to compute the next state $($with Boolean algebra,

or with gates$).[10$ points$]$

$($d$)$ Design the combinational logic to compute the output $($with Boolean algebra, or

with gates$).[10$ points