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 $Z_1=1$ permanently. Else $Z_1=0.$

If a sequence of $3$ zeros is received on $x,$ then $Z_2=1$ permanently. Else $Z_2=0.$

If the last three bits received on $x$ are $101$ or $010,$ then $Z_3=1.$ Else $Z_3=0.$

If any of the outputs i$,$e $Z_1,Z_2,$ or $Z_3$ is set to $1,$ then the other outputs cannot

be set to $1.$ For example, is $Z_1=1$ permanently, then $Z_2=0$ and $Z_3=0$

permanently.

$($a$)$ Pick one or the other, Moore or Mealy. Draw a state diagram. $[10$ points$]$

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

logic and D flip$-$flops. $[5$ points$]$

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

or with gates$).[5$ points$]$

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

with gates$).[5$ points$]$