A sequential circuit has three inputs $x,Y,Z$ and two outputs $F$ and $G.$

If the number of ones received on $x$ is odd, the number of ones received on $Y$ is

odd, and the number of ones received on $Z$ is odd, then $F=1$ and $G=1.$

If the number of ones received on $x$ is even, the number of ones received on $Y$

is even, and the number of ones received on $Z$ is even, then $F=0$ and $G=0.$

If the number of ones received on $x$ is odd, the number of ones received on $Y$ is

even, and the number of ones received on $Z$ is odd, then $F=1$ and $G=0.$

If the number of ones received on $x$ is even, the number of ones received on $Y$

is odd, and the number of ones received on $Z$ is even, then $F=0$ and $G=1.$

Else the values of $F$ and $G$ are don't cares.

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

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

logic and D flip$-$flops. $1$

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

or with gates$)$

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

with gates$).($