Moore Design $[50$ points$]$

A sequential circuit has two inputs X and Y $,$ and an output F$.$

$$ If the number of ones received on X is odd, and the number of ones received on

Y is odd, then F $=1.$

$$ If the number of ones received on X is even, and the number of ones received on

Y is even, then F $=1.$

$$ Else F $=0.$

$($a$)$ Draw a state diagram for a Moore 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$]$