Apply all design steps to determine a circuit with output $f$ and inputs $x1,x0,y1,$ and $y0.$ Let $x=x1x0$ and $Y=y1y0$ represent two $2-$digit binary numbers. The output $f$ should be $1$ if the numbers represented by $x$ and $Y$ are equal. Otherwise, $f$ should be $0.$

Write Verilog code to implement the function $f(x1,x2,x3)={\displaystyle \underset{?}{\overset{?}{}}}m(0,1,3,4,5,6)$ using the continuous assignment.

A circuit with two outputs is defined by the logic functions

$f=x_1{x}_2^{\text{'}}{x}_3^{\text{'}}+x_2^{\text{'}}{x}_4^{\text{'}}+x_2^{\text{'}}{x}_3^{\text{'}}{x}_4+x_1{x}_2{x}_3{x}_4$

$g=x_1{x}_3^{\text{'}}{x}_4+x_1{x}_2{x}_4+x_1^{\text{'}}{x}_3{x}_4+x_2^{\text{'}}{x}_3{x}_4^{\text{'}}$

Derive a minimum$-$cost implementation of this circuit. What is the cost of your circuit?

$8.$ Convert the decimal numbers $73,-95,$ and $-1630$ into signed $12-$bit numbers in the following representations:

$($a$)$ Sign and magnitude

$($b$)1\text{'}$s complement

$($c$)2\text{'}$s complement