$*$URGENT$*$answer the following$($DIGITAL SYSTEMS$)$:

a$)$Desing a circuit that multiplies two $2-$bit $1$s complement numbers $($A$=$a$1$a$0$and B$=$b$1$b$0)$to produce a $4-$bit $1$s complement output $($F$=$F$3$F$2$F$1$F$0).$

$[$Note if the result of the multiplication is $0$then use the POSITIVE zero value $+0($i$.$e F$=0000),$ example: if you have a$0$a$1=-0$ and b$0$b$1=+1$ then $-0*+1=+0$ i$.$e$.$ F$=0000]$

b$)$Design the previous circuit using $4$x$1$multiplexers$.$

Important remarks:

For part a$)$include the correct truth table, do not use ChatGPT it will give you wrong values. Provide the simplified boolean expressions for each Fi$($F$3,$F$2,$F$1,$F$0),$and draw the circuit for each Fi$($F$3,$F$2,$F$1,$F$0).$

For part b$),$please DRAW the implementation of the circuit using $4$x$1$multiplexers$.$ Do not only explain how to do it$,$just provide a sketch$/$drawing of how to implement part a$\text{'}$s question using $4$x$1$multiplexers$.$ You can do this on paper or any other way but provide a clear drawing that shows the LABELED inputs and LABELED selector lines for the multiplexers.