Question $2$: $(2$ marks$)$

Simplify the following equation and design its corresponding circuit based on:

$F=\frac{B}{b}ar\frac{C}{b}ar(D)+A\frac{B}{b}ar(D)\frac{+}{b}ar(A)B\frac{C}{b}ar(D)$

a$)2-$inputs NOR gates

b$)2-$inputs NAND gates

a$)$ Deduce the simplified logic functions F$,$ G$,$ H from the following Karnaugh tables as functions of the inputs $(x,y,z).$

b$)$ Design these functions by a single circuit.

$\backslash$table$[[,$Fonction F$,10,$fonction G$],[,00,01,11,,00,01,11,10],[$XY$,],[$Z$],[0,1,1,1,0,0,0,1,0,1],[1,0,1,0,1,1,1,1,1,0],[,00,01,11,10,,,,,],[$XY$],[0,0,1,1,1,,,,,],[1,0,1,0,1,,,,,]]$