Problem $2$: $(16$ marks$)$ Gate circuits and Boolean Equations

marks$)$ Conver

$f=(AB)+(CD)$ to the required form. The inputs are: $A,B,C,$ and $D$

b$)$ NORs with inverters

$(4$ marks$)$ Implement the following Boolean function with a $4$ to $1$ mult

$F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}m(1,3,6,7,9,10,11,12,15)$

$(4$ marks$)$ Design a combinational circuit that compares two $4-$bit numbers to check if they are equal. The circuit output is equal to $1$ if the two numbers are equal and $0$ otherwise.