iv$)$ Simplify the below expression using Boolean Algebra:

$F\frac{?}{b}=ar((A+(\frac{?}{\text{b}\text{a}\text{r}}(A))(\frac{?}{\text{b}\text{a}\text{r}}(B))))(A+B\frac{+}{b}ar(C))\frac{+}{b}ar((A+(\frac{?}{\text{b}\text{a}\text{r}}(B))+A(\frac{?}{\text{b}\text{a}\text{r}}(B))))(\frac{?}{\text{b}\text{a}\text{r}}\frac{A}{b}ar(B)C)$

v$)$ Write the VHDL code for the following circuit:If the function $f(w,x,y,z)$ is $1$ if the decimal representation of the $4$ bit binary number wxyz is a non$-$

zero even number. Otherwise, the output is equal to $0.$

i$)$ Draw the corresponding $K-$map for $F(w,x,yz).$

ii$)$ Use the K$-$map from part $($i$)$ to derive the minimum$-$cost POS expression

for $F.$

iii$)$ Draw the circuit form the POS expression from part $($ii$).$ Label all inputs and outputs.