QUESTION $4[25]$

a$)$ Consider the expression, $(\frac{?}{\text{b}\text{a}\text{r}}\frac{A}{b}ar(B)+\frac{A}{b}ar(B))(CD+\frac{C}{b}ar(D))$ Convert it into canonical SOP form and minimize it using the Karnaugh map method

b$)$ Derive the Canonical SOP expression for $F(A,B,C)=(3,5,6,7).$ Simplify $F$ using Boolean axioms$/$theorems$.$ Draw the logic circuit using AND$-$OR gates. Also, draw the NAND$-$only logic circuit.

$[10]$

c$)$ Draw a truth table for a two input $($ A and $B)$ logic system whose output is $B$ only if $A$ is zero; otherwise F inverts B$.$ State what type of logic gate would be needed to implement such a system $[5]$