Consider a Boolean function $F$ given below.

$F(p,q,r)=(p+q+r)*(p+q+r^{\text{'}})*(p+q^{\text{'}}+r)*(p^{\text{'}}+q^{\text{'}}+r)$

$($a$)$ Use Boolean algebraic manipulation to find the minimum product$-$of$-$

sum expression of function F$.$ Implement the function using the

minimum number of gates.

$(9$ marks$)$

Question No$.5$ continues on Page $5$

Page $4$ of $5,04-$BS$-8,$ May $2017$

$($b$)$ Implement the function $F$ by employing the minimum number of AND

gates and only one OR gate.

$(10$ marks$)$

$($c$)$ Implement the minimized form of $F$ obtained in part $($a$)$ by using only

$2-$input NAND gates.

$(6$ marks$)$