K$-$Map

Question $1.$ Optimize the following Boolean functions F together with the don't care conditions $d.$ Find all prime

implicants and essential prime implicants, and apply the selection rule.

$[10$ marks$]$

$($a$)F(A,B,C)=m(3,5,6),d(A,B,C)=m(0,7)$

$($b$)F(W,x,Y,Z)=m(0,2,4,5,8,14,15),d(W,x,Y,Z)=m(7,10,13)$

Question $2.$ Optimize the following Boolean functions $F$ together with the don't care conditions $d$ in

$($a$)$ sum$-$ of$-$ products and $($b$)$ product$-$ of$-$ sums form:

$[10$ marks$]$

$F(W,x,Y,Z)=m(5,6,11,12),d(W,x,Y,Z)=m(0,1,2,9,10,14,15)$