Given the following Boolean function: $F=A^{\text{'}}C+A^{\text{'}}B+A{B}^{\text{'}}C+BC,$

$($a$)$ express it in sum of minterms;

$($b$)$ find the minimal boolean expression using K$-$Map; and

$($c$)$ represent the minimized function using logic gates.

Simplify the Boolean function: $F(w,x,y,z)=(0,1,2,4,5,6,8,9,12,13,14)$ using K$-$

Map.

Design a combinational circuit with three inputs, $x,y,$ and $z,$ and three outputs, $A,B,$

and $C.$ When the binary input is $0,1,2,$ or $3,$ the binary output is one greater than the

input. When the binary input is $4,5,6,$ or $7,$ the binary output is one less than the

input.