$3\mathrm{.}3*3.$Using a $3-$variable K$-$map, simplify the

$()$a$){?}^{**}F(x,y,z)=x^{\text{'}}{y}^{\text{'}}z+xy{z}^{\text{'}}+x^{\text{'}}yz+xy$ the following Boolean expression.

$($b$)**F(x,y,z)=x^{\text{'}}{y}^{\text{'}}z+xyz+x^{\text{'}}yz+xy$

$($e$)**F(x,y,z)=x^{\text{'}}yz+x{y}^{\text{'}}+yz$

$($d$)F(x,y,z)=x{z}^{\text{'}}+x^{\text{'}}z+x^{\text{'}}y+x$

$3\mathrm{.}4$ Using the $K-$map, simplify the following Boolean function.

$($a$)($:$(a{)}^{**}\}$

$($c$)**F(w,x,y,z)=(1,3,5,6,7,9,11)$

$($b$)F(w,x,y,z)=(4,6,9,11,12,14)$

$($e$)F(w,x,y,z)=(9,10,11,12,13,15)$

$($d$)**F(w,x,y,z)=(2,6,7,10,14,15)$

$($g$)F(w,x,y,z)=(0,1,2,4,6,8,9)$

$($f$)F(w,x,y,z)=(0,2,4,6,9,11,13,15)$

$($h$)F(w,x,y,z)=(0,3,6,7,8,11,14,15)$

$3\mathrm{.}5$ Using a $4-$variable K$-$map, simplify the following Boolean function.

$($a$)*F(w,x,y,z)=(0,2,3,4,6,8,9,12)$

$($b$)**F(w,x,y,z)=(0,1,2,3,5,813)$

$($c$)F(w,x,y,z)=(2,3,5,7,11,13)$

$($d$)F(w,x,y,z)=(1,2,3,6,7,8,9,12,13)$

$3\mathrm{.}6$ Using a $4-$variable K$-$map, simplify the following Boolean expression.

a$)(a{)}^{***}AB{C}^{\text{'}}{D}^{\text{'}}+A{B}^{\text{'}}C+B^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}+A{B}^{\text{'}}CD+B^{\text{'}}{C}^{\text{'}}D$

$w^{\text{'}}{x}^{\text{'}}{y}^{\text{'}}+w^{\text{'}}{x}^{\text{'}}yz+x^{\text{'}}{y}^{\text{'}}z+xyz+y^{\text{'}}{z}^{\text{'}}$

$($c$)A^{\text{'}}{B}^{\text{'}}CD+A^{\text{'}}BC+C^{\text{'}}D+$ABCD$+A{B}^{\text{'}}C$

$($d$)A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}+A^{\text{'}}BD+A^{\text{'}}B{C}^{\text{'}}{D}^{\text{'}}+B{C}^{\text{'}}D+$ABCD

$3\mathrm{.}7$ Using a $4-$variable K$-$map, simplify the following Boolean expression.

$($a$)w^{\text{'}}{x}^{\text{'}}z+x{y}^{\text{'}}+w^{\text{'}}x+wxy$

$($b$)A^{\text{'}}B{D}^{\text{'}}+BDC+AB{C}^{\text{'}}+BD+$ABC

e$)(e)$

$($d$)wxyz+w{x}^{\text{'}}+w{x}^{\text{'}}y+wxy+w^{\text{'}}y{z}^{\text{'}}$

$3\mathrm{.}8$ First display each of the following functions on the $K-$map, and then find a minimal term for the Boolean expression.

$($b$)**$:$AB{D}^{\text{'}}+B{C}^{\text{'}}D+CD$

$($a$)(a{)}^{***}{w}^{\text{'}}x+xz+wyz$

$($c$)x^{\text{'}}{y}^{\text{'}}{z}^{\text{'}}+xy+y^{\text{'}}z$

$($d$)AB+B^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}+BCD+A^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$

$3\mathrm{.}9$ Find all the main terms from the following Boolean function, and answer which one is the $($required main term.

$($a$)?45.6.7\mathrm{.}8,10,13,15$

b$)(b{)}^{**}F(A,B,C,D)=E(0,2,3,5,7,8,10,11,14,15)$

$($c$)F(A,B,C,D)=(2,3,4,5,6,7,9,11,12,13)$

$($d$)F(w,x,y,z)=(1,3,6,7,8,9,12,13,14,15)$

$($e$)F(A,B,C,D)=(0,1,2,5,7,8,9,10,13,15)$

$($f$)F(w,x,y,z)=(0,1,2,5,7,8,10,15)$