$3\mathrm{.}1[10$ marks$]$ Determine the Midterm and Maxterm Expansions from given Boolean Algebra and find out the truth table of it$.$

$F1=x^{\text{'}}{Y}^{\text{'}}Z+x^{\text{'}}{Y}^{\text{'}}{Z}^{\text{'}}+xYZ$

$=m1+m4+m7={\displaystyle \underset{?}{\overset{?}{}}}m(1,4,7)$

$F2=x^{\text{'}}YZ+x{Y}^{\text{'}}Z+xY{Z}^{\text{'}}+xYZ$

$=m3+m5+m6+m7={\displaystyle \underset{?}{\overset{?}{}}}m(3,5,6,7)$

$3\mathrm{.}2[10$ marks$]$ Design of Arithmetic Circuits with truth table and Boolean algebra of $1$ bit$-$ Half Subtractor.

Question $4(20$ marks$)$:

$4\mathrm{.}1[10$ marks$]$ Simplify the given function using $3$ variables K$-$map.

$F(A,B,C)\frac{?}{b}=ar\frac{A}{b}ar\frac{B}{b}ar(C)\frac{+}{b}ar(A)\frac{B}{b}ar(C)\frac{+}{b}ar(A)\frac{B}{b}ar(C)$

$4\mathrm{.}2[10$ marks$]$ simplify the Boolean expression by using K$-$Map

$F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}m(0,2,4,6,12,14,15,8,10)$