Convert the function $G_1(a,b,c)=(a^{\text{'}}+b+c)+(a{c}^{\text{'}})$ to a function with only two$-$input

NAND gates. Draw the gate level circuit of the converted function. $(12$ Points$)$

Convert the function $G_2(a,b,c)=(a^{\text{'}}{b}^{\text{'}}c).(a^{\text{'}}+b)$ to a function with only two$-$input

NOR gates. Draw the gate level circuit of the converted function. $(12$ Points$)$

Evaluate each of the function $F_1(a,b,c)=a{b}^{\text{'}}+b{c}^{\text{'}}+a^{\text{'}}bc$ and $F_2(a,b,c)=a^{\text{'}}b+$

a'b'c $+$ ac$\text{'}$ when: $(8$ Points$)$

a$)a=1,b=0,$ and $c=1$

b$)a=0,b=1,$ and $c=1$

Simplify the function $F_3(a,b,c,d)=$prodM$(0,1,3,11,15)$ using K$-$Map. $(8$ Points$)$

Simplify the function $F_4(a,b,c,d)=a^{\text{'}}{b}^{\text{'}}{c}^{\text{'}}{d}^{\text{'}}+a^{\text{'}}{b}^{\text{'}}{c}^{\text{'}}d+a^{\text{'}}b{c}^{\text{'}}d+a{b}^{\text{'}}{c}^{\text{'}}{d}^{\text{'}}+a{b}^{\text{'}}{c}^{\text{'}}d+$

ab'cd' $+$ ab'cd $+$ abc'd using Boolean laws, axioms, and identities. Clearly state the

laws, axioms, and identities used. $(20$ Points$)$

Is function $F_1$ described in question $7$ equal to $F_5(a,b,c)={\displaystyle \underset{?}{\overset{?}{}}}m(2,3,4,5,6)?$ Use

Boolean algebra laws, axioms, and identities to show if the functions are equal.

Clearly state the laws, axioms, and identities used. $(8$ Points$)$