Question $1$: Consider a $32-$bit adder.

$($i$)$ Identify the knowns and unknowns. Explain the complexity of the problem

if a $2-$level implementation is to be followed.

$($ii$)$ Describe the strategy you follow to design such a $32-$bit adder and

formulate it accordingly.

Question $2$: Simplify the following expressions as much as possible:

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

b$)x^{\text{'}}*(y^{\text{'}}+z^{\text{'}})(x+y+z^{\text{'}})$

c$)A^{\text{'}}*B*(D^{\text{'}}+C^{\text{'}}*D)+B(A+A^{\text{'}}*C*D)$

d$)x*y+y*z+x^{\text{'}}*z$