Q$4(10$ points$)$ Answer the following questions:

a$)(1$ point$)$ How many gates exist in a full adder and what are their types?

b$)(1$ point$)$ How many full adders exist in a $16-$bit ripple carry adder?

c$)(1$ point$)$ To detect overflow in a $16-$bit adder requires $......$

d$)(4$ points$)$ Draw cell i of a magnitude comparator showing all the gates.

e$)(3$ points$)$ Using design by contraction, redraw a simplified cell i of a magnitude comparator if the input Bi is guaranteed to be always constant $0.$