Question $2$:

Using Binary full adders, which adding $3$ bits $($two inputs and one carry in bit$)$ and output a result bit and a carry out bit, build a system that adds $6$ unsigned binary numbers $4$ bits wide each.

The numbers are:

$A=[a3,a2,a1,a0],B=[b3,b2,b1,b0],C=[c3,c2,c1,c0],D=[d3,d2,d1,d0],$

$E=[e3,e2,e1,e0],F=[f3,f2,fl,f0].$

The system calculates $Y=A+B+C+D+E+F.$

$2\mathrm{.}1)$ How many bits are required for Y$?$ Explain your answer.

In the solution you need to draw all the FA$-$s you will use and their connections. You have space to do that drawing in the next page.

Assume that the delay from any input to any output of the FA is T seconds and that the FA cost is $1.$ We want the fastest possible design $(1^{st}$ priority$)$ and the less expensive one $(2^{nd}$ priority$)$

$2\mathrm{.}2)$ Draw your deign in the next page. The grading will be according to correctness, delay and cost.

$2\mathrm{.}3$ What is the cost of your design?

$2\mathrm{.}4$ What is the delay of your design? Explain your reply. For the explanation, you should mark down the delay from the starting of the calculation till the output of the FA near all FAs in your drawing.