Problem $7.(20$ points$)$:

A new microprocessor company PISTOLPETE wants to build a new adder that computes carries differently

than a ripple carry adder. In class, we discussed a ripple carry adder that computes the sum by sending the

$c_{\text{o}\text{u}\text{t}}$ of the full adder to the $c_{in}$ of the next full adder. $($Hint: the carry out equation of the original full adder

is shown in Equation $1)$

$c_{\text{o}\text{u}\text{t}}=c_{k+1}=a_k*b_k+a_k*c_k+b_k*c_k$

This new adder computes the carries by computing outputs differently than the original full adder. By using

this new organization, the $c_{\text{o}\text{u}\text{t}}$ of the full adder can be removed from the original full adder and avoid the

messy carry chain. The whole idea for this new company is to make the adder faster!

However, your new full adder must also compute $g_k=a_k*b_k$ and $p_k=a_k+b_k$ as outputs in addition to

the sum. Therefore, the new full adder has three inputs $a_k,b_k,$ and $c_k($or $c_{in})$ and three outputs ${\displaystyle \underset{k}{\overset{?}{}}},p_k,$

and $g_k.$ The subscript $k$ represents the specific bit of the block $($e$.$g$.,g_1$ represents the output of bit $1).$

Design a $3-$bit adder that uses this new system. Your new adder should have $4$ blocks: three new full

adders and a single carry generation block to compute the $c_{\text{o}\text{u}\text{t}}$ from these three new blocks that is

used to compute the sum for each weight. That is$,$ the three new full adders should output $p_k$ and $g_k$ to a

new block that computes $c_k($i$.$e$.,c_1$ and $c_2).$ The carries are sent to your new full adders to compute the sum.

Can you draw the complete schematic that represents this new $3-$bit adder? Also, show an example of all

outputs on this schematic using the example ${100}_2+{011}_2$ assuming $c_{in}=c_0=0.$ That is$,$ show all the

resulting outputs of each of your $4$ blocks. Extra Credit: is this new adder faster or slower than the original

ripple carry adder?