A $4-$bit adder is to add two $4-$bit numbers A$3..$A$0$ and B$3..$B$0.$ For each bit position i$,$ of the adder, we define two Boolean functions named Generate $($Gi$)$ and Propagate $($Pi$).$ Gi $=$ Ai$.$Bi Pi $=$ Ai$+$Bi

Using the Generate and Propagate functions for each bit position, show how the carry out for each of the four bit positions may be expressed as a sum of products in two levels of gates, in other words, show how all the carry$-$outs from each bit position can be generated in parallel.