$($a$)$ Estimate the time required $($in units of gate delay$)$ to perform $64-$bit addition using cascaded $4-$bit

carry$-$lookahead units.

$($b$)$ ABCD $($Binary$-$Coded Decimal$)$ number is a $4-$bit representation with $0000B($i$.$e$.\text{'}0\text{'})$ through to

$1001B(\text{'}9\text{'})$ considered to be the 'valid' values. The key to adding two $BCD$ numbers A and $B$ to

yield another BCD number S $($plus a 'carry', if sum exceeds TEN$-$decimal$)$ is to first simply add

A and $B$ as binary numbers. If the said addition generates a carry $OR$ the binary$-$sum is an invalid

BCD number $($i$.$e$.,$ greater than $1001$B$),$ then add SIX $($i$.$e$.0110$B$)$ again to the sum to get S and

consider the carry of the second addition as the $BCD-$Carry. Otherwise, $S$ is same as the binary

sum and there's no carry. Design a circuit for $1-$digit BCD adder. Show that your adder generates

$0101B($i$.$e$.\text{'}5\text{'})$ and a carry when you add $1000B($i$.$e$.\text{'}8\text{'})$ with i$.$e$.\text{'}7\text{'}).$

$($c$)$ Suppose four cascaded $4-$bit Carry$-$lookahead adders are given the $16-$bit input numbers $4321H$

and DCBAH. Find the 'propagate' and 'generate' values coming out of each of the four

Carry$-$lookahead adders. There is NO input carry.

$3+(6+1)+4$