Hardware Design Question:

Answer #1
Adders are generally of five types:
1) Ripple Carry Adder:
The Ripple carry adder(RCA) consists of a building block named Half
Adder(HA) which is cascaded to form a Full Adder(FA). These building
blocks HAs and FAs are also the building blocks of all types of
adders.The n full adders are cascaded to form n bit RCA.
The full adder has three input pins(input Ai,input Bi,carryin Ci) and
two output pins(Sum and Ci+1).Its equations are:
Sum=Ai^Bi^Ci
Ci+1=Ai.Bi+Bi.Ci+Ai.Ci

2)Carry Lookahead Adder:
The Carry Lookahead Adder(CLA) reduces the delay as that in RCA. Let
Gi=Ai.Bi, and Pi=Ai^Bi, then Ci+1=Gi+Pi.Ci.
The expressions for Sum and Ci+1 is then defined completely in terms of
input pins rather wait for input carry to appear.

3)Carry Select Adder:
The carry select adder uses duplicate modules for each combination of
input carry(i.e. 1 and 0).The multiplexers then select the appropriate
sum and carry output according to the carry output of the preceding
stages.

Answer #2
4)Carry Skip Adder:
The carry skip adder are as fast as carry lookahead adders which are
the fastest adders but its speed decreases to about 20-30% if input
operands are 64-bit or more. In these adders we divide the input bit
stream into various blocks and make use of two observations:
-if each element of the two bit streams are unequal,i.e. Ai!=Bi than
the carry input of the block is equal to the carry input.
-if each element of the two bit streams are equal,i.e. Ai=Bi than the
carry input of the block is opposite of the carry input.

5)Carry Save Adder:
The carry save adder reduces the addition of three elements into
addition of two elements,i.e. if you want sum of nine numbers it
reduces it into sum of six numbers. In first step the sum of three
numbers is calculated without bothering for the carry.During the second
step only carry is calculated which is then added to the generated sum
to give the required sum.