## What are the different Adder circuits you studied?

Adders are generally of five types:
The Ripple carry adder(RCA) consists of a building block named Half
blocks HAs and FAs are also the building blocks of all types of
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

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.

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.

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.