**
RIPPLE CARRY ADDER
**

The
fundamental unit of a ** Ripple Carry Adder (RCA)** given in Fig. 3.1
is a full adder which computes a sum bit and a carry bit.

Sum bit can be represented as

*S _{i = }(a_{i}
XOR b_{i}) XOR c_{i
}*(3.7)

Carry bit can be represented as

*Carry = a_{i}b_{i
}+ b_{i}c_{i}+ c_{i}a_{i
}*(3.8)

Figure 3.1

An
*n*-bit Ripple Carry Adder

The architecture signifies that it adds two operand bits to produce a sum bit and a carry bit, since in the worst case the carry can propagate from the least significant bit position to most significant bit position.

In
this case one single bit full adder is adding three bits viz.( ** a_{0},
b_{0}, c_{0}**), where