In electronics, an adder is a device which will perform the addition, S, of two numbers. In computing the adder is part of the ALU, and some ALUs contain multiple adders. Although adders can be constructed for many numerical representations, such as BCD or excess-3, the most adders operate on binary numbers. Binary devices will be the focus of this article.
Binary adders are classified by two main criteria. First, the size of the numbers an adder can compute are limited by the number of bits of input and output. Generally, an N-bit adder will have two N-bit inputs and one N-bit output, as well as a one-bit output carry. The second classification criterion is whether the adder has a one-bit input carry. Those adders with the input carry are referred to as full adders and those without are termed half adders. Most half adders are one-bit.
There are many advantages to having an input carry on an adder. The obvious advantage is that you can chain several adders together to get an adder that supports larger numbers than the component adders. Connecting the output carry of one adder to the input carry of another adder creates what is known as a ripple adder.
Another advantage of the full adder is that if you are using two's complement to represent signed integers, you can easily create a subtractor by inverting one of the input numbers and setting the adder's input carry to one. (The input carry of the least-significant adder, if you're using a ripple adder.)