In electronics, an adder or summer is a digital circuit that performs addition of numbers. In modern computers adders reside in the arithmetic logic unit (ALU) where other operations are performed. Although adders can be constructed for many numerical representations, such as Binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement or one's complement is being used to represent negative numbers, it is trivial to modify an adder into an adder-subtractor. Other signed number representations require a more complex adder.
A full adder can be implemented in many different ways such as with a custom transistor-level circuit or composed of other gates. One example implementation is with S = A \oplus B \oplus C_{in} and C_{out} = (A \cdot B) + (C_{in} \cdot (A \oplus B)).
Example full adder circuit diagram
Inputs: {A, B, Cin} → Outputs: {S, Cout}
File:Full Adder.JPG
Example full adder circuit diagram using only NAND and XOR gates
Inputs: {A, B, Cin} → Outputs: {S, Cout}
In this implementation, the final OR gate before the carry-out output may be replaced by an XOR gate without altering the resulting logic. Using only two types of gates is convenient if the circuit is being implemented using simple IC chips which contain only one gate type per chip.
A half adder is a logical circuit that performs an addition operation on two one-bit binary numbers often written as A and B. The half adder output is a sum of the two inputs usually represented with the signals Cout and S where sum = 2 \times C_{out} + S. Following is the logic table for a half adder:
