In electronics, an adder or summer is a digital circuit

Digital circuit

Digital electronics represent signals by discrete bands of analog levels, rather than by a continuous range. All levels within a band represent the same signal state...

 that performs addition

Addition

Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....

 of numbers.
In many computer

Computer

A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...

s and other kinds of processors, adders are used not only in the arithmetic logic unit

Arithmetic logic unit

In computing, an arithmetic logic unit is a digital circuit that performs arithmetic and logical operations.The ALU is a fundamental building block of the central processing unit of a computer, and even the simplest microprocessors contain one for purposes such as maintaining timers...

(s), but also in other parts of the processor, where they are used to calculate addresses, table indices, and similar.

Although adders can be constructed for many numerical representations, such as binary-coded decimal

Binary-coded decimal

In computing and electronic systems, binary-coded decimal is a digital encoding method for numbers using decimal notation, with each decimal digit represented by its own binary sequence. In BCD, a numeral is usually represented by four bits which, in general, represent the decimal range 0 through 9...

 or excess-3

Excess-3

Excess-3 binary-coded decimal ' or Stibitz code, also called biased representation or Excess-N, is a complementary BCD code and numeral system it is used on some older computers that uses a pre-specified number N as a biasing value. It is a way to represent values with a balanced number of positive...

, the most common adders operate on binary

Binary numeral system

The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

 numbers.
In cases where two's complement

Two's complement

The two's complement of a binary number is defined as the value obtained by subtracting the number from a large power of two...

 or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor.
Other signed number representations

Signed number representations

In computing, signed number representations are required to encode negative numbers in binary number systems.In mathematics, negative numbers in any base are represented by prefixing them with a − sign. However, in computer hardware, numbers are represented in binary only without extra...

 require a more complex adder.
A half adder adds two one-bit binary numbers A and B.