Adder (electronics)

An adder is a digital circuit designed to perform integer addition in the Arithmetic Logic Unit on board a computer. These circuits are fundamental to the operation of a computer and have an analog in traditional pencil-and-paper addition.

Integers can be represented by the sum of a series from 0 to infinity.

$\sum _{k=0}^{\infty }nx^{k}$

• Where n is an integer from zero to (base - 1)
• Where x is an integer equal to the base value.

An adder performs a binary operation (two operands) where the n of one power in integer A is added to the n of the same power in integer B. This produces two outputs, a sum, and a carry. The carry is always equal to (sum - (base - 1)). The carry is then added to the sum of the next power's sum, and so on. This represents what is known as a Full Adder. Each addition operation performed is known as a Half Adder. Chain a number of half adders together, and a full adder emerges.

The Half Adder

Computers operate in base-2, or binary. To the computer, a presence of electrons represents a 1 and a lack of electrons represents a 0. A computer's ALU (Arithmetic Logic Unit) consists of a variety of circuits that perform different operations, the Adders are composed mostly of half adders.

Lines A and B represent the inputs to the adder, and lines S and C represent sum and carry respectively.