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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.

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

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

${\displaystyle 123=(3)(10)^{0}+(2)(10)^{1}+(1)(10)^{2}+(0)(10)^{3}+...+(0)(10)^{\infty }}$

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.