Full adder

Full adder

A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full-adder adds three one-bit numbers, often written as ${\displaystyle A}$, ${\displaystyle B}$, and ${\displaystyle C_{in}}$; ${\displaystyle A}$ and ${\displaystyle B}$ are the operands, and ${\displaystyle C_{in}}$ is a bit carried in from the previous less-significant stage. The circuit produces a two-bit output. Output carry and sum are typically represented by the signals ${\displaystyle C_{out}}$ and ${\displaystyle S}$, where the sum equals ${\displaystyle 2C_{out}+S}$. The full adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. bit binary numbers.