Adder (electronics)

An adder is a circuit designed to perform addition. It is composed of several logic gates. In computer processors, adders operate on binary numbers. If two's complement binary is used, then an adder can also be modified for subtraction.

A half-adder is a single bit adder that can take in two inputs (A and B) and produce a Sum and a Carry. The output is the sum of A+B, with Carry being the most significant digit. The Carry can be represented by the AND of A and B, while the Sum is the XOR of A and B.

A full-adder is a single bit adder that takes three inputs (A, B, and a Carry-in) and produces a Sum and a Carry-out. The Sum is represented by (A XOR B) XOR Cin, and the Carry-out is true if any two inputs are true.

Single-bit full adders can be chained together to form multiple-bit adders, if the Carry-out of the first adder is linked to the Carry-in of the second, and so forth. This is called a ripple-carry adder, and allows the linking of an infinite number of full-adders. However, the gate delay of a ripple-carry adder grows quickly, since each operation must wait on the previous operation to complete. Thus a 4-bit adder would consist of 4 single-bit additions working in succession.