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 A, B, and C_in; A and B are the operands, and C_in is a bit carried in (in theory from a past addition). The circuit produces a two-bit output sum typically represented by the signals C_out and S, where . The one-bit full adder's truth table is:

Inputs			Outputs
A	B	Cin	Cout	S
0	0	0	0	0
1	0	0	0	1
0	1	0	0	1
1	1	0	1	0
0	0	1	0	1
1	0	1	1	0
0	1	1	1	0
1	1	1	1	1

A full adder can be implemented in many different ways such as with a custom transistor-level circuit or composed of other gates. One example implementation is with and .

In this implementation, the final OR gate before the carry-out output may be replaced by an XOR gate_out can be implemented as .^{[citation needed]} without altering the resulting logic. Using only two types of gates is convenient if the circuit is being implemented using simple IC chips which contain only one gate type per chip. In this light, C

A full adder can be constructed from two half adders by connecting A and B to the input of one half adder, connecting the sum from that to an input to the second adder, connecting C_i to the other input and OR the two carry outputs. Equivalently, S could be made the three-bit XOR of A, B, and C_i, and C_o could be made the three-bit majority function of A, B, and C_i.