fulladders

Full adders are a fundamental building block in digital electronics used to perform binary addition. A full adder is a combinational circuit that adds three binary inputs: A, B, and Cin (carry-in). It produces two outputs: Sum and Cout (carry-out).

The Sum output is A xor B xor Cin; the Cout output is true if at least two of the inputs are true, equivalently (A and B) or (A and Cin) or (B and Cin). These relationships define the logical operation of a full adder and underlie its implementation in various technologies.

A common implementation uses two half adders. The first half adder adds A and B producing S1 and C1. The second half adder adds S1 and Cin producing Sum and C2. The final carry-out is Cout = C1 or C2. This structure highlights how the full adder combines the results of two simpler additions to yield both a sum bit and a carry bit.

In multi-bit addition, full adders are chained so that the Cin of a stage is the Cout of the previous stage, forming a ripple-carry adder. The overall delay is dominated by carry propagation through the chain, making performance sensitive to operand width. To address this, carry-lookahead and other optimized adder architectures compute carries in parallel to reduce delay.

Full adders are implemented in various technologies and form part of standard cell libraries in digital design. They are used in arithmetic units, processors, and any system that requires binary addition, from simple counters to complex computational arrays.