A full adder is a digital circuit that performs the arithmetic operation of addition on three binary digits, producing a sum and a carry output. Unlike a half adder, which adds only two binary digits and produces a sum and carry, a full adder considers an additional carry input from a previous less significant bit addition. The full adder's design includes three inputs: A, B, and Cin (carry-in), and two outputs: Sum (sum) and Cout (carry-out). The sum output Sum is derived by XOR-ing the three inputs, while the carry-out Cout is obtained by considering the majority function of the inputs. This means Cout is set when any two or more of the three inputs are high (logical 1). Full adders are fundamental components in the construction of arithmetic logic units (ALUs), binary adders, and other computational circuits in digital systems, enabling the handling of multi-bit binary addition by cascading multiple full adders.
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Ram et al. (2024) studied this question.
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