A full adder circuit has:

Concept

A full adder is the combinational circuit used to add binary numbers of more than one bit. Unlike a half adder, which only combines two bits, a full adder is built to accept three single-bit inputs -- the two bits being added at that position, plus a carry bit coming in from the addition of the previous (lower-order) position -- and it produces two output bits: the sum bit for that position and a carry bit to pass on to the next (higher-order) position.

Application

Labelling the three inputs A, B, and Cin (carry-in), and the two outputs S (sum) and Cout (carry-out): S = A XOR B XOR Cin, and Cout = AB + B.Cin + A.Cin. Counting the ports directly from this definition gives exactly 3 inputs (A, B, Cin) and 2 outputs (S, Cout).

Contrast

• 1 input, 2 outputs -- no adder stage can form a sum from a single input bit; this count does not match any binary-addition circuit.

• 2 inputs, 1 output -- this is the port count of a plain two-input logic gate, which has no carry-in port and so cannot chain with a neighbouring addition stage.

• 4 inputs, 1 output -- collapsing to one output line loses the separate carry-out signal that every addition stage must pass forward.

Cross-check

Chaining several full adders by feeding each stage's Cout into the next stage's Cin builds a ripple-carry adder for multi-bit numbers. That chaining is only possible because each stage exposes a dedicated carry-in port alongside the two operand bits -- confirming that 3 inputs and 2 outputs is the structurally necessary port count, not an incidental one.