Full Adder

A full adder is a fundamental combinational circuit used in computer science and electronics for performing binary addition.

A full adder adds three binary inputs - two operands (A and B) and a carry-in (C-in) from a previous addition - and produces two outputs: a sum and a carry-out (C-out)

We can conclude the outputs using Boolean logic:

$$\mathrm{Sum}=\mathrm{A}\oplus \mathrm{B}\oplus {\mathrm{C}}_{\mathrm{in}},{\mathrm{C}}_{\mathrm{out}}=(\mathrm{A}\wedge \mathrm{B})\vee (\mathrm{B}\wedge {\mathrm{C}}_{\mathrm{in}})\vee (\mathrm{A}\wedge {\mathrm{C}}_{\mathrm{in}})$$

See also Ripple-carry Adder