Table 1.

Logic operations that can be performed with a Full Adder by fixing one or more of the inputs. In this case A, B and C_in are the three inputs while S and C_out are the output (sum and output carry,  respectively).

Fixed Input	S	Cout
A = 0	B ⊕ Cin	B $·$ Cin
A = 1	$\overline{\mathrm{B}\oplus {\text{C}}_{\mathrm{in}}}$	B + Cin
A = 0 & B = 1	$\overline{{\text{C}}_{\mathrm{in}}}$	Cin
A = 1 & B = 0	$\overline{{\text{C}}_{\mathrm{in}}}$	Cin