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Full-adder A full adder is a combinational circuit that forms the arithmetic sum of three bits. It consists of three inputs and two outputs. Two of the inputs variables, denoted by x and y, represent the two significant bits to be added. The third input, z, represents the carry from the previous lower significant position. Two outputs are necessary because the arithmetic sum of three binary digits ranges in value from 0 to 3, and binary 2 or 3 needs two digits. The two outputs are designated by the symbols S for sum and C for carry. The binary variable S gives the value of the least significant bit of the sum. The binary variable C gives the output carry. The truth table of the full adder is listed in table 2. The eight row under the input variables designate all possible combinations of the three variables. The output variables are determined from the arithmetic sum of the input bits. When all input bits are 0, the output is 0. The S output is equal to 1 when only one input is equal to 1 or when all three inputs are equal to 1. The C output has a carry of 1 if two or three inputs are equal to 1. A input and output bits of the combinational circuit have different interpretations at various stages of the problem. Physically, the binary signals of the inputs are considered binary digits to be added arithmetically to form a two-digit sum at output. On the other hand, the binary values are considered as variables of Boolean functions when expressed in the truth table or when the circuit is implemented with logic gates.