Arithmetic Circuits

The basic process of adding two binary digits can be accomplished with a half-adder circuit.
In a half-adder, the sum output is the Exclusive-OR of the two input bits. The carry output is the logical AND of the two input bits.

If a third input is required (carry in from previous-significant digit) then a full-adder circuit must be used.
A full-adder is really two half-adders with the carry outputs ORed together.

The full-adder and the half-adder can be represented with a block symbol. The half-adder has two inputs and the full-adder has three inputs.
In order to add two binary words with several bits, an adder circuit is required for each bit of the date word. to make the circuit complete, the carry input for each full-adder is connected to the carry output of the previous least-significant bit.