**Half Adder and Full Adder Circuit:**

Adders are divided into two categories namely, half adder and full adder circuit.

**Half Adder Circuit:**

The Half Adder Circuit operation needs two binary inputs : augend and addend bits; and two binary outputs : sum and carry. The half adder truth table shown in 3.6 gives the relation between input and output variables for Half Adder Circuit operation.

**Half Adder Truth Table:**

**K-map simplification for carry and sum:**

**Half Adder Logic Diagram:**

**Full Adder Circuit:**

We have seen that a full adder is a combinational circuit that forms the arithmetic sum of three input bits. It consists of three inputs and two outputs. Two of the input variables, denoted by A and B, represent the two significant bits to be added. The third input C_{in}, represents carry from the previous lower significant position.

**Full Adder Truth Table:**

The Full Adder Truth Table is shown in Table 3.7.

**K-map simplification for carry and sum:**

**Full Adder Logic Diagram:**

The **Boolean Expression** for sum can be further simplified as follows :

With this simplified Boolean function circuit for full-adder can be implemented as shown in the Fig. 3.17.

A full-adder can also be implemented with two half-adders and one OR gate, as shown in the Fig. 3.18. The sum output from the second half-adder is the exclusive-OR of C_{in} and the output of the first half-adder, giving

and the carry output is