The Half Adder is a simple logic circuit that is used to perform binary addition. It is one of the simplest forms of digital circuit and is made up of only two logic gates: an EXOR gate and an AND gate. The half adder takes two binary numbers, or signals, as inputs and outputs a single binary number, or signal, which represents the addition of the two original signals. The half adder can be represented using logic diagrams, which contain Boolean logic gates and wires, or using the schematic diagram format, which uses the circuit components themselves to show the circuit’s layout and structure.

The half adder is a logic gate that performs a simple Boolean logic operation: the binary addition of two Boolean inputs. It is the simplest possible digital circuit and was the first logic gate to be discovered. The half adder was invented independently by George Boole and Charles Babbage, who used it in the design of their early mechanical computers. Today, half adders have been superseded by more complex logic gates such as full adders and Boolean logic gates, but they are still used to demonstrate the principles of binary logic in the classroom.

This Half Adder circuit is obtained by using EX-OR gate and AND gate, and the output getting from the EX-OR gate is the sum of the two numbers, and Carry is obtained from AND gate. In the Half Adder circuit no forwarding of carrying addition because there is no such logic gate to process that is called as Half Adder Circuit. Logical Expression for half adder is : S=a⊕b ; C=a*b.

Logical Expression for EX-OR is AB’ + A’B 