An adder circuit is one of the important digital circuits used in computers, calculators, digital processing units, etc. There are two types adder circuits named half-adder and full-adder. Both the half adder and the full adder circuits are used to perform addition and also widely used for performing various arithmetic functions in the digital circuits.

## What is a Half Adder?

A combinational logic circuit which is designed to add two binary digits is known as half adder. The half adder provides the output along with a carry value (if any). The half adder circuit is designed by connecting an EX-OR gate and one AND gate. It has two input terminals and two output terminals for sum and carry.

In case of half adder, the output of the EX-OR gate is the sum of two bits while the output of the AND gate is the carry. However, the carry obtained is one addition will not be forwarded in the next addition, so it is called half adder.

The output equations of the half adder are −

$$Sum,S\:=\:A\oplus{B}$$ $$Carry, C\:=\:A.B$$

## What is a Full Adder?

A combinational circuit which is designed to add three binary digits and produce two outputs is known as full adder. The full adder circuit adds three binary digits, where two are the inputs and one is the carry forwarded from the previous addition.

The circuit of the full adder consists of two EX-OR gates, two AND gates and one OR gate, which are connected together as shown in the full adder circuit.

The output equations of the full adder are −

$$Sum,S\:=\:A\oplus{B}\oplus{C_{in}}$$ $$Carry, C\:=\:AB\:+\:BC_{in}\:+\:AC_{in}$$

The following table shows the main differences between half adder and full adder circuit.

DefinitionHalf adder is a combinational digital circuit which can add two 1-bit binary numbers.Full adder is a combinational digital circuit which can add three single-bit binary number, where two are the inputs and the third is the carry forwarded from the previous output.
Circuit componentsThe circuit of the half adder consists of one EX-OR gate and one AND gate.The circuit of full adder consists of two EX-OR gates, two AND gates and one OR gate.
Number of input and output terminalsHalf adder circuit has two input terminals viz. A and B and two output terminals, viz. Sum and Carry.Full adder circuit has three input terminals viz. A, B and Cin and two output terminals, i.e., Sum and Carry.
Logical ExpressionsFor half adder circuit, the logical expressions of the outputs are −$$S\:=\:A\oplus{B}$$ $$C\:=\:A.B$$For full adder circuit, the logical expressions of the outputs are −$$S\:=\:A\oplus{B}\oplus{C_{in}}$$ $$C\:=\:AB\:+\:BC_{in}\:+\:AC_{in}$$