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# Difference between Half Adder and Full Adder

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.

Read through this article to find out the basics of half adders and full adders and how they function.

## 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 −

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

## Difference between Half Adder and Full Adder

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

Parameter | Half Adder | Full Adder |
---|---|---|

Definition | Half 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 components | The 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. |

Addition of carry bit | The half adder does not add the carry generated in the previous addition to the next addition. | In case of full adder, the carry produced in the previous addition is added in the next addition. |

Number of input and output terminals | Half 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 Expressions | For 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 −$$S\:=\:A\oplus{B}\oplus{C_{in}}$$ $$C\:=\:AB\:+\:BC_{in}\:+\:AC_{in}$$ |

Substitution | A half adder circuit cannot be used as a full adder circuit. | A full adder circuit can substitute a half adder circuit. |

Design | The circuit of a half adder is simple and easy to implement. | The circuit of a full adder has relatively complex design. |

Alternate name | For half adder, there is no alternate name. | Full adder is also called ripple-carry adder. |

Applications | Half adder circuits are used in computers, calculators, and various digital measuring instruments. | Full adders are mainly used for multiple bit addition, in digital processing devices, etc. |

## Conclusion

From the above discussion, it is clear that there are several differences between a half-adder circuit and a full-adder circuit. However, both **half adder** and **full adder** circuits are the basic building blocks of many digital circuits that are used to perform arithmetic operations such as calculators, computers, digital measuring devices, digital processors, etc.

One of the main advantage of using half adders and full adders in the digital circuits is that they are designed by using logic gates that process the input data very fast. The typical processing speed of the logic gates is of the order of μs (microseconds). Hence, for performing arithmetic operations at high speed, we use half adder and full adder circuits.

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