An adder is used to add numbers in the digital logic circuit. It uses OR operation. Adder is also used to compute addresses and many more activities. They can be formulated for numerous numerical representations and are divided into Half Adder and Full Adder.

The other combinational circuits include an encoder, decoder, multiplexer, and many more.

## Key Takeaways

- A half adder is a digital circuit that only adds two bits, while a full adder can add three bits, including carry.
- The carry output of a half adder cannot be used as an input to the next addition stage, unlike a full adder.
- Full adders are used in complex digital circuits involving multiple addition stages. In contrast, half-adders are useful in simple circuits where only two bits must be added.

## Half Adder vs Full Adder

The difference between Half Adder and Full Adder is that two one-bit digits addition is done in Half Adder whereas three one-bit digits addition is carried in Full Adder. In Half Adder, the previous addition carry cannot be included in the next step. The machinery of both Half Adder and Full Adder is different. They both possess their features. Carryout Multiplication is carried out to execute using Full Adders. Ripple Adders also use Full Adder as an element in its architecture.

Half Adder is a logic circuit that adds two one-bit digits. Augend and Addend are the terms used for the input bits. The result consists of the sum and the carry. XOR is applied to both inputs to carry out the addition. Both inputs do AND operation to produce a carry.

It is used in calculators, computers, and other digital measuring devices.

Full Adder is a logic circuit that is used for the addition of three one-bit digits. The two inputs are referred to as operands, and the third bit is known as the bit carried in. It is a bit difficult to implement as compared to a half-adder. It has three inputs and two outputs.

Multiplexers and adders can be implemented using Full Adders.

## Comparison Table

Parameters Of Comparison | Half Adder | Full Adder |
---|---|---|

Definition | A combinational circuit is used for the addition of two one-bit digits. | A combinational circuit is used for the addition of three one-bit digits. |

Input Bits | A, B | A, B, C-in |

Carry Bit | Not added in the next step | Added to the next step |

Sum Expression | XOR of A and B | An XOR B XOR C(in) |

Carry Expression | A*B | (A*B) + (C-in*(A XOR B)) |

Logic Gates | AND XOR gates | 2 XOR, 2 OR, 2 AND gates |

Usage | Computers, Calculators, Digital Measuring Devices | Digital Processors, Multiple Bit Addition |

## What is Half Adder?

It is a type of combinational circuit. It consists of two input bits and outputs, the sum and carries. The two inputs are attributed to augend and Addend. The sum is the standard production moved to carry out. It is useful when in binary digit addition.

The Boolean equations for sum and carry operations are A XOR B = A.B + A.B’ and A AND B = A*B, respectively.

High-speed CMOS digital logic integrated circuits are utilized to implement the half adder. 74HCxx series are used in the implementation. The sum operation is practised using the XOR operation, and the carry process is implemented using AND gate.

If the input to a half adder has a carry, it will only add A and B bits.

This affirms that the binary addition process is incomplete and is known as Half Adder. In Half Adders, no range is available to include a carry bit using an earlier bit. The last carry is not included. There will be no forwarding of the carry bit as no logic gate is there to process the carry bit.

Half Adder exhibits the sum of the two inputs. It is used in calculators, computers, and other digital measuring devices.

## What is Full Adder?

An adder with three inputs and produces two outputs is termed a Full Adder. The inputs are A, B, and C-in. C-out contains the output. The sum is first made using the XOR of inputs A and B. The result is then XOR with C-in. C-out is true. Only two of three outputs are high.

K-map can obtain the Full Adder expressions.

The Boolean equations for sum and carry operation is A XOR B XOR C-in and AB + BC-in +C-in A, respectively.

The implementation of Full Adder is done through two half-adders. Full Adders can add a carry bit resulting from the previous addition. High output is obtained using Full Adder. Multiplexers and adders can be implemented using Full Adders.

Arithmetic Logic Unit and Graphics Processing Unit both use Full Adder. Carryout Multiplication is carried out to execute using Full Adders. Full Adders are used as an element in Ripple Adder as the adder adds the bits simultaneously. Half Adder combination is used to design a Full Adder circuit.

## Main Differences Between Half Adder and Full Adder

- Half Adder calculates the sum and carries using two binary inputs, whereas Full Adder adds three binary inputs to calculate the sum and carry.
- The system architecture is different for Half Adder and Full Adder.
- Electronic devices use Half Adder to evaluate addition, whereas digital processors use Full Adder to add long bits.
- Half Adder does not use the previous carry, and Full Adder uses the previous carry.
- A logical expression is different for both adders. Half Adder sum and carry expressions are A XOR B and A AND B, respectively. Full Adder’s sum and carry expressions are A XOR B XOR C-in and AB + BC-in +C-in A, respectively.

**References**

- https://www.sciencedirect.com/science/article/pii/S0030401803012033
- https://ieeexplore.ieee.org/abstract/document/133177/

Last Updated : 11 June, 2023

Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.