An adder is used for the addition of 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 two types: Half Adder and Full Adder. The other combinational circuits include an encoder, decoder, multiplexer, and many more.

## 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 own 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 is used to add two one-bit digits. Augend and Addend are the terms used for the input bits. The result consists of sum and the carry. XOR is applied to both the inputs to carry out the addition. Both inputs do AND operation to produce 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 bit carried in. It is a bit difficult in implementation as compared to a half adder. It has three inputs and two outputs. Multiplexers and adders can be implemented using Full Adders.

## Comparison Table Between Half Adder and Full Adder

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 next step | Added to next step |

Sum Expression | XOR of A and B | A 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 two outputs which are the sum and carry. The two inputs are attributed to augend and Addend. The sum is normal output, and carry is carryout. 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 in implementation for the half adder. 74HCxx series are used in the implementation. The sum operation is practised using XOR operation, and carry operation is implemented using AND gate. If the input to a half adder has a carry, then it will only add A and B bits.

This affirms the binary addition process is not complete, and therefore it is known as Half Adder. In Half Adders, no range is available to include carry bit using an earlier bit. The previous 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 as Full Adder. The inputs are A, B, and C-in. C-out contains the output. The sum is produced first by using the XOR of input A and B. The result is then XOR with C-in. C-out is true. Only two of three outputs are high. The Full Adder expressions can be obtained by K-map.

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 which is the result of 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 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 uses the addition of 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 for evaluation of addition, whereas digital processors use Full Adder for the addition of long bit.
- Half Adder does not use the previous carry, and Full Adder uses the previous carry.
- A logical expression is different for both adders. The expressions for Half Adder sum and carry are A XOR B and A AND B, respectively. The sum and carry expressions for Full Adder are A XOR B XOR C-in and AB + BC-in +C-in A, respectively.

## Conclusion

Adder is a part of a digital circuit. Full Adders adds a carry bit which comes from the previous result. High Output is obtained using Full Adder. Full Adders are employed to overcome the drawback of Half Adders. These adders are added to the inverter to form a half subtractor. Logic gates process the input very fast. The speed is in microseconds of logic gates. The utilization of logic gates makes the addition process fast.

Half Adder and Full Adder are widely used in digital circuits for performing arithmetic functions. Half Adder and Full Adder are both combinational logic circuits, but they differ in the way they process the inputs. Half Adder is used in a low degree of addition, while the high degree of addition is done by using Full Adder.

## References

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

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