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

1. A half adder is a digital circuit that only adds two bits, while a full adder can add three bits, including carry.
2. The carry output of a half adder cannot be used as an input to the next addition stage, unlike a full adder.
3. 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.

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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.

## Comparison Table

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.

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.

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.

1. Half Adder calculates the sum and carries using two binary inputs, whereas Full Adder adds three binary inputs to calculate the sum and carry.
2. The system architecture is different for Half Adder and Full Adder.
4. Half Adder does not use the previous carry, and Full Adder uses the previous carry.
5. 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

Last Updated : 11 June, 2023

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