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.

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.

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.

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.

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.

1. 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.
2. The system architecture is different for Half Adder and Full Adder.