#### What is the adder? Explain both of the adders (Half & Full) with a proper circuit diagram and truth table.

Adder: Component of a computer processor that adds two numbers sent from the processing instructions. Adders are used not only for arithmetic logic units but also in the other parts of the processor. They may use for calculating table index, address, and many other logical works. Adders can be constructed for many numerical representations, such as binary-coded decimals or excess-3, the most common adders operate on binary numbers.

There are two types of adders:

- Half adder

### Half adder

Half adder always adds only two single binary digits X and Y. It has two outputs, a sum bit, and carries a bit. Sum bit represents the X-OR of X and Y, again the carry bit represents the AND of X and Y input bits.

The truth table of half adder:

INPUTS OUTPUTS

X Y SUM CARRY

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1

Full adder

The full adder is a little bit complex than a half adder. The full adder has three inputs but two outputs. On the other hand, the half adder has only two inputs and two outputs.

A full circuit can be constructed by using the X-OR gate, OR gate, and AND gate. The first two input is common bits and the last one is called carry input.

The truth table of full adder:

INPUTS OUTPUTS

A B CIN COUT S

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Summary:

From the above discussion we come to know that, the use and construction of half adder and full adder, different between the half adder and full adder.

References:

- Digital and computer logic diagram by M. Morris Mano

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