What is adder?

What is the adder? Explain both of the adder (Half & Full) with 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:
  1. Half adder
  2. Full 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 following diagram represents the circuit diagram of half adder:

Fig: Half adder
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, half adder has only two inputs and two outputs.
A full circuit can be constructed by using the X-OR gate, OR gate, an AND gate. The first two input is common bits and the last one is called carry input.
The circuit diagram of a full adder:

Fig: Full adder
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:

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