There are two types of adders: half adders and full adders. A half adder can add two binary digits and produces a sum and carry output. It has two inputs and two outputs. A full adder can add three binary digits - two input digits and a carry digit. It has three inputs and produces a sum and carry output. Full adders were developed to overcome the limitation of half adders only being able to add two numbers.

1. HALF ADDER
AND
FULL ADDER

2. •Adder : In electronics an adder is digital circuit
perform addition of numbers. In modern computer adder
reside in arithmetic logic unit (ALU).
•Adder are not important not only in the computer but
also in many types of digtal system in which the numeric
data are processed .

3. 2: Full Adder
There are 2 types of Adder.
1: Half Adder

4. Representation of half adder :
•The Half Adder accept two binary digits on its input and produce two binary digits output ,a
sum bit and a carry bit (i.e. It contains 2 inputs and 2 outputs .)
Truth-Table :

5. Boolean expression for the logic diagram :
1: For Sum : A`B + AB`
2: For Carry : AB

6. Using NAND Gate : Using NOR Gate :

7. Representation of Full Adder :
The half adder is used to add only two numbers. To overcome this problem, the
full adder was developed. The full adder is used to add three 1-bit binary
numbers A, B, and carry C. The full adder has three input states and two output
states i.e. sum and carry .
Truth Table :

8. SOP form of sum and carry :
1: Sum : A`B`C + A`BC` + AB`C` + ABC
2: Carry : A`BC + AB`C + ABC` + ABC