1. ADDER, HALF ADDER & FULL ADDER

2. Binary Addition
Sum
Carry

3. ADDER
In electronics, an adder is a digital circuit that performs addition of numbers.
In modern computers and other kinds of processors, adders are used in the arithmetic logic unit (ALU), but also in other parts of the processor, where they are used to calculate addresses, table indices, and similar operations.
Although adders can be constructed for many numerical representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers.

4. Types of Adder
There are two types of Adder
Half Adder
Full Adder

5. Half Adder
The half adder accepts two binary digits on its inputs A and B.
It produce two binary digits outputs, a sum bit (S) and a carry bit (C).
The simplest half-adder design, pictured incorporates an XOR gate for S and an AND gate for C.
Carry <= X AND Y;
Sum <= X XOR Y;

6. Diagram Input Output Logic Symbol: Half Adder Logic Diagram: A B
 (sum)
C0 (carry out)
Half
Adder
Input Output
Logic Symbol:
Logic Diagram:

7. Diagram
Logic Diagram:
Logic Diagram:

8. Truth Table
Inputs
Outputs X Y C S 1

9. Full Adder
A full adder adds binary numbers and accounts for values carried in as well as out.
A one-bit full adder adds three one-bit numbers input , often written as A, B, and Cin; A and B are the operands, and Cin is a bit carried in.
A full adder can be constructed from two half adders by connecting A and B to the input of one half adder, connecting the sum from that to an input to the second adder, connecting Cin to the other input and OR the two carry outputs
S = X xor Y xor Cin
Cout = X.Y + X.Cin + Y.Cin

10. Diagrams Input Output Logic Symbol: Full Adder Logic Diagram: A B
 (sum)
C0 (carry out)
Full
Adder
Input Output
Cin
Logic Symbol:
Logic Diagram:

11. Diagram a
Half
Adder b
Cout OR
Half
Adder
Sum
cin

12. Truth Table Inputs Output S is 1 if an odd number of inputs are 1.
Cin
Cout
Sum 1
S is 1 if an odd number of inputs are 1.
COUT is 1 if two or more of the inputs are 1.

13. Sum is `1’ when one of the following four cases is true:
a=1, b=0, c=0
a=0, b=1, c=0
a=0, b=0, c=1
a=1, b=1, c=1

14. Circuit of Adder A B

15. Circuit of Adder A X B

16. Circuit of Adder A B ∑
Cin

17. Circuit of Adder A B ∑
Cin Y

18. Circuit of Adder A B ∑
Cin Y
= A.B

19. Circuit of Adder A B ∑
Cin
Cout
Cout= (A B). Cin + A.B

20. The Full Adder X Y
Cin S
Cout

21. The Full Adder
Half Adder
Cin
Cin + xy