Logic Gates

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The logic gates have one or many input and only one output.The gates used to form integrated circuits (IC's) for digital circuit with combination and sequential of gates.this gates are of mainly 6 types .The three are basic gates and others are the prepared from basic gates called as derived gates.They are as follow:-
I ) Basic gates :-
                               i ) OR gate
                               ii) AND gate
                               iii)NOT gate
II) Derived gates :-
                              i ) NOR gate
                              ii) NAND gate
                              iii)EX-OR gate
The Logic gates have the following details:
1)Logic:-It is the statement.
2)Truth table:-It shows the input provided and output get.It is combination of input provided  making rows in the table with inputs and output column.
3)Boolean equation :-It is the mathematical representation with the equation.
4)Symbol:-It is the logical symbol of the logic gate.

1) OR gate

    Logic :- If A is true or B is true  then Y is true

    Boolean Equation :- Y=A+B

    Symbol:-

   Truth table:

A	B	Y
0	0	0
0	1	1
1	0	1
1	1	1

2) AND gate

    Logic :- If A is true and B is true  then Y is true

    Boolean Equation :- Y=A.B or Y=AB

   Symbol :-

                       
   Truth table:

A	B	Y
0	0	0
0	1	0
1	0	0
1	1	1

3) NOT gate

    Logic :- If A is true then Y is false and A is false  then Y is true

    Boolean Equation :- Y=A.B or Y=AB

    Symbol :- 

     
   Truth table:

A	Y
0	1
1	0

4) NAND gate
   Logic:- If A is true and B is true then Y is false.

   Boolean Equation :- Y=A.B 

   Symbol:-

   Truth table:

A	B	Y
0	0	1
0	1	1
1	0	1
1	1	0

5) NOR gate
Logic :- If A is true or Bis true then Y is false.

Boolean Equation :- Y=A+B 

Symbol:-

Truth table:

A	B	Y
0	0	1
0	1	0
1	0	0
1	1	0

6)EX-OR gate:

Logic :When A is true or Bis true but not both then Y is true.

Boolean Equation:- Y=A.B+A.B

Symbol:-

Truth table:

A	B	Y
0	0	0
0	1	1
1	0	1
1	1	0

• De Morgan's  Law :-

First law :-
Statement:-The compliment of sum is equal to product of compliments.

OR

                   The NOR gate is equivalent to bubbled NAND gate.
 Boolean Equation :-  A+B  = A.B
Second Law :-
Statement:-The compliment of product is equal to sum of compliments.

OR

                   The NAND gate is equivalent to bubbled OR gate.
 Boolean Equation :-  A.B  = A+B 

•  Half Adder:-

For addition of two bits half adder is used .
Truth table:

A	B	Carry	SUM
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	0

 From the above table we can conclude that gates used in half adder are AND gate for carry and EX-OR gate for Sum.

Combinational circuits :- The logic gates can be combined to form the different logic circuits like multiplexer, demultiplexer,encoder,decoder,etc.
Multiplexers:-
Multeplexing is the process of connecting many inputs to one output it is "many to one" process with appropriate logic control signals.
It is a basic block or basic logic combinational circuit with
i) 'n' input data lines.
ii) 'm' control lines /selector lines
iii) one output line 'Y'

Example:-4:1 Multiplexer :-
It has  4 input lines D₀ , D_{1 ,}  D _{2  ,} D₃ and two control lines S_{1  ,}  S₀ and one output denoted by 'Y'.
Truth table:-

S 1	S0	Y=
0	0	D0
0	1	D1
1	0	D2
1	1	D3

It cannot be used a decoder .

It requires OR gate in the Output 

example -IC 74153,74157