What is Logic Gates? What are Different Types and Rules?

LOGIC GATES

Today we will learn about What is the logic gates? Different types of logic gates rules and laws of boolean algebra and what are the postulates of Boolean algebra.

The Boolean expression which can be perform by simplest taken as a basic elements , is called a logic gates

Logic gates are represented  by some special symbols.

The logic gate identify there function operations

The most common logic gates are  OR, AND, NOT ,NAND , NOR, Exclusive OR , Exclusive  NOR gates. Boolean algebra allows any combinational logic circuit to be constructed with AND,OR and NOT gates .Any combinational logic gates are ( NOT +AND ) NAND or (NOT+OR ) NOR gate;

NAND or NOR gates are called the universal gates

OR Gates:

INPUTS		OUTPUT
A	B	Z
0	0	0
0	1	1
1	0	1
1	1	1

Z=A OR B
   =A+B

In a OR gate two inputs gives but output will be a A or B. Given input is high then output will be high and given input is low then output will be low.

AND Gates:

INPUTS		OUTPUT
A	B	Z
0	0	0
0	1	0
1	0	0
1	1	1

Z=A AND  B
   =A.B

In a AND gate two inputs gives but output will be a A and B. Given all input are high so input provide a high output.

NOT Gates

INPUT	OUTPUT
A	Z
0	1
1	0

Z=NOT A
  = A
 

A NOT gate (or inverter gate) .It has one input and one output. Its output always opposite of input.

NAND Gates

INPUTS		OUTPUT
A	B	Z
0	0	1
0	1	1
1	0	1
1	1	0

Z=A NOT AND B
  =A.B

NOR Gates

INPUTS		OUTPUT
A	B	Z
0	0	1
0	1	0
1	0	0
1	1	0

Z=A NOT OR B
  =A.+B

Exclusive –OR Gates

INPUTS		OUTPUT
A	B	Z
0	0	0
0	1	1
1	0	1
1	1	1

Z=A EX-OR B
  =AB+AB

Exclusive- NOR Gates

INPUTS		OUTPUT
A	B	Z
0	0	1
0	1	0
1	0	0
1	1	1

Z=A EX-OR B
    =A EX-OR B
    =AB+AB

BOOLEAN ALGEBRA LAWS AND RULES

 Boolean expression depends on three algebraic laws

1.Commutative laws
2.Associative Laws
3.Distributive Laws

1.Commutative laws – A+B = B  and A.B = B. A

2.Associative Laws – A+(B+C)=(A+B)+C and A .(B . C) = (A .C) .C

3.Distributive Laws -  A . (B+C) = A . B+A .C

Boolean algebra rules are given below 

OR Rules – A+0 =A;   A+1= 1;  A+A=A ;  A+ A =1

AND Rules – A .0=0;   A . 1=1;  A.A=A ;  A .  A=0

Complementation  Rule – A=A

Absorptive Rule –A+AB=A ;  A+AB= A+B;  (A+B)(A+C)=A+BC

BOOLEAN  POSTULATES

There are five basic postulates of Boolean algebra. A list of these postulates is given below

1. If A=1 ,then A=0        1. If A=0 ,then A=1

2. 0.0=0                           2.1+1=1

3.1.0=0                            3.0+0

4.1.0=0                            4.0+1=1

5.1=0                               5.0=1

HERE we see  that the each postulates has two parts  a and b .they are called dual each other .by dual
we mean that ‘b’form  is made from  ‘a’ from by charging the Boolean operation AND to OR and logic 0to1or 1to 0.