introduction to Logic gates and Boolen algebra

1. LOGIC GATES &
BOOLEN ALGEBRA
BY
M.VENKATESH

2. OUTLINE
 INTRODUCTION TO LOGIC GATES
 TYPES OF LOGIC GATES
 ADVANTAGES,DIADVANTAGES &
APLLICATIONS
 INTROUCTION TO BOOLEN ALGEBRA
 RULES OF BOOLEN ALGEBRA
 EXAMPLE FOR BOOLEN ALGEBRA

3. INTRODUCTION TO LOGIC GATES
 A logic gate is an elementary building block of a DIGITAL CIRCUIT
 Most logic gates have two inputs and one output.
 In most logic gates, the low state is approximately zero volts (0 V),
while the high state is approximately five volts positive (+5 V).
 binary conditions low for 0V or high for 1V
 There are three common ways in which to represent the working of a
logic circuit.
1. Truth Tables
2. Logic Circuit Diagram
3. Boolean Expression

4. LOGIC GATES
 A truth table is a chart of Boolean values (1s and 0s) arranged to
indicate the results (or outputs) of all possible inputs combinations.
 The lists of all possible inputs combination are arranged in columns
on the left and the resultant outputs are listed in columns on the right
side of the table.
 A logic circuit diagram uses the graphical representation or
description of logic gates in combination to represent a logic
expression.
 Boolean algebra can be used to write a logic expression in the form
of an equation.

5. TYPES OF LOGIC GATES

6. NOT GATE
 It Is also called as complementary or inversion gate.
 NOT gate perform the ‘~’ operation.
 It has one input and one output.

7. NOT GATE

8. NOT GATE APPLICATION
.

9. AND GATE
 It perform Multiplication operation.
 AND gate represented as ‘.’
 When both inputs are high then output will high

10. AND GATE

11. AND GATE APPLICATION

12. OR GATE
 It perform Addition operation.
 OR gate represented as ‘+’
 When both inputs are low then output will low

13. OR GATE

14. OR GATE APPLICATION
.

15. NAND GATE
 NAND gate Complement of AND gate.
 When both inputs are low then output will low

16. NAND GATE

17. NOR GATE
 NOR gate is Complement of OR gate
 When both inputs are low then output will be low

18. NOR GATE

19. EXCLUSIVE OR GATE
 It is also called as Athematic Gate
 When any one input is then output will high
 XOR gate is represented as 

20. XOR GATE

21. EXCLUSIVE NOR GATE
 XNOR gate is complement of XOR gate
 When both inputs are high or low then the output will high
 XNOR is represented as


22. XNOR GATE

23. ADVANTAGES
 The switching time is much faster than analog circuits.
 logic gates is less expensive
DISADVANTAGES
 Logic circuits uses more energy than other circuits like analog
circuits to accomplish the same tasks resultant circuit produces more
heat.
 For activation, logic circuits require power system i.e. portable or
battery power systems which are limited in power.

24. APPLICATIONS
 Personal Computers
 Mobile Phones
 Tablets
 Calculators and
 Digital Watches

25. BOOLEN ALGEBRA
 Boolen algebra is given by English Mathematician GEORGE
BOOLE
 It is set of rules used to simplify the given logic
expression without changing its functionality.
 It is used when number of variables are less.
GEORGE BOOLE
(1815-1864)

26. BOOLEN ALGEBRA
 Set of rules it is used to simply and minimize the equation.
 Logic Expression : F=A`B+BC+ABC ------(1)
---
F=A`B+BC ---------(2)
The above two functions are same
 To reduce the variable we use the map method or k-map method
 For (1) we required 5 logic gates
 For (2) we required 4 logic gates

27. BOOLEN ALGEBRA

28. RULES OF BOOLEN ALGEBRA
1. COMPLEMENT RULE
A COMPLEMENT=A` Or (NOT A) Or
A.(A`)`=A
2. AND RULE
A.A=A
A.1=A
A.0=0
A.A`=0
A

29. RULES
3. OR RULE
A+A=A
A+0=1
A+1=1
A+A`=1
4.DISTRUBTIVE LAW
A.(B+C) = A.B+A.C
A+(B.C) = (A+B).(A+C)

30. RULES
5. COMMULATATIVE LAW
A+B = B+A
A.B = B.A
6. ASSOCITATIVE LAW
(A.B).C =A.(B.C)
7. DEMORGANS LAW
(A+B)`=A`.B`
(A.B)`=A`+B`

31. EXAMPLE OF BOOLEN ALGEBRA
DCBAY 