The document discusses digital logic gates and Boolean algebra. It defines logic gates as electronic circuits that make logic decisions. Common logic gates include OR, AND, and NOT gates. Boolean algebra uses truth values of 0 and 1 instead of numbers, and has fundamental laws and operations for AND, OR, and NOT. Boolean algebra can be used to simplify logical expressions and save gates in digital circuit design.

1. DIGITAL LOGIC GATES
AND BOOLEAN ALGEBRA
Dr. C. SARITHA
LECTURER IN ELECTRONICS
SSBN DEGREE & PG COLLEGE
ANANTAPUR

2. LOGIC GATES
INTRODUCTION:
 A logic gate is an electronic circuit/device
which makes logic decisions.
 Most logic gates are two inputs and one
outputs.
 At any given moment, every terminal is in
one of the two binary conditions low (0) or
high(1), represented by different voltage
levels.

3.  The logic state of a terminal can, and
generally does, change often as the circuit
processes data.
 In most logic gates, the low state is
approximately 0v, while the high state is
approximately 5v.
 Logic gates are also called as switches.
with the advent of integrate circuits,
switches have been replaced by TTL
circuit and CMOS circuits.
 symbolic logic uses values, variables and
operations.

4. TYPES OF LOGIC GATES:
The most common logic gates used are,
Basic gates
1.OR
2.AND
3.NOT
Universal gates
1.NAND
2.NOR
 X-OR or Exclusive-OR

5. OR GATE:
 The OR gate has two or more inputs and
one output.
 Its output is true if at least one input is
true.
SYMBOL:

6.  The OR operation may be defined as “Y
equals A OR B”.
Y=A+B
 Where, the symbol ‘+’ indicates the OR
concept.
 Each terminal may assume two possible
values either zero or one.

7. TRUTH TABLE:
A B A+B
0 0 0
0 1 1
1 0 1
1 1 1

8. AND GATE:
 The AND gate is also a basic kind of
digital circuit.
 It has also two or more inputs and one
output.
SYMBOL:

9.  The AND operation for the output is
defined as, “y equals A AND B”.
Y=A.B
 Where ‘.’ symbol indicates AND
operation.
 The output of the AND gate is one only
when both inputs are one.

10. TRUTH TABLE:
A B A+B
0 0 0
0 1 0
1 0 0
1 1 1

11. NOT GATE or Inverter Gate:
 A NOT gate is a basic gate that has one
input and one output.
SYMBOL:

12.  The NOT circuit serves to invert the
polarity of any input pulse apply to it.
 If A is the input then output “Y equals to
NOT A or Ā.
Y= Ā
 Where, the bar symbol over A represents
NOT or compliment operation

13. TRUTH TABLE:
A Ā
0 1
1 0

14. NAND GATE:
 The NAND gate is known as an universal
gate because it can be used to realize all
the three basic functions of OR, AND &
NOT gates.
 It is also called as NOT-AND gate.
SYMBOL:

15.  The Boolean expression for the NAND
operation is given by,
Y=A.B

16. TRUTH TABLE:
A B AB
0 0 1
0 1 1
1 0 1
1 1 0

17. NOR GATE:
 The NOR gate is also a universal gate
and it is a combination of a NOT and OR
gates.
SYMBOL:

18.  The Boolean expression for NOR gate is
given by,
Y=A+B

19. TRUTH TABLE:
A B A+B
0 0 1
0 1 0
1 0 0
1 1 0

20. Exclusive OR or X-OR GATE:
 The X-OR gate is a logic gate having two
inputs with and single output.
SYMBOL:

21.  The Boolean expression for the X-OR gate
is given by,
Y=A+B+
 Where + indicates the exclusive OR
+
operation and in terms of expression it can
be expanded as
Y=AB+AB

22. TRUTH TABLE:
A B AB+AB
0 0 0
0 1 1
1 0 1
1 1 0

23. ADVANTAGES OF LOGIC GATES:
 It is generally very easy to reliably
distinguish between logic 1 or logic 0.
 The simplest flip-flop is the RS which is
made up of two gates.
 K-map is also designed by using logic
gates. That simplification helps when you
start to connect gates to implement the
functions.
 These gates are also used in TTL and
CMOS circuitary.

24. BOOLEAN ALGEBRA
 Boolean Algebra derives its name from the
mathematician George Boole in 1854 in his book
“An investigation of the laws of taught”.
 Instead of usual algebra of numbers Boolean
algebra is the algebra of truth values 0 or 1.
 In order to fully understand this the relation
between the AND gate, OR gate & NOT gate
operations should be appreciated.

25. POSTULATES OF BOOLEAN ALGEBRA:
 The Boolean algebra has its own set of
fundamental laws which differ from the
ordinary algebra. They are,
OR laws:
 A+0=A
 A+1=1
 A+A=A
 A+Ā=1

26. AND laws:
 A.0=0
 A.A=A
 A.1=A
 A.Ā=0
NOT laws:
 0=1
 1=0
 If A=0 then Ā=1
 If A=1 then Ā=0
 Ā=A

27. Commutative law:
 A+B=B+A
 A.B=B.A
Associative laws:
 A+(B+C)=(A+B)+C
 A.(B.C)=(A.B).C
 (A+B)+(C+D)=A+B+C+D

28. Distributive laws:
 A.(B+C)=(A.B)+(A.C)
 (A+B).C=A.C+B.C
 A+ĀB=A+B
 A+B.C=(A+B).(A+C)
Absorptive laws:
 A+A.B=A
 A.(A+B)=A
 A.(Ā+B)=AB
Demorgan’s laws:
 A+B=A.B
 A.B=A+B

29. EXAMPLE:
(AB+C)(AB+D)=AB+CD
 AB.AB+AB.D+C.AB+C.D
 AB+ABD+ABC+CD {A.A=A}
 AB(1+D)+ABC+CD {1+A=1}
 AB+ABC+CD
 AB(1+C)+CD
 AB+CD

30. Advantages:
 If we use Boolean algebra for your logical
problem you can save more gates and
operations. so your design will be
cheaper, more comprehensible, more
serviceable .
 It allows logical steps quickly and
repeatedly.
Disadvantages:
 Can only arrive at direct results not implied
once.