BOOLEAN ALGEBRA AND LOGIC GATE

BOOLEAN ALGEBRA & LOGIC
CIRCUIT APPLICATION

Presented By
• SHEHAB SHARIER
• MARINA SULTANA
• TAMIM TANVIR
• PROSHANTO PODDER

Objectives
• Introduction to Boolean algebra.
• Basic concepts and functions of
Boolean algebra.
• Introduce to Logic gates.
• Logic circuits and Boolean
expressions.

Boolean Algebra
An algebra which is use for simplifying the
presentation & manipulation of propositional
logic.
It is also know as Switching Algebra.
Invented by George Boole in 1854.
Boolean algebra is mainly use for simplify
and Manipulate electronic logic circuits in
computers .

Basic concepts of Boolean algebra
 It deals with the binary number system
(0,1).
 The three basic logical operations are:
I. AND
II.OR
III.NOT

AND operation is use for logical multiplication.
The dot symbol (“.”) used for representing AND
operation. AND operator has an output 1 if
all the inputs are 1 otherwise the output is 0.
AND Operation
Truth Table for logical AND operation.
Input Input Output
A B C
0 0 0
0 1 0
1 0 0
1 1 1

OR operation is use for logical addition.
The symbol (“+”) used for represent OR operation.
OR operator has an output 1 if
any of the inputs are 1 otherwise the output is 0.
OR Operation
Truth Table for logical OR operation.
Input Input Output
A B C
0 0 0
0 1 1
1 0 1
1 1 1

NOT operation is use for complementation.
The over bar symbol (“¯”) used for represent NOT
operation. NOT operator has an output 1 if
input is 0 or output 0 if the the input is 1.
NOT Operation
Truth Table for logical NOT operation.
Input Output
A
_
A
0 1
1 0

Boolean Theorems
Basic Theorems:-
OR AND NOT
A+0=A A.0=0
_
A+A=1
A+1=1 A.1=A
_
A . A=0
A+A=A A . A=A
_
A+A=1
_
A . A=0
Other Theorems:-
• A+B=B+A
• A . B=B . A
• A+(B+C)=(A+B)+C
• A+B . C=(A+B).(A+C)

Boolean Function
Boolean function is an expression formed with
binary variable. It is the combination of
Boolean operators such as AND, OR & NOT
operators.
Input Output
X Y X X+Y X.(X+Y) =X.Y
0 0 1 1 0 0
0 1 1 1 0 0
1 0 0 0 0 0
1 1 0 1 1 1
X.( X+Y)=X.Y
Truth table for Boolean function.

Logic Gate
 Computer carries out all operations by the
combination of signals that pass through standard
blocks of built-in circuits.
 Logic gate is an elementary building block of digital
electronic circuits that operates one or more input
signals to produce standard output.
 The common use of logic gate elements is to act as
switch.
 In computer logic gates are use to implement
Boolean functions.

BASIC
GATES
AND
OR
NOT
Type of Logic Gates

AND Gate
o AND gate is use for logical multiplication
input signals.
o If the input values for an AND gate are 1 then
the output is 1 otherwise the output is 0.

OR Gate
OR gate performs the logical addition operation.
It is an electronic circuit that generates an
output signal 1 if any of the input signal is 1.

NOT Gate
NOT gate performs the logical
complementation operation.
It is an electronic circuit that generates the
reverse of the input signal as output signal.

Logic Circuits
An electronic circuit that is consist with a number of
logic gates which is use in computer to perform
logical operation on its two or more input signals
to produce a combined standard output signal.
Logic circuit for Boolean expression Z.(X+Y)
X X+Y
Y
Z.(X+Y)
Z
Z

Logic circuit for Boolean expression (X.Y.Z).(X+Y+Z)
X X
X.Y.Z
Y X.Y.Z
Z (X.Y.Z).(X+Y+Z)
X X
X+Y+Z
Y
Z Z

Boolean algebra simplifies logic circuits to increase
work efficiency of digital device.
Logic circuits can be built for any binary electric or
electronic devices including switches, relays, electron
tubes and transistors.
circuits that perform complex logical functions . A
computer can perform its logical functions along with
proper execution of other commands.
Conclusion

BOOLEAN ALGEBRA AND LOGIC GATE

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