introduction logical operations truth table and rules

INTRODUCTION

LOGICAL OPERATIONS

TRUTH TABLE AND RULES

INTRODUCTION

1

854: Logical algebra was published by George Boole

known today as “Boolean Algebra”• It’s a convenient way and systematic way of expressing

and analyzing the operation of logic circuits.

1

938: Claude Shannon was the first to apply Boole’s

work to the analysis and design of logic circuits.

TRUTH TABLE

A

TRUTH TABLE is a table which represents

all the possible values of logical variables

along with all possible results of the given

combination of values

LOGICAL OPERATORS/GATE

NOT operator/GATE

OR operator/GATE

AND operator/GATE

NOT OPERATOR/GATE

This operator operates on single variable.

Operation performed by the NOT operator is called

complementation.

The symbol for NOT operator is represented by

“~”.

Thus X means complement of X.

TRUTH TABLE FOR NOT OPERATOR/GATE

A

ssume only one of the two values 0 and 1.

W

here 0 denotes false value

A

nd 1 denotes true value

TABLE

X X

0 1

1 0

VENN DIAGRAM

x x

OR OPERATOR/GATE

This operator denotes operation called logical

addition.

The symbol is represented by “+”.

Thus X+Y can be read as X OR Y.

For OR operation the possible input and

output combinations are as follows.

TABLE

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 1

TRUTH TABLE FOR OR

X Y X+Y

0 0 0

0 1 1

1 0 1

1 1 1

AND OPERATOR/GATE

A

ND operator performs another important operation of

boolean algebra calleid logical multiplication.

T

he symbol for AND operation “(.)” dot.

T

hus X.Y is read as X AND Y.

THE RULES FOR AND

0 . 0 = 00 . 1 = 01 . 1 = 11 . 0 = 0

TRUTH TABLE FOR AND

X Y X.Y

0 0 0

0 1 0

1 0 0

1 1 1

BOOLEAN ALGEBRA RULES

P

roperties of 0 :- 0+0=0; 0.X=0

P

roperties of 1:- 1+X=1; 1.X=X

I

ndempotence law:-

X +X = X

RULES

X . X = X

Involution

X = X

C

omplementary law

X + X = 1

X

. X = 0

THANKS

M

ONICA J

C

LASS XII –A(2012-13)

C

OMPUTER SCIENCE