introduction logical operations truth table and rules
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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
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