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INTRODUCTION LOGICAL OPERATIONS TRUTH TABLE AND RULES

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INTRODUCTION 1854: Logical algebra was published by George Boole known today as Boolean Algebra Its a convenient way and systematic way of expressing and analyzing the operation of logic circuits. 1938: Claude Shannon was the first to apply Booles work to the analysis and design of logic circuits.

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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

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LOGICAL OPERATORS/GATE NOT operator/GATE OR operator/GATE AND operator/GATE

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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.

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TRUTH TABLE FOR NOT OPERATOR/GATE Assume only one of the two values 0 and 1. Where 0 denotes false value And 1 denotes true value

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TABLE XX 0 1 10

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VENN DIAGRAM x x

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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.

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TABLE 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 1

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TRUTH TABLE FOR OR X Y X+Y 0 0 0 0 1 1 1 0 1 1 1 1

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AND OPERATOR/GATE AND operator performs another important operation of boolean algebra calleid logical multiplication. The symbol for AND operation (.) dot. Thus X.Y is read as X AND Y.

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THE RULES FOR AND 0. 0 = 0 0. 1 = 0 1. 1 = 1 1. 0 = 0

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TRUTH TABLE FOR AND X Y X.Y 0 0 0 0 1 0 1 0 0 1 1 1

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BOOLEAN ALGEBRA RULES Properties of 0 :- 0+0=0; 0.X=0 Properties of 1:- 1+X=1; 1.X=X Indempotence law:- X +X = X

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RULES X. X = X Involution X = X Complementary law X + X = 1 X. X = 0

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THANKS MONICA J CLASS XII –A(2012-13) COMPUTER SCIENCE

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