The presentataion is about laws of boolean aljebra.

1. MODERN INSTITUTE OF ENGINEERING & TECHNOLOGY
NAME– RANITHALDER
SUBJECT– ANALOGANDDIGITAL
ELECTRONICS
REGNO.– 212690100110017
ROLLNO.– 26900121016
YEAR– 2NDYEAR
SEM– 3RD SEM
DEPT– COMPUTERSCIENCEAND
ENGINEERING
BOOLEAN ALGEBRA

3. INTRODUCTION
• DEVELOPMENTBY ENGLISHMATHEMATICIAN GEORGE BOOLE IN BETWEEN1815-1864.
• IT IS DESCRIBED AS AN ALGEBRA OF LOGIC OR AN ALGEBRA OF TWO VALUES I. E TRUE
OR FALSE
• THE TERM LOGIC MEANS A STATEMENTS HAVING BINARY DECISION I. E TRUE/YES OR
FALSE/NO

4. BOOLEANALJEBRALAWS ANDTHEOREMS
• BOOLEAN ALGEBRA IS A FORM OF MATHEMATICAL ALGEBRA THAT IS USED IN DIGITAL
LOGICIN DIGITALELECTRONICS.
• ALGEBRA CONSISTS OF SYMBOLIC REPRESENTATION OF A STATEMENT(GENERALLY
MATHEMATICALSTATEMENTS).
• SIMILARLY,THERE ARE EXPRESSIONS , EQUATIONS AND FUNCTIONS IN BOOLEAN ALGEBRA
AS WELL.

5. BASICLAWS AND PROOFS
THEBASICRULEANDLAWS OF BOOLEANALGEBRAICSYSTEMAREKNOWNAS “ LAWSOF BOOLEAN
ALGEBRA“,SOMEOF THE BASICSLAWS(RULES) OF THE BOOLEANALGEBRAARE
• ASSOCIATIVELAW
• DISTRIBUTIVE LAW
• COMMUTATIVE LAW

6. ASSOCIATIVE LAW
ASSOCIATIVELAWSARETWOTYPES !
ASSOCIATIVELAWSOF ADDITION
STATEMENT:
ASSOCIATIVELAWOFADDITIONSTATESTHATOR INGMORETHANTWOVARIABLEI. E MATHEMATICALADDITION
OPERATIONPERFORMEDONVARIABLEWILLRETURNTHESAMEVALUEIRRESPECTIVEOFTHEGROUPINGOFVARIABLE
INGROUPS.

7. ASSOCIATIVE LAWOF ADDITION IS WRITTENAS ::
A+(B+C) = (A+B) +C
PROOF :

8. ASSOSIATIVE LAWOF MULTIPLICATION
STATEMENT:-
ASSOCIATIVELAWOFMULTIPLICATIONSTATESTHATANDIN MORETHANTWOVARIABLE I.EMATHEMATICAL
MULTIPLICATIONOPERATIONPERFOMEDONVARIABLEWILLRETURNTHESAMEVALUEIRRESPECTIVEOFTHE
GROUPINGOF VARIABLEIN AN EQUATION.
THEASSOCIATIVELAWUSINGANDOPERATORCANBE WRITTENAS

9. ASSOCIATIVE LAWOF MULTIPLICATION IS WRITTENAS ::
A*(B*C)=(A*B)*C
PROOF :

10. DISTRIBUTIVE LAW
STATEMENT::
THE MULTIPLICATIONOF TWO VARIABLE AND ADDING THE RESULT WITH
A VARIABLE WILLRESULT IN SAME VALUE AS MULTIPLICATIONOF
ADDITIONOF THE VARIABLE WITHINDIVIDUALVARIABLE.

11. THE DISTRIBUTATIVE LAWCANBE WRITTENAS
A(B+C)=AB+AC
A+BC=(A+B).(A+C)

12. COMMUTATIVE LAW
STATEMENT:-
COMMUTATIVELAWSTATESTHATTHEINTERCHANGEINGOF THE ORDEROF OPERANDS IN A
BOOLEANEQUATIONDOESNOT CHAANGEIT’SRESULT.

13. The COMMUTATIVE law canbe writtenas
• A+B=B+C
• A.B=B.A

14. CONCLUSION
CONCLUSION, IN MANY APPLICATIONS OF BOOLEANALGEBRA, YOU HAVE
TO REDUCE A PARTICULAR EXPRESSION TO ITS SIMPLESTFROMOR
CHANGE ITS FORMTO A MORE CONVENIENT ONE TO IMPLEMENT THE
EXPRESSION MOST EFFICIENTLY.

15. ACKNOWLEDGMENTS
I WOULDLIKETO EXPRESSMY SPECIALTHANKSTO MY E.C.ETEACHER(RIANKAMAM) WHOGAVE
ME THEGOLDENOPPORTUNITY TO DO THISWONDERFUL PROJECTON THETOPIC(LAWSOF
BOOLEANALGEBRA) .WHICHHELPEDMETO DO A LOTSOF RESEARCHANDI CAMETOKNOW
ABOUTSO MANYNEWTHINGS.I AM REALLYTHANKFUL TOTHEM.SECONDLYI WOULDLIKETO
THANKSMY FRIENDS& PARENTSWHOHELPEDME IN DOINGTHISPROJECTWITHINLIMITEDTIME
FRAME.