1) The document discusses Boolean algebra, which was developed by English mathematician George Boole between 1815-1864. It describes an algebra of logic or an algebra of two values - true or false. 2) The document outlines some basic laws and theorems of Boolean algebra, including the associative law, distributive law, and commutative law. It provides statements and proofs for each law. 3) Boolean algebra is concluded to be important for reducing expressions to their simplest form or changing their form for more efficient implementation in digital electronics and logic.

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.