Boolean algebra, Computer Engineering

Boolean algebra.

Boolean algebra mathematical method based on human reasoning. In Boolean algebra only two states exist; true and false which are written as 1 (true) and 0 (false). Boolean variables can only take one of these two values. The basic laws of Boolean algebra govern how an expression can be manipulated. The first three laws define the basic Boolean operations NOT, AND and OR.


1) Definition of NOT.

NOT(True) = False            1¯   ->0

NOT(False) = True            0‾ ->1


2) Definition of AND (two variables).

False.AND.False = False        0.0  =  0

False.AND.True = False         0.1  =  0

True.AND.False = False         1.0  =  0

True.AND.True = True           1.1  =  1


3) Definition of OR (two variables).

False.OR.False = False           0 + 0  =  0

False.OR.True = True             0 + 1  =  1

True.OR.False = True             1 + 0  =  1

True.OR.True = True              1 + 1  =  1


4) Zero and unit rules (here we introduce the Boolean variable, X, which can be either true or false).

True.AND.X = X                 1.X  =  X

False.AND.X = False          0.X  =  0

True.OR.X = True                1 + X  =  1

False.OR.X = X                   0 + X  =  X


5) Complement relations.

X.AND.(NOT(X)) = False  

X.OR.(NOT(X)) = True       

NOT(NOT(X)) = X             



6) Idempotence.

X + X = X

X.X = X


7) Commutative laws (now have two variables X and Y).

X + Y = Y + X

X.Y = Y.X


8) Associative laws (insertion of brackets).

X + Y + Z = X + (Y + Z) = (X + Y) + Z

X.Y.Z = X.(Y.Z) = (X.Y).Z


9) Distribution laws.

X.(Y + Z) = X.Y + X.Z

X + Y.Z = (X + Y).(X + Z)


10) Absorption rules.

X + X.Y = X

X.(X + Y) = X



11) de Morgan's Theorem (for any number of variables).


155_de morgans.png

Posted Date: 8/20/2012 10:52:54 PM | Location : United States

Related Discussions:- Boolean algebra, Assignment Help, Ask Question on Boolean algebra, Get Answer, Expert's Help, Boolean algebra Discussions

Write discussion on Boolean algebra
Your posts are moderated
Related Questions
A set of techniques that allow executing a program which is not entirely in memory is called ? Ans. virtual memory which allows executing a program that is not entirely in me

Web server security through SSL (Secure Socket Layer) As it is well known that the Intranets and internet are purely based on use of powerful web servers to deliver information

What are the Counters? 1. The Counter is a sequential circuit which consists of a set of flip flops connected in a appropriate manner to count the sequence of input pulses.

Define Minterm and the Maxterm - Canonical Form? Any Boolean expression perhaps expressed in terms of either minterms or maxterms. The literal is a single variable within a t

Use Microsoft SQLServer to make the following queries.  You should also download the Pirate Sports DM-DD that gives the fields for every table.  Be sure to use proper alignment wit

Using Module-Instance Parameter: Parameter values can be overridden while a module is instantiated. New parameter values are passed at the time of module instantiation. Top-

What is a Development class? Related objects from the ABAP/4 repository are assigned to the similar development class.  This enables you to right and transport related objects

Method : The master from which the copies will be taken is first prepared from a special non-absorbent glazed sheet of paper and special carbon paper which acts as the reproducing

Define ROM? It is a non-volatile memory. It includes only reading of stored data.

Explain the working of Interpreter? The Interpreter is a program that executes instructions written in a high-level language. There are two manners to run programs written in a