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
Describe the properties of Attributesand operations Attributes are named slots for data values that belong to the class. Previously we have studied in MCS-024, different o

What is the maximum size of the memory that can be used in a 16-bit computer and 32 bit computer? The maximum size of the memory that can be used in a 16-bit computer is 2 memo

Q. Define the Register Addressing mode? When operands are taken from registers implicitly or explicitly it is known as register addressing. These operands are termed as regis

Performance and Issues in Pipelining Efficiency:  The efficiency of a pipeline can be calculated as the ratio of busy time span to the entire time span including the idle time

What is the advantage of using interrupt initiated data transfer over transfer under program control without interrupt? In the interrupt initiated data transfer, the processor

Question 1: a) How do you track down a transition by name? b) Why Premiere Pro is considered a non-linear editor? c) Explain clearly the main problem that may arise wh

Explain Debug monitors. Debug monitors give debugging support for a program. A debug monitor executes the program being debugged in its own control thereby giving execution e

Q. Which Colour technologies used in Monitors and Printer? Monitor screens and Printers use different colour technologies.  The monitor uses RGB and the Printer CMYK. So, how d

Main problems with evaluation functions: Superlatively, evaluation functions should be quick calculates. Wherever is chance they take a long time to estimate, so after then le

What are the main characteristics of Horizontal Organizational Structure? Horizontal Organization’s main characteristics are given below: The work is structured all aroun