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
Define the various actions a process might be take upon receiving a signal? There are various actions a process might be take upon receiving a signal here are three different d

Define data type and abstract data type comment upon the significant of both

Q. Compute Physical address of data byte? Offset of data byte = 0020h Value of data segment register (DS) = 3000h Physical address of data byte   This computation

What are the types of consumer oriented applications of E-commerce? Four types of Consumer Oriented applications within E-Commerce are as given below: 1. B2C (business-to-c

Question: (a) What is the purpose of CDATA in an XML document? Explain your answer using extract codes. (b) Consider the following definition for an address element:

A given microprocessor has words of 1 byte.  What is the smallest and largest integer that can be characterized in the following representations?   a) unsigned b) sign- ma

Describe ARP message format in brief.                             0                                        8                                      16

How would you implement inheritance using VB.NET/C#? When we set out to execute a class using inheritance, we must first start with an existing class from which we will derive

Nested Macro calls are expanded using the? Ans. By using the LIFO (Last in First out) Nested Macro calls are expanded.

Describe what happens when recursion functions are declared inline? Ans) Inline functions property says whenever it will call; it will copy the whole definition of that functi