Skip to main content

THEORITICAL ALGEBRA IN COMPUTERS


ALGEBRA IN COMPUTERS
algebra,computers,computer science,linear algebra,computer,linear algebra tutorial,logical operations in computer,number system in computer,boolean algebra,number systems in computer science,great theoretical ideas in computer science,logical operations in computer architecture,great ideas in theoretical computer science,computer algebra,computer algebra system,chapter 1 boolean algebra in hindi,udemy algebra course


Algebra is a subject in which the problem of the sum is solved with the help of letters (I mean the letters of English language as well as Greek language).  It is mostly used by the mathematicians, engineers, scientist as well as businessmen to solve any problem of the world.  Algebra is very important in many science as well as commerce studies.  So we are going to dig deep in algebra used in computers.
We will consider Boolean algebra as it is used by the computers to solve real life problems.  So let us begin.

Boolean algebra, like any other   mathematical system , may be with a set of elements , a set of operators and a number of unproved axioms or postulates.    A set of elements is any collection of objects having a common property. 
If S is a set and x is an element of that set the x€ S denotes that x is an element of that set.   A set with de-numberable (means a small number) number of elements is specified by braces:  A={1, 2, 3, 4} that is the element of set are the number 1 , 2 , 3 ,4.
  A binary operator defined on a set S of elements is a rule that assigns to each pair of elements from S a unique element from S.  As an example consider the relation A * B = C.  We say that * is a binary operator if it specifies a rule for finding c from that pair (a,b) and also if a,b ,c element of S.  However * is not a binary operator if a, b element of S while the rule finds c not element of S.

 The postulates of a mathematical system form the basic assumptions from which it is possible to deduce the rules , theorems and property of the system.  The most common postulates used to formulate various algebraic structures are.

 1 Closure :-  A set S is closed with respect to a binary operator if, for every pair of elements of S, the binary operator specifies a rule for obtaining a unique element of S.  For example, a set of natural numbers N = {1,2,3,4......} is closed with respect to the binary operator plus by the rule of arithmetic addition, since for any a, b element of N  we obtain a unique C element of   a + b = c.  The set of natural numbers i not closed with respect to the binary operator minus (-) by the rules of arithmetic subtraction because 2 - 3 =  - 1 and 2, 3 element of N while (-1) not element of N.

2 Associative law :- A binary operator * on a set S is set to associative whenever: 
(x * y)*z = x * (y * z)  for all x, y, z element of S.

3 Commutative law :- A binary operator * on a set S is said to be commutative whenever :
 x * y = y  *  x for all x ,y element of S

4. Identity element :- A set S is said to have an identity element with respect to a binary operation * on S if there exist an element e element of S with the property:  

5. Inverse :- A set s having an identity element e with respect to binary operator * is said to have an inverse whenever, for every x element of S there exist an element y element s such that:
   x * y = e

6. Distributive law :- If * and . are two binary operators on a set S, * is said to be distributive over . whenever:
                                                       x *(y . z) = (x*y).(x*z)

    An example of an algebraic structure is a field.  A field is a set of elements, together with two binary operators each having properties 1 to 5 and both operators give the combination of the above 5 principles to give the 6 law.  The set of real numbers together with binary operators + and . form the field of real numbers.  The field of real numbers is the basis of for arithmetic and ordinary algebra.  The operators and postulates have the following meanings:

The binary element of + defines addition
The addiditive element is 0.
The additive inverse defines subtraction.
The multiplicative identity is 1.

This is all i got.  Thank you for reading.

    





Comments

Popular posts from this blog

EXPANSION SLOTS IN MOTHERBOARD

EXPANSION SLOTS IN MOTHERBOARD  Friends today i am going to share my knowledge and understanding of the expansion slots. So lets begin with our topic. Expansion slots are used to provide additional properties for carrying the computation task such as additional video, audio and sound, advanced graphics and Ethernet.   So lets begin with our knowledge hunting. I will start by AGP expansion slots. AGP AGP stands for ACCELARATED GRAPHICS PORT.  AGP was introduced with high speed 3D graphics display in 1996.  It is used for older graphics card types which is discontinued by PCI EX16 graphics port in 2005.   These were kernel version of AGP most of the brand in 1.5 volt DC.  AGP 1x channel and 66MHZ clock speed resulting a data table of 266 MBPS.   AGP 2x, 4x ,8x specification multiply MHZ clock to produce increase throughput. AGP 8x produces effective clock frequency of 533 MHZ resulting a throughput of 2 GBPS (2133MHZ) resulting a throughput of over a 32 bit channel. PCI PCI  stands for P

PROCESSOR AND HYPER THREADING A SHORT SUMMARY

PROCESSOR AND HYPERTHREADING Friends in the last post i tried to say something about computer science and mathematics relationship.   Now i am going to say something about processor and hyperthreading.   So let’s get started. The Physical Component By Which A Computer Is Made Which We Can See, Touch And Feel Is Called Computer Hardware Example Ram, Motherboard. ·          INPUT DEVICE   : These hardware are used to input any data, instruction on command insidea computer device.   example keyboard mo9use scanner microphone, webcam etc ·          OUTPUT DEVICE :   these hardware are used to get any output from a computer system.   example: monitor, printer, speaker. ·          CENTRAL PROCESSIG UNIT (CPU) : This Device Proceses All Instruction Given By A User, And It Also Other Haqrdwqaar Peripherals Example   :Microprocessor ·          MOTHERBOARD: It is the main electric circuit board which is made by a pcb(printed circuit board).   It hods all hardware componen

CODES OF LANGUAGE IN COMPUTER SYSTEM. WHAT ARE THE OTHER CODES WHICH ARE USED IN COMPUTER SYSTEM?

  CODES OF LANGUAGE IN COMPUTER SYSTEM.   WHAT ARE THE OTHER CODES WHICH ARE USED IN COMPUTER SYSTEM?   There are many codes in computer system which may remain unnoticed by many computer geeks and nerds.   I also first didn’t see it but I am going to share it because these are important codes and used by many computer hardware developers, vendors and computer software developers.    They are mostly understood by ELECTRONICS AND ELECTRICAL ENGINEERING geeks or nerds.   They are as under : ·         ERROR DETECTION CODES ·         ALPHANUMERIC CODES ·          REFTLECTED CODES First we will discuss something about ERROR DETECTION CODES.                                                                                                              ERROR DETECTION CODES:   Binary information , be it pulse modulated signals or digital computer input or output, may be transmitted though some form of communication medium or electrical wires or radio waves.   Any external noi