Showing posts with label THEORITICAL ALGEBRA. Show all posts
Showing posts with label THEORITICAL ALGEBRA. Show all posts

Wednesday, March 17, 2021

TOPOLOGIES OF COMMUNICATING MACHINES


TYPES OF NETWORK TOPOLOGY

NETWORK TOPOLOGY IS THE SCHEMATIC DESCRIPTION OF NETWORK ARRANGEMENT, CONNECTING VARIOUS NODES (SENDER AND RECEIVER) THROUGH LINES OF CONNECTION.

 

BUS TOPOLOGY


BUS TOPOLOGY IS A NETWORK TYPE IN WHICH EVERY COMPUTER AND NETWORK DEVICE IS CONNECTED TO A SINGLE CABLE.  WHEN IT HAS EXACTLY TWO END POINTS, THEN IT IS CALLED LINEAR BUS TOPOLOGY.

 

FEATURE OF BUS TOPOLOGY

1.       IT TRANSMITS DATA ONLY IN ONE DIRECTION

2.       EVERY DEVICE IS CONNECTED TO A SINGLE CABLE.

 

ADVANTAGES OF BUS TOPOLOGY

1.       IT IS COST EFFECTIVE CABLE REQUIRED IS LEAST COMPARED TO OTHER NETWORK TOPOLOGY.

2.       USED IN SMALL NETWORKS

3.       IT IS EASY TO UNDERSTAND

4.       EASY TO EXPAND JOINING TWO CABLES TOGETHER.

 

DISADVANTAGES OF BUS TOPOLOGY

1.       CABLE FAILS THEN WHOLE NETWORK FAILS.

2.       IF A NETWORK TRAFFIC IS HEAVY OR NODES ARE MORE THE PERFORMANCE OF THE NETWORK DECREASES.

3.       CABLE HAS LIMITED LENGTH

4.       IT IS SLOWER THAN RING TOPOLOGY.

 

 

RING TOPOLOGY


IT IS CALLED RING TOPOLOGY BECAUSE IT FORMS A RING AS EACH COMPUTER IS CONNECTED TO ANOTHER COMPUTER, WITH THE LAST ONE CONNECTED TO THE FIRST.  EXACTLY TWO NEIGHBOR FOR EACH DEVICE.

 

FEATURE OF RING TOPOLOGY

1.       A NUMBER OF REPEATERS ARE USED FOR RING TOPOLOGY WITH LARGE NUMBER OF NODES, BECAUSE OF SOMEONE WANTS TO SEND SOME DATA TO THE LAST NODE IN THE RING TOPOLOGY WITH 100 NODES THEN THE DATA WILL PASS THROUGH 99 NODES T EACH THE 100TH NODE.  HENCE TO PREVENT DATA LOSS REPEATERS ARE USED IN THE NETWORK.

2.       THE TRANSMISSION IS UNIDIRECTIONAL BUT IT CAN BE MADE BIDIRECTIONAL BY HAVING TWO CONNECTORS BETWEEN EACH NETWORK NODE.  IT IS CALLED DUAL RING TOPOLOGY.

3.       IN DUAL RING TOPOLOGY, TWO RING NETWORKS ARE FORMED AND DATA FLOW IS OPPOSITE DIRECTION IN THEM.  ALSO IF ONE RING FAILS THE SECOND RING ACTS AS BACKUP TO KEEP THE NETWORK UP.

4.       DATA IS TRANSFERRED IN SEQUENTIAL MANNER I.E. BIT BY BIT.  DATA TRANSMITTED HAS TO PASS THROUGH EACH NODE OF THE NETWORK TILL THE DESTINATION NODE.

 

ADVANTAGES OF RING TOPOLOGY

 

1.       TRANSMITTING NETWORK IS NOT AFFECTED BY HIGH TRAFFIC OR BY ADDING MORE NODES AS THE ONLY NODES HAVE TOKEN CAN TRANSMIT DATA.

2.       CHEAP TO INSTALL AND EXPAND

 

DISADVANTAGES OF RING TOPOLOGY

 

1.       TROUBLESHOOTING IS DIFFICULT IN RING TOPOLOGY.

2.       ADDING OR DELETING THE COMPUTERS DISTURB THE NETWORKING ACTIVITIES.

3.       FAILURE OF ONE COMPUTER DISTURBS THE WHILE NETWORK.

 

 

STAR TOPOLOGY


IN THIS TYPE OF TOPOLOGY ALL THE COMPUTERS ARE CONNECTED TO A SINGLE HUB THROUGH A CABLE. THIS HUB IS THE CENTRAL NODE AND ALL OTHER NODES ARE CONNECTED TO A CENTRAL NODE.

 

FEATURES OF STAR TOPOLOGY

 

1.       EVERY NODE HAS ITS OWN DEDICATED CONNECTION TO THE HUB.

2.       HUB ACTS AS A REPEATER FOR DATA FLOW.

3.       CAN BE USED WITH TWISTED PAIR, OPTICAL FIBER OR COAXIAL CABLE.

 

ADVANTAGES OF STAR TOPOLOGY

 

1.       FAST PERFORMANCE WITH FEW NODES AND  LOW NETWORK TRAFFIC.

2.       HUB CAN BE UPGRADED EASILY.

3.       EASY TO TROUBLESHOOT.

4.       EASY TO SETUP AND MODIFY.

5.       ONLY THAT NODE IS AFFECTED WHICH HAS FAILED, REST OF THE NODES CAN WORK SMOOTHLY.

 

DISADVANTAGES OF STAR TOPOLOGY

 

1.       COST OF INSTALLATION IS HIGH

2.       EXPENSIVE TO USE

3.       IF THE HUB FAILS THEN WHOLE NETWORK IS STOPPED BECAUSE ALL THE NODES UPON THE HUB.

4.       PERFORMANCE IS BASED ON THE HUB I.E. IT DEPENDS ON ITS CAPACITY.

 

 

MESH TOPOLOGY


 

IT IS POINT TO POINT CONNECTION TO OTHER NODES OR DEVICES.  ALL THE NETWORK NODES ARE CONNECTED TO EACH OTHER.  MESH HAS  (n(n-1))/2 PHYSICAL CHANNELS TO LINK N DEVICES.  THERE ARE TWO TECHNIQUES TO TRANSMIT DATA OVER THE MESH TOPOLOGY.

 

THEY ARE

1.       ROUTING

2.       FLOODING

 

MESH TOPOLOGY ROUTING

 

IN ROUTING, THE NODES HAVE A ROUTING LOGIC, AS PER THE NETWORK REQUIREMENTS.  THE ROUTING LOGIC TO DIRECT THE DATA TO REACH THE DESTINATION USING THE SHORTEST DISTANCE.  OR ROUTING LOGIC WHICH HAS INFORMATION ABOUT THE BROKEN LINKS, AND IT AVOIDS THOSE LINKS., AND IT AVOIDS THOSE NODES.

WE CAN HAVE ROUTING LOGIC, TO RECONFIGURE THE FAILED NODES.

 

MESH TOPOLOGY FLOODING

 

IN FLOODING, THE SAME DATA IS TRANSMITTED TO ALL NETWORK NODES, HENCE NO ROUTING LOGIC IS REQUIRED.   THE NETWORK IS ROBUST AND IT IS VERY UNLIKELY TO LOOSE THE DATA. BUT IT LEADS UNWANTED LOAD OVER THE NETWORK.

 

TYPES OF MESH TOPOLOGY

 

PARTIAL MESH TOPOLOGY

IN THIS TOPOLOGY SOME OF HE SYSTEMS ARE CONNECTED IN SOME FASHION AS ESH TOPOLOGY BUT SOME DEVICES ARE ONLY ONNECTED TO TWO OR THREE DEVICES.

 

FULL MESH TOPOLOGY

EACH AND EVERY NODES ARE CONNECTED TO EACH OTHER.

 

FEATURES OF MESH TOPOLOGY

 

1.       FULLY CONNECTED

2.       ROBUST

3.       NOT FLEXIBLE

 

 

ADVANTAGES OF MESH TOPOLOGY

 

1.       EACH CONNECTION CAN CARRY ITS OWN DATA LOAD.

2.       IT IS ROBUST

3.       FAULT IS DIAGNOSED EASILY

4.       PROVIDES SECURITY AND PRIVACY

 

DISADVANTAGES OF MESH TOPOLOGY

 

1.       INSTALLATION AND CONFIGURATION IS DIFFICULT

2.       CABLING COST IS MORE

3.       BULK WIRING IS REQUIRE

 

TREE TOPOLOGY


 

IT HAS ROOT NODE AND ALL OTHER NODES ARE CONNECTED TO IT FORMING HIERARCHY  IT IS ALSO CALLED HIERARCHICAL TOPOLOGY.  IT SHOULD AT LEAST THREE LEVELS TO THE HIERARCHY.

 

FEATURES OF TREE TOPOLOGY

 

1.       IDEAL IF WORKSTATION ARE ARRANGED IN GROUP

2.       USED IN WIDE AREA NETWORK.

 

 

ADVANTAGES OF TREE TOPOLOGY

 

1.       EXTENSION OF BUS AND STAR TOPOLOGY

2.       EXPANSION OF NODES IS POSSIBLE AND EASY

3.       EASILY MANAGED AND MAINTAINED

4.       ERROR DETECTION IS EASILY DONE

 

DISADVANTAGES OF TREE TOPOLOGY

 

1.       HEAVILY CABLED

2.       COSTLY

3.       IF MORE NODES ADDED MAINTENANCE IS DIFFICULT

4.       CONTROL HUB FAILS NETWORK FAILS

 

 


Tuesday, August 18, 2020

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 noise introduced into physical communication medium or electric wires changes bit values from 0 to 1 or vice versa.  An error detection code can be used to detect errors during transmission.  The detected error cannot be corrected but its presence is indicated.  The usual procedure is to observe the frequency of errors.  If errors occur only once a while, at random and without a pronounced effect on the overall information transmitted then either nothing is done or particular erroneous message is transmitted again.  If errors occur so often to distort the meaning of the received information, the system is checked for malfunction.  A parity bit is added at the end of the message to make the message to become odd if it is even or make it even if it is odd.  I am talking about the binary numbers generated by the software from the message that is passed ,  during transfer of information from one location to another, the parity bit is handled as follows.  In the sending end, the message (in this case the first four bits) is applied in “parity generation” where the parity bit is generated.  The message as well as the parity bit is transferred to its destination.  In the receiving end the message which is converted to binary numbers are taken with along with the parity bit into the parity bit network to check the parity bit.  An error is generated if the parity bit is not the same as generated or let’s says an error is detected if the checked parity does not correspond to the adopted one.  The parity method detect the presence of one, three, or any old combination of errors.   An even combination of errors is undetectable. 

 

ALPHANUMERIC CODES:

 

Many applications of digital computers required the handling of data that consist not only of numbers, but also of letters.  For instance, an insurance company with millions of policy holders may use a digital computer to process its files.  To represent any policy holders may use a digital computer to process its files.  To represent the policy holders name in binary form, it is necessary to have  binary code for that alphabet.  In addition, the same binary code must represent decimal numbers and some other special characters.  An alphanumeric (sometimes abbreviated alphanumeric) code is a binary code of a group of elements consisting of ten decimal digits, the 26 letters of the alphabet and a certain number of special symbols such as $.  The total number of elements in an alphanumeric group is greater than 36.  Therefore, it must be coded with a minimum of six bits (26 = 64, but 25 = 32 is insufficient).  One possible arrangement of a six bit alphanumeric code is also called internal code.  The need to represent more than 64 characters (the lowercase letters and special control characters for the transmission of digital information) gave rise to seven- and eight-bit alphanumeric codes.  One such code is known as ASCII( American Standard Code For Information Interchange);  another is known as EBCDIC(Extended Binary Code Decimal Interchange Code).  Let us discuss something about ASCII codes : In ASCII code listed in various books  consists of seven bits,  but is for all practical purposes an eight bit code , because an eight bit is used as parity.  When discrete information is transferred through a punch card, the alphanumeric characters is used 12bit binary code.  A punch card contains 80 columns and 12 rows.  The 12 rows are marked starting from the 12 the row and preceding backwards such as 12, 11, 10, 9, 8 and so on punches.  The first three are called zone punch and last nine are called numeric punch.  The 12 bit card code can be seen through internet searches.

 

 

REFLECTED CODE:

 

Digital systems can be designed to process data in discrete form only.  Many physical systems supply continuous output data.  These data must be converted into digital or discrete form they are applied to a digital system.  Continuous or analog information is converted into digital form by means of analog to digital converter.  It is sometimes convenient to use the reflected code to represent  digital data converted from analog data.  The advantage of the reflected code over pure binary numbers is that a number in the reflected code changes by only one bit as it proceeds from one number to the next.  A typical application of the reflected code occurs when the reflected code occurs  when the analog data are represented by a continuous change of a shaft position.  The shaft is partitioned into a segments, and each segment is assigned a number.  If theadjacent segments are made to correspond to adjacent reflected code numbers, ambiguity is reduced when detection is sensed in the line that separates any two segments.   

 

Friday, March 13, 2020

IS DIGITAL COMPUTERS ARE VALUABLE?


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DIGITAL COMPUTERS

Today computers are used extensively in every day life.  It is used in basic as well as industrial, scientific and commercial purposes.  Our space program would not have been well developed without the real time monitoring of the machine of the spacecraft which was going to land on moon or any other planet of the scheduled program or launching of satellites on the orbit of earth. This is the scientific purpose i told you about while it has commercial purposes.  Like automatic data processing which the business enterprise uses.

It has many works in educational purposes for example multiple choice question answers can be checked without any error and then the results can be printed out automatically with the help of the printer which is connected to the digital computer.

  Digital computer are also used in air traffic control to control the aviation industry to help them control the planes by sending them data about the distance between the planes and the ground as well as about other planes coming their way.  Digital computers are heavily used because of its simplicity and generality. 

 Generality because it takes data as input for manipulation of input to get a desired output.  In simple words it can follow a sequence of instruction called a program that operates on a given data, then the programmer can change the programs according to his need.

The general purpose digital computers is best known example of a digital system.  Other examples include telephone switching exchanges, digital voltmeter, frequency counters and calculating machines.  I am telling about this machines because these machines take about inputs and give desired outputs. 

 These inputs can be said as discrete elements because most generally there are electrical signals, electrical impulses, frequency counters, decimal digits letters of an alphabet.  Characteristics of digital system is manipulation of discrete elements of information. 

 Such alphabet, arithmetic operations punctuation marks or any other set of meaningful symbols.  The juxtaposition of discrete elements of information represents a quantity of information.  For example the word dog  is formed by letters d , o, and g.  The letter 237 form the number and etc. 

 Thus a sequence of the letter form a language that conveys information.  Early the computer were used only for calculation.  From this case the discrete element of information used are the digits.  From this came the word digital computers.


Thursday, March 12, 2020

LOGIC OF COMPUTERS


LOGIC OF COMPUTER IN PAPER AS WELL AS PRACTICAL USE


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We always use logic in every day matters, so do the machines.  But we were taught by experiences we count and the people we trust and these things matters most because it will help in dark times.  But to make the machine understand the logic is very hefty work. But this is certainly not impossible.  In order to understand logic we use integrated circuits.  But to do this we need to design the integrated circuits on paper.  This requires certain rules of algebra.  This I am going talk about the rule of an algebra called the duality principal.

It states that every algebraic expression deducible from the postulates of Boolean algebra remains valid if the operators and identity elements are interchanged.  In a two value Boolean algebra, the identity elements and the elements of the set B are same 1 and 0.  The duality principal has many applications.  If the dual of an algebraic expression is desired, we simply interchange OR and AND operators and replace 1’s by 0’s and 0’s and 1’s.

I am going to show some of the rules below which some are Boolean algebra theorems and some are postulates, there Is some problem because the notation contains some . which is sometimes misunderstood.  Now the theorems and postulates listed are the most basic relationships in Boolean algebra.  The theorems, like the postulates are listed in pairs each relation is dual of the one paired it.  The postulates are basic axioms of the algebraic and need no proof.  The theorems must be proven from the postulates.  The proof of the theorem with one variable is presented below.  At the right is listed the number of postulates which justifies each step of the proof.

Postulate 2
(a) x + 0 = x
(b) x.1 = x
Postulate 5
(a) x+ x’=1
(b) x*x’ = 0
Theorem 1
(a) x + x=x
(b)x*x=x
Theorem 2
(a)x + 1= 1
(b)x*0=0
Theorem 3, involution
(a)(x’)’ =x

Postulate 3 commutative
(a) x + y = y + x
xy = yx
Theorem 4 associative
(a) x + (y + z) = (x + y) + z
(b) x(yz) = (xy)z
Postulate 4 Distributive
(a)x(y+z) = xy +xz
(b) x + yz=(x + y)(x + z)
Theorem 5, DeMorgan
(a)(x+y)’ = x’y’
(b) (xy) = x’ + y’
Theorem 6, Absorption
(a) x + xy = x
(b) x(x+y) = x





THEORITICAL ALGEBRA IN COMPUTERS


ALGEBRA IN COMPUTERS
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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.

    





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