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The International Standard Book Number System

ISBN Users' Manual
International Edition Sixth Edition

International ISBN Agency London 2012

The most up-to-date version of the ISBN Users’ Manual will be found on the website of the International ISBN Agency: http://www.isbn-international.org

ISBN 978-92-95055-02-5 ©2012 by International ISBN Agency, London, UK Sixth Edition Permission is granted for the reprinting of any material in this brochure, subject to due acknowledgement of the source and to a copy, preferably electronic, being sent to the International ISBN Agency.

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Contents
1. Background ......................................................................................................... 5 2. Benefits of the ISBN ............................................................................................ 6 3. The Function and Scope of the ISBN ................................................................. 6 4. Structure of the ISBN .......................................................................................... 8 4.1 Prefix element .................................................................................................. 9 4.2 Registration group element .............................................................................. 9 4.3 Registrant element ........................................................................................... 9 4.4 Publication element .......................................................................................... 9 4.5 Check digit ....................................................................................................... 9 5. Application of ISBN ........................................................................................... 10 5.1 General .......................................................................................................... 10 5.2 Changes to publications ................................................................................. 10 5.3 Facsimile reprints ........................................................................................... 10 5.4 Publications in different product forms ............................................................ 10 5.5 Loose-leaf publications................................................................................... 10 5.6 Multi-volume publications ............................................................................... 10 5.7 Backlist .......................................................................................................... 11 5.8 Collaborative publications .............................................................................. 11 5.9 Publications sold or distributed by agents....................................................... 11 5.10 Acquisition of one publisher by another ........................................................ 11 5.11 Acquisition of complete stock of and rights in publication ............................. 11 5.12 Publishers with more than one place of publication ...................................... 11 5.13 Register of ISBNs and accompanying metadata .......................................... 12 5.14 ISBNs can never be reused.......................................................................... 13 6. ISBN for Electronic Publications and Educational/Instructional Software ... 13 6.1 ISBN for eligible electronic publications .......................................................... 13 6.2 ISBN for eligible software products................................................................. 13 6.3 Principles for assignment of ISBN to electronic publications........................... 14 7. ISBN for Print-on-Demand Publications .......................................................... 16 8. Location and Display of the ISBN on Publications ......................................... 16 8.1 General .......................................................................................................... 16 8.2 ISBN in bar coded form .................................................................................. 17 8.3 Five-digit add-on code .................................................................................... 18 8.4 Algorithm for generating the ISBN and EAN.UCC bar code ........................... 18 9. Administration of the ISBN System ................................................................. 18 9.1 General .......................................................................................................... 18 9.2 International administration ............................................................................ 18 9.3 ISBN registration agencies ............................................................................. 19 9.4 Publisher administration ................................................................................. 20

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10. Non-participating Publishers.......................................................................... 20 11. ISBN and GS1 .................................................................................................. 21 12. ISBN and Other Identifiers .............................................................................. 21 12.1 DOI .............................................................................................................. 21 12.2 ISBN-A ......................................................................................................... 21 12.3 GTIN ............................................................................................................ 22 12.4 URN ............................................................................................................. 22 12.5 ISAN ............................................................................................................ 22 12.6 ISMN ............................................................................................................ 23 12.7 ISRC ............................................................................................................ 23 12.8 ISSN ............................................................................................................ 23 12.9 ISTC............................................................................................................. 24 12.10 ISWC.......................................................................................................... 24 12.11 ISNI ............................................................................................................ 25 13. ONIX for Books ................................................................................................ 25 14. Publications ..................................................................................................... 26 15. Frequently Asked Questions About the ISBN System .................................. 26 APPENDIX 1 Check digit calculation and distribution of ranges ....................... 27 A1.1 Calculating the Check Digit .......................................................................... 27 A1.2 Distribution of ranges ................................................................................... 28

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1. Background
The question of the need for and feasibility of an international numbering system for books was first discussed at the Third International Conference on Book Market Research and Rationalisation in the Book Trade, held in November 1966 in Berlin. At that time, a number of European publishers and book distributors were considering the use of computers for order processing and inventory control, and it was evident that a prerequisite for an efficient automated system was a unique and simple identification number for a published item. The system that fulfilled this requirement and became known as the International Standard Book Number (ISBN) system was developed out of the book numbering system introduced in the United Kingdom in 1967 by J. Whitaker & Sons, Ltd., and in the United States in 1968 by R. R. Bowker. At the same time, the International Organization for Standardization (ISO) Technical Committee 46 on Information and Documentation set up a working party to investigate the possibility of adapting the British system for international use. During 1968 and 1969 several meetings took place between representatives from various European countries and the United States, and a report was circulated to all countries belonging to ISO. As a result of these meetings the International Standard Book Number (ISBN) was approved as ISO standard 21081 in 1970. In 1992 the third edition of this standard replaced the second edition of 1978. The purpose of the international standard is to coordinate and standardise the international use of ISBNs to identify uniquely one publication or edition of a publication published by one specific publisher in one specific format. The original standard has been revised as book and book-like items begin to appear in new forms of media, and the system is in use today in over 160 countries. In 2001, a working group was formed to revise the standard and draft its fourth edition. It increased the length of the ISBN from 10 to 13 digits, incorporating the 3-digit prefixes provided by GS1 (formerly EAN International and the Uniform Code Council), thereby increasing the numbering capacity of the system and making it completely compatible with the GS1 GTIN-13 (see section11). The new version of the standard also specified the metadata that should be supplied at the time of ISBN assignment, developed rules for the administration and governance of the system and specified the registration authority for the standard. This manual explains the functioning of the system and the steps necessary to ensure that ISBNs are correctly assigned, and provides particular guidance on the assignment of ISBNs to digital publications.

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Obtainable from national standards organisations.

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2. Benefits of the ISBN
 The ISBN is a unique international identifier for monographic publications; assigning a number replaces the handling of long bibliographic descriptive records, thereby saving time and staff costs and reducing copying errors. Correct use of the ISBN allows different product forms and editions of a book, whether printed or digital, to be clearly differentiated, ensuring that customers receive the version that they require. The ISBN facilitates compilation and updating of book-trade directories and bibliographic databases, such as catalogues of books-in-print. Information on available books can be found easily. Ordering and distribution of books is mainly executed by ISBN; this is a fast and efficient method. The ISBN is machine-readable in the form of a 13-digit EAN-13 bar code. This is fast and avoids mistakes. The ISBN is required for the running of electronic point-of-sale systems in bookshops. Many publishing and supply chain systems are based on ISBN The accumulation of sales data is done by the ISBN. This enables the varying successes of different product forms and editions of publications to be monitored, as well as enabling comparisons between different subject areas and even different publishing houses. The national lending right in some countries is based on the ISBN. Such schemes enable authors and illustrators to receive payments proportionate to the number of times that their books are lent out by public libraries.





    



3. The Function and Scope of the ISBN
Recognised in more than 160 countries throughout the world, the International Standard Book Number is a short and clear identifier that is potentially machine-readable. The ISBN denotes a particular monographic publication uniquely and should, therefore, be associated with it from early production stages. An essential instrument in production, distribution, sales analysis, and bibliographic data storage systems in the book trade, ISBN is also of vital importance to library information management. However, where a product is appropriate to another specific numbering system (such as continuing resources and ongoing integrating resources which qualify for the ISSN, and printed music which qualifies for the ISMN), then that system must be used. If appropriate, such identifiers should be used in conjunction with the ISBN. Further information on other types of identifier is provided in section 12. ISBNs are assigned to monographic publications, including related products such as publications available as sets or as completed series that are available to the public, whether those publications and related products are available on a gratis basis or to purchase. In addition, individual sections (such as chapters) of monographic publications

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or issues or articles of continuing resources that are made available separately may also use the ISBN as an identifier. Provided that the publication qualifies for ISBN assignment, it is of no importance in what physical form the content is documented and distributed; however, each product form should be identified separately. Examples of types of monographic publications to which an ISBN shall be assigned are:             Printed books and pamphlets Braille publications Publications that are not intended by the publisher to be updated regularly or continued indefinitely Individual articles2 or issues of a particular continuing resource (but not the continuing resource in its entirety) Maps Educational/instructional films, videos and transparencies Audiobooks on cassette, or CD, or DVD (talking books) Electronic publications either on physical carriers (such as machine-readable tapes, diskettes, or CD-ROMs) or on the Internet (for download or streaming) Digitised copies of printed monographic publications Microform publications Educational or instructional software Mixed media publications (where the principal constituent is text-based)

Some examples of the types of material to which an ISBN shall NOT be assigned are:             Continuing resources3 treated in their entirety as bibliographic entities (individual issues may qualify for ISBNs) Abstract entities4 such as textual works and other abstract creations of intellectual or artistic content Ephemeral printed materials such as advertising matter and the like Printed music Art prints and art folders without title page and text Personal documents (such as an electronic curriculum vitae or personal profile) Greetings cards Music sound recordings Software that is intended for any purpose other than educational or instructional Electronic bulletin boards Emails and other electronic correspondence Games

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Where individual articles are made available separately by a publisher, they qualify as monographic publications and shall be assigned an ISBN. This does not apply in the case of offprint or preprint copies that are ordered by the author(s) of the article for their own distribution purposes.
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A publication that is issued over time with no predetermined conclusion. Such a publication is usually issued in successive or integrating issues, which generally have numerical and/or chronological designations. Typical examples include serials such as newspapers, periodicals, journals, magazines, etc., and integrating resources such as updating loose-leaf publications and updating websites.
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For example, each separate product form of the novel The Old Man and the Sea is eligible for an ISBN, but the novel itself, as an abstract textual work, shall not be assigned an ISBN.

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Where one qualifying product is made available accompanied by a secondary item that does not itself qualify for ISBN, then one ISBN should be used to identify the items in combination, and another ISBN to identify the qualifying product if it is also available separately. However, as it is outside the scope of ISBN, an ISBN shall not be used to identify the secondary element if it too is made available separately. Some identifiers such as the ISSN and ISMN have precise rules as to the scope of materials that qualify for assignment whereas some other identifiers, such as GTIN-13 for trade items, may be used across very broad product ranges. As the ISBN is now fully compatible with GTIN-13 this makes it more convenient for retailers to sell products of related interest, that do not qualify for ISBN and which use the GTIN-13 instead, without having to adapt their systems. For further information including clarification about whether or not a particular type of product may qualify, please contact your local ISBN registration agency. For information about other types of identifier and their applicability, consult Section 12. ISBN and Other Identifiers.

4. Structure of the ISBN
Since 1 January 2007, national ISBN agencies only provide ISBNs that consist of 13 digits, comprising the following elements:      Prefix element Registration group element Registrant element Publication element Check digit

When printed, the ISBN is always preceded by the letters “ISBN”. Note: In countries where the Latin alphabet is not used, an abbreviation in the characters of the local script may be used in addition to the Latin letters “ISBN”. The ISBN is divided into five elements, three of them of variable length; the first and last elements are of fixed length. The elements must each be separated clearly by hyphens or spaces when displayed in human readable form: ISBN 978-0-571-08989-5 or ISBN 978 0 571 08989 5 Note: The use of hyphens or spaces has no lexical significance and is purely to enhance readability. The number of digits in the second, third, and fourth elements of the ISBN (registration group element, registrant element, publication element) varies. The length of the registration group element and of the registrant element is relative to the anticipated publishing output of the registration group or registrant. When these elements are short in length it indicates that the output of the registration group or the registrant (or both) is expected to be a large number of publications.

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4.1 Prefix element
The first element of the ISBN is a three-digit number that is made available by GS1, formerly EAN International. Prefixes that have already been made available by GS1 are 978 and 979, but there may be a further prefix allocation made in the future as required to ensure the continued capacity of the ISBN system. EXAMPLE: 978

4.2 Registration group element
The second element of the ISBN identifies the country, geographical region, or language area participating in the ISBN system. Some members of the ISBN system form language areas (e.g., registration group number 3 = German language group within prefix element 978); others form regional units (e.g., registration group number 982 = South Pacific within prefix element 978). The length of this element varies but may comprise up to 5 digits. Registration group elements are allocated by the International ISBN Agency. EXAMPLE: 978-0

4.3 Registrant element
The third element of the ISBN identifies a particular publisher or imprint within a registration group. The length of this element varies in direct relationship to the anticipated output of the publisher and may comprise up to 7 digits. Publishers with the largest expected title outputs are assigned the shortest registrant elements and vice versa. Potential registrants apply to the ISBN group agency responsible for the management of the ISBN system within the country, region, or language group where they are based in order to be assigned registrant elements that are unique to them. Once they have exhausted the allocation of ISBNs that is linked to their registrant element, they may be assigned an additional registrant element providing further allocations of ISBNs. EXAMPLE: 978-0-11

4.4 Publication element
The fourth element of the ISBN identifies a specific edition of a publication by a specific publisher. The length of this element varies in direct relationship to the anticipated output of the publisher concerned and may comprise up to 6 digits. Publishers with the largest expected title outputs are assigned the longest publication elements and vice versa. To ensure that the correct length of the ISBN is maintained, blank digits are represented by leading zeros. EXAMPLE 978-0-11-000222

4.5 Check digit
The fifth element of the ISBN is the check digit. This is calculated using a modulus 10 algorithm. (See Appendix 1 for calculation method or contact your local ISBN agency for advice).

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5. Application of ISBN
5.1 General
A separate ISBN shall be assigned to each separate monographic publication or separate edition or format of a monographic publication issued by a publisher. A separate ISBN shall be assigned to each different language edition of a monographic publication.

5.2 Changes to publications
A separate ISBN shall be assigned if there have been significant changes to any part or parts of a publication. A separate ISBN shall be assigned if there has been a change to the title and/or to the sub-title of a publication. A change to the cover design or colour or to the price of a monographic publication does not require a separate ISBN. Minor changes in an edition (e.g. corrections to misprints) do not require a separate ISBN.

5.3 Facsimile reprints
A separate ISBN shall be assigned to a facsimile reprint when it is produced by another publisher or republished under the imprint of a different publisher. A separate ISBN shall also be assigned if the same publication is published under a different imprint name by the same publisher. If a book is scanned and digitised by an organisation other than the original publisher (e.g. by a library) then the scanned and digitised version shall be assigned a separate ISBN by the new producer provided that version is made available to the public (as opposed to being purely for archival purposes for example).

5.4 Publications in different product forms
Different product forms of a publication (e.g., hardback, paperback, Braille, audiobook, online electronic publication) require separate ISBNs. Where electronic publications are made available in different file formats each separately available format shall be assigned a unique ISBN. (See section 6.3 for further information on dealing with e-book file formats).

5.5 Loose-leaf publications
An ISBN should be assigned to a finite loose-leaf publication — that is, a loose-leaf publication not intended to continue indefinitely. An ISBN should not be assigned to either a loose-leaf publication that is continually updated (integrating resource) or to the individual updated sections.

5.6 Multi-volume publications
Publications may comprise more than one volume, and in these cases an ISBN must be assigned to cover the entire set. Where individual volumes of the set are available separately, each volume must be assigned a unique ISBN to identify it. The verso of the title page (or an equivalent position in a non-print version) in each case should clearly display the ISBN for the set as a whole as well as the ISBN for that particular volume. Even if the multiple volume publication will only be available as a complete set, the assignment of a separate ISBN to each individual volume is still recommended. Doing so will facilitate various stages of transaction processing, including the handling of shipments

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when not all volumes are simultaneously published or distributed and the supply of replacements in the case of damaged copies.

5.7 Backlist
A publisher is required to number all backlist publications and publish the ISBNs in any catalogues that the publisher produces whether these catalogues are in print or electronic format. The ISBN must also appear in the first available reprint or reissue of a backlist title.

5.8 Collaborative publications
A publication issued as a joint imprint with other publishers is usually assigned an ISBN by the publisher(s) in charge of distribution. However, it is permissible for each of the co-publishers to assign its own ISBN and display each of them on the copyright page. In such cases, only one of these ISBNs shall be displayed as a bar code on the publication.

5.9 Publications sold or distributed by agents
(Below, b and d apply only to countries that are not yet participating in the system.) a. As the ISBN standard states, a particular edition published by a particular publisher receives only one ISBN. This ISBN must be retained no matter where, or by whom, the publication is distributed or sold. A publication imported by an exclusive distributor or sole agent from an area that is not in the ISBN system and has no ISBNs assigned to it may be assigned an ISBN by the exclusive distributor. Publications imported by an exclusive distributor or sole agent to which a new title page, bearing the imprint of the exclusive distributor, has been added in place of the title page of the original publisher are to be given a new ISBN by the exclusive distributor or sole agent. The ISBN of the original publisher should also be given. A publication imported by several distributors from an area not in the ISBN system and that has no ISBNs assigned to it may be assigned an ISBN by the group agency responsible for those distributors.

b.

c.

d.

5.10 Acquisition of one publisher by another
A publisher acquiring another publishing house can continue to use the unassigned ISBNs from the originally assigned registrant element. The national ISBN Agency responsible for that registrant element should be informed of the change of ownership of the registrant element.

5.11 Acquisition of complete stock of and rights in publication
A publisher acquiring the complete stock of and rights to a publication(s) can continue to use the originally assigned ISBN until the new company reprints or reissues the publication under that company’s own ISBN registrant element.

5.12 Publishers with more than one place of publication
A publisher operating in several places that are listed together in the imprint of a publication must assign only one ISBN to that publication. A publisher operating separate and distinct offices or branches in different places may have a registrant element for each office or branch. However, each publication is to be assigned only one ISBN by the office or branch responsible for the publication.

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5.13 Register of ISBNs and accompanying metadata
It is the responsibility of the publishers to inform their group agency, or the organisation responsible for the maintenance of publication registration, of the ISBNs that will be assigned to forthcoming publications. The information shall include some minimum metadata (descriptive) elements and shall be compatible with the ONIX for Books product information standards maintained by EDItEUR and its associated organisations: Data element
ISBN Product form

Comments
In the 13 digit ISBN format, without spaces or hyphens Coding which indicates the medium and/or format of the product

ONIX 3 element(s)

Although not mentioned explicitly in the ISBN User Manual, physical measurements may also differentiate between two physical products otherwise in the same binding and format. Similarly, for digital products, different licence terms (usage constraints) or operating system requirements may differentiate between two otherwise identical products. Title Series Contributor Edition The title of the publication, together with sub-title or other title elements where applicable Series title and enumeration when applicable Contributor role code(s) and contributor name(s) Edition number (for editions after the first), type, and statement

composite composite composite [Identifier (ISNI) optional] composite composite [Identifier (ISNI) optional] composite [Identifier (ISNI) optional]

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...Computer A computer is a programmable machine that receives input, stores and manipulates data, and provides output in a useful format. A computer can process data, pictures, sound and graphics. They can solve highly complicated problems quickly and accurately. Block Diagram Input Unit: Computers need to receive data and instruction in order to solve any problem. Therefore we need to input the data and instructions into the computers. The input unit consists of one or more input devices. Keyboard is the one of the most commonly used input device. Other commonly used input devices are the mouse, floppy disk drive, magnetic tape, etc. All the input devices perform the following functions.  Accept the data and instructions from the outside world.  Convert it to a form that the computer can understand.  Supply the converted data to the computer system for further processing. Storage Unit: The storage unit of the computer holds data and instructions that are entered through the input unit, before they are processed. It preserves the intermediate and final results before these are sent to the output devices. It also saves the data for the later use. Memory Size: All digital computers use the binary system, i.e. 0’s and 1’s. Each character or a number is represented by an 8 bit code. The set of 8 bits is called a byte. A character occupies 1 byte space. A numeric occupies 2 byte space. Byte is the space occupied in the memory. The size of the primary storage...

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...COMPUTER HARDWARE AND COMPONENTS COMPUTER HARDWARE AND COMPONENTS Computer Basics     Equipment (Hardware) COMPUTER | A machine that processes information and performs computations. | Tower or Desktop | The "box" or case that holds the parts that make up a computer:  CPU, hard disk drive, floppy drive, memory chips, power supply, interface cards, etc. Click here to learn more. | |      CPU | Central Processing Unit, or "brains" of the computer | Monitor | An output display device (looks similar to a TV) in a computer system.  You see information on the monitor's screen. | |      Screen | The viewing area on a monitor or the information or image displayed. | | | | Disk Drive | A device that reads data from (input) or records data onto a disk for storage (output). |     Floppy  | Floppy Drive | . 3-1/2" Floppy Disk |     Hard Drive | The main device that a computer uses to store information. Most computers come with a hard drive, called drive C, located inside the computer case. |     CD-ROM | ROM means Read-Only-Memory - you can only "read" information, not save. A CD can store a large amount of data including documents,  photographs, software, and music (about 20 songs) | | CD Drive | Compact Disk | | CD-R A CD-Recordable drive can put data onto a disk in just one session, and then is "closed" - one "burn" only - you can't add to it after you create it.  | CD-RW A CD-ReWritable drive can be written onto more than once - similar...

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...(introduction) What is a Computer? B. History of computers C. (thesis) Types of computer 4.1 Supercomputer 4.2 Mainframe 4.3 Workstation 4.4 The Personal Computer or PC 4.5 Microcontroller 4.6 Server D. Hardware & software 5.7 hardware 5.8 software 5.9 firmware E. Basic operations 6.10 input 6.11 output 6.12 processing 6.13 storage F. Names for different sizes of data 7.14 Bit 7.15 Byte 7.16 kB 7.17 MB 7.18 GB 7.19 TB 7.20 PB G. Measurement of data speed 8.21 Mbps 8.22 Gbps H. Purpose of computer 9.23 performing calculations 9.24 storing data 9.25 retrieving data 9.26 processing data INTRODUCTION: WHAT COMPUTER IS? I. What is computer? A computer is a "box" that you put some "stuff" in, the box does "stuff" with it, and then the box has some way of showing the world what it's done. The stuff you put into a computer is called data, and gets into the computer using the input. Data is simply a form of information. You can put data into a computer by your keyboard, a mouse, a trackpad, a camera, an infrared sensor; anything that will give the computer more information about the world around it. Based on what information the computer has gotten, it can decide to do stuff with it. What the computer does with information is known as processing. A computer will process information...

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...types of computers, the computers are classified according to their functions and capabilities, as: Sample essay analysis ... Types of Computers - College Essay - Scodger - StudyMode.com www.studymode.com › ... › Computers & Internet › Computer Hardware‎ Types of computers. Firstly, what is a computer? Well, a modern computer is typically an electronic or digital device that manipulates data. Computers can ... Types of Computers - Term Papers - Maliktaimurarif www.termpaperwarehouse.com › Computers and Technology‎ May 9, 2012 - Read this essay on Types of Computers . Come browse our large digital warehouse of free sample essays. Get the knowledge you need in ... History of Computers Essay - Custom Writing Service www.customwritings.com/blog/...essays/history-computers-essay.html‎ You can order a custom essay, term paper, research paper, thesis or dissertation on History of Computers topics at our professional custom essay writing service ... Computer Technology Essay - Custom Writing Service www.customwritings.com/blog/...essays/computer-technology-essay.html‎ Free sample essay on Computer Technology: Since the beginning of time ... Computers play a significant role in the school system as well. ... Categories. Essay of computer and its uses - WikiAnswers wiki.answers.com › ... › Categories › Technology › Computers‎ ... Categories > Technology > Computers > Essay of computer and its uses? ... computer is a...

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...Computers Today’s generation could never ever imagine in their wildest dreams about the world, ages before, when there were no computers or any other technologies. So much we have advanced that now every information is just a click away and is in your hands 24/7. All this advancement was possible only with the introduction of a small device called the “Computer”. Basically, computer is a device that accepts the message by the imputer and processes this message and stores the information at the storage devices and later gives an output of the message through the output devices. A simple explanation of the computer. Normally, a computer consists of a processing unit called the Central Processing Unit or the CPU and a form of memory. In the years between 1940 and 1945 were the first electronic digital computers developed. The initial sizes were as big as a room and consumed power as much as today’s personal computers. Initially, computer was related to a person who carries out calculations or computations and as such the word computer was evolved in 1613 and continued till the end of 19thcentury. Later it as re-described as a machine that carries computations. The early computers were limited in their functions. It was the fusion of automatic calculation and programmability that produced the first computers that were recognized in 1837. Charles Babbage in 1837 was the first to introduce and design a fully programmed mechanical computer, his analytical engine. Due to limited finances...

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...The computer is the most wonderful gift of science to the modern man. The computer can do all the works of man. Thus, after the invention of computer, the gap between man and machine has been bridged up. The dictionary meaning of the word "Computer" is an electronic calculating machine. It is derived from the word compute which means to reckon. But the function of the computer has expanded beyond the act of reckoning. Though a machine, it contains and provides innumerable information's and artificial intelligence of a very high order. It may seem strange, but it is true that the memory and intelligence of a computer can surpass those of a living human being. The mechanism of the computer is very simple. Information processing is the essence of computing. It is a data based machine. The data is fed into the machine. The machine is manipulated and then the due information is retrieved. Computer was invented due to the pressures of World War-II which witnessed the use of such sophisticated weapons as night bombers, submarines, and long range guns on ships and tanks, etc. The defenders have to fight back by shooting at targets and those targets of the enemy can be located by radar. Radar can inform not only about the location of the enemy but also about the direction and the speed of the enemy weapons. Detailed mathematical calculations are necessary to find out these things accurately. Firing tables are required by the front line soldiers. Thus the necessity of calculations...

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