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{{for|reader help on ISBNs|Help:ISBN}}
{{Use dmy dates|date=March 2013}}
[[File:EAN-13-ISBN-13.svg|thumb|A 13-digit ISBN, 978-3-16-148410-0, as  represented by an [[International Article Number (EAN)|EAN-13 bar code]].]]
The '''International Standard Book Number''' ('''ISBN''') is a unique<ref>Occasionally, publishers erroneously assign an ISBN to more than one title — the first edition of ''[[The Ultimate Alphabet]]'' and ''The Ultimate Alphabet Workbook'' have the same ISBN, 0-8050-0076-3. Conversely, books are published with several ISBNs: A ''German'', second-language edition of ''[[Emil und die Detektive]]'' has the ISBNs 87-23-90157-8 ([[Denmark]]), 0-8219-1069-8 (United States), 91-21-15628-X ([[Sweden]]), 0-85048-548-7 (England) and 3-12-675495-3 (Germany).</ref><ref>In some cases, books sold only as sets share ISBNs. For example, the [[Vance Integral Edition]] used only 2 ISBNs for 44 books.</ref> numeric commercial [[book]] [[identifier]] based upon the 9-digit '''Standard Book Numbering''' ('''SBN''') [[code]] created by [[Gordon Foster]],  Emeritus Professor of Statistics at [[Trinity College, Dublin]],<ref>Gordon Fosters original 1966 report can be found at  [https://web.archive.org/web/20110430024722/http://www.informaticsdevelopmentinstitute.net/isbn.html Informaticsdevelopmentinstitute.net]</ref> for the booksellers and stationers [[WHSmith]] and others in 1965.<ref name="history">{{citation | url = http://www.isbn.org/standards/home/isbn/international/history.asp | title = History | publisher = ISBN.org}}</ref>


The 10-digit ISBN format was developed by the [[International Organization for Standardization]] (ISO) and was published in 1970 as international standard ISO 2108.<ref name="history"/> (However, the 9-digit SBN code was used in the United Kingdom  until 1974.) An SBN may be converted to an ISBN by prepending the digit "0". ISO has appointed the International ISBN Agency as the registration authority for ISBN worldwide and the ISBN Standard is developed under the control of ISO Technical Committee 46/Subcommittee 9 [[TC 46/SC 9]]. The [[International Organization for Standardization|ISO]] on-line facility only refers back to 1978.<ref>{{citation | format = PDF | url = http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=6897 | title = ISO 2108:1978 | publisher = ISO}}</ref>


Since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with "[[Bookland]]" [[European Article Number|EAN]]-13s.<ref>{{citation | url = http://www.lac-bac.gc.ca/iso/tc46sc9/isbn.htm | title = Frequently Asked Questions about the new ISBN standard from ISO | author = TC 46/SC 9 | publisher = LAC‐BAC | place = CA}}</ref>
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Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure; however, this can be rectified later.<ref>Bradley, Philip (1992). "{{PDFlink|[http://www.theindexer.org/files/18-1/18-1_025.pdf Book numbering: The importance of the ISBN]|245KB}}. ''The Indexer.'' '''18''' (1): 25&ndash;26.</ref>
 
Another identifier, the [[International Standard Serial Number]] (ISSN), identifies periodical publications such as [[magazine]]s.
 
==Overview==
An ISBN is assigned to each edition and variation (except reprintings) of a book, for example an ebook, a paperback, and a hardcover would each have a different ISBN.<ref>{{PDFlink|[http://www.isbn-international.org/pages/media/Usermanuals/ISBN%20Manual%202012%20-corr.pdf See paragraph 5.2 of ISBN Users' Manual International edition (2012)]|548&nbsp;KB}}</ref> The ISBN is 13 digits long if assigned on or after 1 January 2007, and 10 digits long if assigned before 2007. An International Standard Book Number consists of 4 parts (if it is a 10 digit ISBN) or 5 parts (for a 13 digit ISBN):
 
[[File:ISBN Details.svg|thumb|The parts of a 10-digit ISBN and the corresponding EAN‑13 and barcode. Note the different check digits in each. The part of the EAN‑13 labeled "EAN" is the [[Bookland]] country code.]]
 
#for a 13-digit ISBN, a prefix element - a ''[[GS1]] prefix'': so far 978 or 979 have been made available by GS1,<ref>[http://www.isbn-international.org/pages/media/Usermanuals/ISBN%20Manual%202012%20-corr.pdf The ISBN Users' Manual International Edition, 6th edition]</ref>
#the ''registration group element'', (language-sharing country group, individual country or territory)<ref>Some books have several codes in the first block: e.g. A. M. Yaglom's ''Correlation Theory...'', published by [[Springer Verlag]], has two ISBNs, 0-387-96331-6 and 3-540-96331-6. Though Springer's 387 and 540 codes are different for English (0) and German (3); the same item number 96331 produces the same check digit: 6. Springer uses 431 as their publisher code for Japanese (4) and 4-431-96331-? would also have check digit ? = 6.  Other Springer books in English have publisher code 817, and 0-817-96331-? would also get check digit ? = 6. This suggests special considerations were made for assigning Springer's publisher codes, as random assignments of different publisher codes would ''not'' lead the same item number to get the same check digit every time. Finding publisher codes for English and German, say, with this effect amounts to solving a linear equation in modular arithmetic.
</ref>
#the ''registrant'' element,
#the ''publication element'',<ref name="ReferenceA">The ISBN Users' Manual International Edition, 6th edition</ref> and
#a ''[[checksum]] character'' or [[check digit]].<ref name="ReferenceA"/>
 
The 13 digit ISBN separates its parts (''prefix element'', ''registration group'', ''registrant'', ''publication'' and ''check digit'') with either a hyphen or a space. Other than the prefix element and the check digit, no part of the ISBN has a fixed number of digits.
 
The 10 digit ISBN also separated its parts (''registration group'', ''registrant'', ''publication'' and ''check digit'') with either a [[hyphen]] or a space.<ref>The international ISBN agency's ''ISBN User's Manual'' says: "The ten-digit number is divided into four parts of variable length, which must be separated clearly, by hyphens or spaces" although permitting their omission for internal data processing. If present, hyphens must be correctly placed; see [http://www.isbn.org/standards/home/isbn/international/hyphenation-instructions.asp hyphenation instructions] at ISBN.org.</ref>
 
===ISBN issuance===
International Standard Book Numbers issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for that country or territory. The ranges of ISBNs assigned to any particular country are based on the publishing profile of the country concerned - e.g. the number of books and the number, type and size of publishers that are active. Some ISBN registration agencies are based in National Libraries or within Ministries of Culture and thus may receive direct funding from government to support their services. In other cases the ISBN registration service is provided by organisations such as bibliographic data providers who are not government funded. In Canada the stated purpose of issuing International Standard Book Numbers for no cost was to encourage Canadian culture. In the United Kingdom, United States, and some other countries, where the service is provided by non-government funded organisations the issuing of International Standard Book Numbers is a chargeable service.
 
Australia: In Australia ISBNs are issued by the commercial library services agency [https://www.myidentifiers.com.au/isbn/main Thorpe-Bowker], and prices range from $42 for a single ISBN (plus a $55 registration fee for new publishers) through to $2,890 for a block of 1,000 ISBNs.<ref>{{cite web
  | title = Bowker -- ISBN
  | publisher = Thorpe-Bowker  | date = 5 Jan 2009
  | url = https://www.myidentifiers.com.au/isbn/main
  | accessdate = 29 March 2012}}</ref>
 
[[Canada]]: In Canada [[Library and Archives Canada]], a government agency, is the responsible entity, and there is no cost. Works in [[French language|French]] are issued an ISBN by the [[Bibliothèque et Archives nationales du Québec]].
 
Pakistan: [[National Library of Pakistan]]<ref>National Library of Pakistan</ref> is responsible for ISBN registrations for Pakistani Publishers, Authors, Universities, Institutions and Government Departments who are responsible for publishing books.
 
India: In India, Raja Rammohan National Agency for ISBN is responsible for registration of Indian Publishers, Authors, Universities, Institutions and Government Departments who are responsible for publishing books.
 
United Kingdom and [[Republic of Ireland|Ireland]]: In the United Kingdom and Ireland the privately held company, [[Nielsen Book Services]], part of [[Nielsen Holdings|Nielsen Holdings N.V.]], is the responsible entity, and there is a charge. ISBNs are sold in lots of ten or more.
 
United States: In the United States the privately held company [https://www.myidentifiers.com/Get-your-isbn-now RR Bowker] is the responsible entity, and there is a charge, which varies depending upon the number of ISBNs purchased, with prices ranging from $125.00 for a single number.<ref>{{cite web
  | title = Bowker -- ISBN
  | date = 8 March 2013
  | publisher = RR Bowker
  | url = http://www.bowker.com/en-US/products/servident_isbn.shtml
  | accessdate = 8 March 2013}}</ref>
 
Publishers and authors in other countries need to obtain ISBNs from their respective national ISBN registration Agency. A directory of ISBN Agencies is available on the [[International ISBN Agency]] website.
 
===Registration Group identifier===
The [[list of ISBN identifier groups|registration group identifier]] is a 1 to 5 digit number. The single digit group identifiers are: 0 or 1 for English-speaking countries; 2 for French-speaking countries; 3 for German-speaking countries; 4 for Japan; 5 for [[Russian language|Russian]]-speaking countries, 7 for People's Republic of China. An example 5 digit group identifier is 99936, for [[Bhutan]]. The allocated group IDs are: 0–5, 600–621, 7, 80–94, 950–989, 9927–9989, and 99901–99972.<ref>See [http://www.isbn-international.org/page/ranges a complete list of group identifiers].  ISBN.org sometimes calls them ''group numbers''. Their table of identifiers now refers to ''ISBN prefix ranges,'' which must be assumed to be group identifier ranges.</ref>  Books published in rare languages typically have longer group identifiers.<ref>Hailman, Jack Parker (2008). ''Coding and redundancy: man-made and animal-evolved signals''. Harvard University Press. P. 209. ISBN 978-0-674-02795-4</ref>
 
The original standard book number (SBN) had no registration group identifier, but affixing a zero (0) as prefix to a 9-digit SBN creates a valid 10-digit ISBN.
 
===Registrant element===
The national ISBN agency assigns the registrant element ([[cf.]] [[:Category:ISBN agencies]]) and an accompanying series of ISBNs within that registrant element to the publisher; the publisher then allocates one of the ISBNs to each of his books. Generally, in most countries a book publisher is not required by law to assign an ISBN, however, most book stores only handle ISBN-bearing merchandise.
 
A listing of more than 900,000 assigned publisher codes is published, and can be ordered in book form ([[Euro|€]]1399, [[United States dollar|US$]]1959). The web site of the ISBN agency does not offer any free method of looking up publisher codes.<ref>See [http://www.isbn-international.org/page/directory Publisher's International ISBN Directory]</ref> Partial lists have been compiled (from library catalogs) for the English-language groups: [[List of group-0 ISBN publisher codes|identifier 0]] and [[List of group-1 ISBN publisher codes|identifier 1]].
 
Publishers receive blocks of ISBNs, with larger blocks allotted to publishers expecting to need them; a small publisher may receive ISBNs of one or more digits for the registration group identifier, several digits for the registrant, and a single digit for the publication element. Once that block of ISBNs is used, the publisher may receive another block of ISBNs, with a different registrant element. Consequently, a publisher may have different allotted registrant elements. There also may be more than one registration group identifier used in a country. This might occur once all the registrant elements from a particular registration group have been allocated to publishers.
 
By using variable block lengths, registration agencies are able to customise the allocations of ISBNs that they make to publishers. For example, a large publisher may be given a block of ISBNs where the digits allocated for the registrant element are few and there are many digits allocated for the publication element; likewise countries publishing a large output of titles have few allocated digits for the registration group identifier, and many for the registrant and publication elements.<ref>Splane, Lily (2002). ''The Book Book: A Complete Guide to Creating a Book on Your Computer.'' Anaphase II Publishing. p. 37. ISBN 978-0-945962-14-4.</ref> Here are some sample ISBN-10 codes, illustrating block length variations.
{| class="wikitable" style="width:100%; max-width:40em;"
|-
! ISBN || Country or area || Publisher
|-
| <tt>99921-58-10-7</tt><!--ISBN-13: 978-99921-58-10-4--> || Qatar || NCCAH, Doha
|-
| <tt>9971-5-0210-0</tt><!--ISBN-13: 978-9971-5-0210-2--> || Singapore || World Scientific
|-
| <tt>960-425-059-0</tt><!--ISBN-13: 978-960-425-059-2--> || Greece || Sigma Publications
|-
| <tt>80-902734-1-6</tt><!--ISBN-13: 978-80-902734-1-2--> || Czech Republic; Slovakia || Taita Publishers
|-
| <tt>85-359-0277-5</tt><!--ISBN-13: 978-80-902734-1-2--> || Brazil || Companhia das Letras
|-
| <tt>1-84356-028-3</tt><!--ISBN-13: 978-0-14-015098-8--> || English-speaking area || Simon Wallenberg Press
|-
| <tt>0-684-84328-5</tt><!--ISBN-13: 978-0-684-84328-5--> || English-speaking area || Scribner
|-
| <tt>0-8044-2957-X</tt><!--ISBN-13: 978-0-8044-2957-3--> || English-speaking area || Frederick Ungar
|-
| <tt>0-85131-041-9</tt><!--ISBN-13: 978-0-85131-041-1--> || English-speaking area || J. A. Allen & Co.
|-
| <tt>0-943396-04-2</tt><!--ISBN-13: 978-0-943396-04-0--> || English-speaking area || Willmann–Bell
|-
| <tt>0-9752298-0-X</tt><!--ISBN-13: 978-0-9752298-0-4--> || English-speaking area || KT Publishing                                                                                                             
|}
 
====Pattern====
English-language publisher codes follow a systematic pattern, which allows their length to be easily determined, as follows:<ref>[http://www.isbn.org/standards/home/isbn/international/hyphenation-instructions.asp Hyphenation Instructions]. ISBN.org.</ref>
 
{| class="wikitable" style="text-align:right;"
|-
! rowspan="2" | Item number length
! colspan="3" | 0- group identifier
! colspan="3" | 1- group identifier
! rowspan="2" | Total
|-
! From !! To !! Publishers !! From !! To !! Publishers
|-
! 6 digits
| style="font-family:monospace;" | 0-00-xxxxxx-x
| style="font-family:monospace;" | 0-19-xxxxxx-x
| 20
| style="font-family:monospace;" | 1-00-xxxxxx-x
| style="font-family:monospace;" | 1-09-xxxxxx-x
| 10
| 30
|-
! 5 digits
| style="font-family:monospace;" | 0-200-xxxxx-x
| style="font-family:monospace;" | 0-699-xxxxx-x
| 500
| style="font-family:monospace;" | 1-100-xxxxx-x
| style="font-family:monospace;" | 1-399-xxxxx-x
| 300
| 800
|-
! 4 digits
| style="font-family:monospace;" | 0-7000-xxxx-x
| style="font-family:monospace;" | 0-8499-xxxx-x
| 1,500
| style="font-family:monospace;" | 1-4000-xxxx-x
| style="font-family:monospace;" | 1-5499-xxxx-x
| 1,500
| 3,000
|-
! 3 digits
| style="font-family:monospace;" | 0-85000-xxx-x
| style="font-family:monospace;" | 0-89999-xxx-x
| 5,000
| style="font-family:monospace;" | 1-55000-xxx-x
| style="font-family:monospace;" | 1-86979-xxx-x
| 31,980
| 36,980
|-
! 2 digits
| style="font-family:monospace;" | 0-900000-xx-x
| style="font-family:monospace;" | 0-949999-xx-x
| 50,000
| style="font-family:monospace;" | 1-869800-xx-x
| style="font-family:monospace;" | 1-998999-xx-x
| 129,200
| 179,200
|-
! 1 digit
| style="font-family:monospace;" | 0-9500000-x-x
| style="font-family:monospace;" | 0-9999999-x-x
| 500,000
| style="font-family:monospace;" | 1-9990000-x-x
| style="font-family:monospace;" | 1-9999999-x-x
| 10,000
| 510,000
|-
! colspan="3" style="text-align:right;" | Total
| 557,020
! colspan="2" style="text-align:right;" | Total
| 172,990
| 730,010
|}
 
==Check digits==
A [[check digit]] is a form of redundancy check used for [[error detection]], the decimal equivalent of a binary [[check bit]].  It consists of a single digit computed from the other digits in the message.
 
===ISBN-10 check digits===
The 2001 edition of the official manual of the [http://www.isbn-international.org/ International ISBN Agency] says that the ISBN-10 [[check digit]]<ref>{{cite web|url=http://www.isbn.org/standards/home/isbn/international/html/usm4.htm |title=ISBN Users' Manual - 4. Structure of ISBN |publisher=Isbn.org |date= |accessdate=2013-05-27}}</ref>&nbsp;– which is the last digit of the ten-digit ISBN&nbsp;– must range from 0 to 10 (the symbol X is used for 10), and must be such that the sum of all the ten digits, each multiplied by its (integer) weight, descending from 10 to 1, is a multiple of [[11 (number)|11]].
 
For example, for an ISBN-10 of 0-306-40615-2:
:<math>
\begin{align}
  s &= (0\times 10) + (3\times 9) + (0\times 8) + (6\times 7) + (4\times 6) + (0\times 5) + (6\times 4) + (1\times 3) + (5\times 2) + (2\times 1) \\
  &=    0 + 27 +  0 +  42 +  24 +  0 + 24 +  3 + 10 + 2\\
  &= 132 = 12\times 11
\end{align}
</math>
 
Formally, using [[modular arithmetic]], we can say:
:<math>(10x_1 + 9x_2 + 8x_3 + 7x_4 + 6x_5 + 5x_6 + 4x_7 + 3x_8 + 2x_9 + x_{10})\mod{11} \equiv 0. </math>
 
It is also true for ISBN-10's that the sum of all the ten digits, each multiplied by its weight in ''ascending'' order from 1 to 10, is a multiple of 11. For this example:
:<math>
\begin{align}
s &= (0\times 1) + (3\times 2) + (0\times 3) + (6\times 4) + (4\times 5) + (0\times 6) + (6\times 7) + (1\times 8) + (5\times 9) + (2\times 10) \\
  &=    0 + 6 +  0 +  24 +  20 +  0 + 42  +  8 + 45 + 20\\
  &= 165 = 15\times 11
\end{align}
</math>
 
Formally, we can say:
:<math>(x_1 + 2x_2 + 3x_3 + 4x_4 + 5x_5 + 6x_6 + 7x_7 + 8x_8 + 9x_9 + 10x_{10})\mod{11} \equiv 0. </math>
 
The two most common errors in handling an ISBN (e.g., typing or writing it) are a single altered digit or the transposition of adjacent digits. It can be [[mathematical proof|proved]] that all possible valid ISBN-10's have at least two digits different from each other. It can also be proved that there are no pairs of valid ISBN-10's with eight identical digits and two transposed digits. (These are true only because the ISBN is less than 11 digits long, and because 11 is a [[prime number]].)
The ISBN check digit method therefore ensures that it will always be possible to detect these two most common types of error, i.e. if either of these types of error has occurred, the result will never be a valid ISBN - the sum of the digits multiplied by their weights will never be a multiple of 11. However, if the error occurs in the publishing house and goes undetected, the book will be issued with an invalid ISBN.<ref>For example ''I'saka: a sketch grammar of a language of north-central New Guinea.'' Pacific Linguistics. ISBN "0-85883-554-4".</ref>
 
In contrast, it is possible for other types of error, such as two altered non-transposed digits, or three altered digits, to result in a valid ISBN number (although it is still unlikely).
 
===ISBN-10 check digit calculation===
<!-- "Damm algorithm" links here -->
[[Modular arithmetic]] is convenient for calculating the check digit using modulus 11. Each of the first nine digits of the ten-digit ISBN&nbsp;– excluding the check digit, itself&nbsp;– is multiplied by a number in a sequence from 10 to 2, and the remainder of the sum, with respect to 11, is computed. The resulting remainder, plus the check digit, must equal 11; therefore, the check digit is 11 minus the remainder of the sum of the products.
 
For example, the check digit for an ISBN-10 of 0-306-40615-''?'' is calculated as follows:
:<math>
\begin{align}
s &= (0\times 10) + (3\times 9) + (0\times 8) + (6\times 7) + (4\times 6) + (0\times 5) + (6\times 4) + (1\times 3) + (5\times 2) \\
  &=    0 + 27 +  0 +  42 +  24 +  0 + 24  +  3 + 10 \\
  &= 130 = 12\times 11 - 2
\end{align}
</math>
 
Thus the check digit is 2, and the complete sequence is <nowiki>ISBN 0-306-40615-2</nowiki>.
The value <math>x_{10}</math> required to satisfy this condition might be 10; if so, an 'X' should be used.
 
====Alternative calculation====
<source lang="php">
//PHP
function is_isbn_10_valid($ISBN10){
    if(strlen($ISBN10) != 10)
        return false;
    $a = 0;
    for($i = 0; $i < 10; $i++){
        if ($ISBN10[$i] == "X" || $ISBN10[$i] == "x"){
            $a += 10*intval(10-$i);
        } else if (is_numeric($ISBN10[$i])) {
            $a += intval($ISBN10[$i]) * intval(10-$i);
        } else {
            return false;
        }
    }
    return ($a % 11 == 0);
}</source>
<source lang="python">
#Python
def is_isbn10(isbn10):
    if len(isbn10) != 10:
        return False
    r = sum((10 - i) * (int(x) if x != 'X' else 10) for i, x in enumerate(isbn10))
    return r % 11 == 0
</source>
<source lang="ruby">
#Ruby
def is_valid?(isbn)
   (isbn.length == 10) && (isbn.split('').inject([10,0]){|a, c| i,s = a; [s+i*c.to_i,i-1]}.first%11==0)
end
</source>
<source lang="javascript">
//Javascript
function ValidateISBN10(x){
    var isbn = x.replace( /[^0-9x]/g, '' );
    var isbn_check = isbn.substr(0, isbn.length-1);
    var sum = 0;
    if (isbn.length==10){
        for(var i = 2; i<11; i++){
            sum = sum + (isbn.substr(10-i,1)*i)
        }
        var CheckDigit = 11-(sum%11);
        if (CheckDigit == 10){
            CheckDigit = 'x';
        }
        if (isbn.substr(isbn.length-1, 1).toLowerCase()==CheckDigit){
            return true;
        } else {
            return false;
        }
    } else {
        return false;
    }
}
 
</source>
 
===ISBN-13 check digit calculation===
The 2005 edition of the International ISBN Agency's official manual<ref>{{PDFlink|[http://www.isbn-international.org/en/download/2005%20ISBN%20Users%27%20Manual%20International%20Edition.pdf ISBN Users' Manual International edition (2005)]|284&nbsp;KB}}</ref> describes how the 13-digit ISBN [[check digit]] is calculated. The ISBN-13 check digit, which is the last digit of the ISBN, must range from 0 to 9 and must be such that the sum of all the thirteen digits, each multiplied by its (integer) weight, alternating between 1 and 3, is a multiple of [[10 (number)|10]].
 
Formally, using [[modular arithmetic]], we can say:
:<math>(x_1 + 3x_2 + x_3 + 3x_4 + x_5 + 3x_6 + x_7 + 3x_8 + x_9 + 3x_{10} + x_{11} + 3x_{12} + x_{13})\mod{10} \equiv 0. </math>
 
The calculation of an ISBN-13 check digit begins with the first 12 digits of the thirteen-digit ISBN (thus excluding the check digit itself). Each digit, from left to right, is alternately multiplied by 1 or 3, then those products are summed [[modular arithmetic|modulo]] 10 to give a value ranging from 0 to 9. Subtracted from 10, that leaves a result from 1 to 10. A zero (0) replaces a ten (10), so, in all cases, a single check digit results.
 
For example, the ISBN-13 check digit of 978-0-306-40615-''?'' is calculated as follows:
<!-- This is what we'd like to do, but it is far too wide.
:<math>\textstyle \begin{array}{rlllllllllllll}
s &{}= 1 \times 9 &{}+ 3 \times 7 &{}+ 1 \times 8 &{}+ 3 \times 0 &{}+ 1 \times 3 &{}+ 3 \times 0 &{}+ 1 \times 6 &{}+ 3 \times 4 &{}+ 1 \times 0 &{}+ 3 \times 6 &{}+ 1 \times 1 &{}+ 3 \times 5 \\
&{}= 9 &{}+21 &{}+ 8 &{}+ 0 &{}+ 3 &{}+ 0 &{}+ 6 &{}+ 12 &{}+ 0 &{}+ 18 &{}+ 1 &{}+ 15 \\
&{}= 93
\end{array}</math>
-->
s = 9×1 + 7×3 + 8×1 + 0×3 + 3×1 + 0×3 + 6×1 + 4×3 + 0×1 + 6×3 + 1×1 + 5×3
  =  9 +  21 +  8 +  0 +  3 +  0 +  6 +  12 +  0 +  18 +  1 +  15
  = 93
93 / 10 = 9 remainder 3
10 –  3 = 7
 
Thus, the check digit is 7, and the complete sequence is <nowiki>ISBN 978-0-306-40615-7</nowiki>.
 
Formally, the ISBN-13 check digit calculation is:
:<math>x_{13} = \big(10 - \big(x_1 + 3x_2 + x_3 + 3x_4 + \cdots + x_{11} + 3x_{12}\big) \,\bmod\, 10\big) \,\bmod\, 10. </math>
 
This check system&nbsp;– similar to the [[Universal Product Code|UPC]] check digit formula&nbsp;– does not catch all errors of adjacent digit transposition. Specifically, if the difference between two adjacent digits is 5, the check digit will not catch their transposition. For instance, the above example allows this situation with the 6 followed by a 1. The correct order contributes 3×6+1×1 = 19 to the sum; while, if the digits are transposed (1 followed by a 6), the contribution of those two digits will be 3×1+1×6 = 9. However, 19 and 9 are congruent modulo 10, and so produce the same, final result: both ISBNs will have a check digit of 7. The ISBN-10 formula uses the [[prime number|prime]] modulus 11 which avoids this blind spot, but requires more than the digits 0-9 to express the check digit.
 
Additionally, if the sum of the 2nd, 4th, 6th, 8th, 10th, and 12th digits is tripled then added to the remaining digits (1st, 3rd, 5th, 7th, 9th, 11th, and 13th), the total will always be divisible by 10 (i.e., end in 0).
 
<source lang="java">
// Java
public static boolean isISBN13Valid(String isbn) {
    int check = 0;
    for (int i = 0; i < 12; i += 2) {
        check += Integer.valueOf(isbn.substring(i, i + 1));
    }
    for (int i = 1; i < 12; i += 2) {
        check += Integer.valueOf(isbn.substring(i, i + 1)) * 3;
    }
    check += Integer.valueOf(isbn.substring(12));
    return check % 10 == 0;
}
</source>
<source lang="javascript">
//JavaScript
function isValidISBN13(ISBNumber) {
    var sum, check, i;
   
    ISBNumber = ISBNumber.replace(/[^\d]/g,'');
 
    sum = 0;
    for (i = 0; i < 12; i += 1) {
      // checks for odd/even position to multiply by 1 or 3
      // uses Javascript implicit conversion of _number string_
      // placing unary operator "+a", better than call function parseInt(a, 10);
      sum += +ISBNumber.charAt(i) * (i % 2 ? 1 : 3);
    }
    check = sum % 10;
    return (+ISBNumber.chatAt(12) === check);
}</source>
<source lang="php">
//PHP
function is_isbn_13_valid($n){
    $check = 0;
    for ($i = 0; $i < 13; $i+=2) $check += substr($n, $i, 1);
    for ($i = 1; $i < 12; $i+=2) $check += 3 * substr($n, $i, 1);
    return $check % 10 == 0;
}</source>
<source lang="ruby">
# Ruby
def isbn_checksum(isbn_string)
  digits = isbn_string.split(//).map(&:to_i)
  transformed_digits = digits.each_with_index.map do |digit, digit_index|
    digit_index.modulo(2).zero? ? digit : digit*3
  end
  sum = transformed_digits.reduce(:+)
end
 
def is_valid_isbn13?(isbn13)
  checksum = isbn_checksum(isbn13)
  checksum.modulo(10).zero?
end
 
def isbn13_checksum_digit(isbn12)
  checksum = isbn_checksum(isbn12)
  remainer = checksum.modulo(10)
   if remainer==0
    0
  else
    10 - checksum.modulo(10)
  end
end</source>
 
<source lang="python">
# Python
def is_valid_isbn13(isbn):
    check = (10 - (sum(int(digit) * (3 if idx % 2 else 1) for idx, digit in enumerate(isbn[:12])) % 10)) % 10
    return check == int(isbn[-1])
</source>
 
<source lang="cpp">
// C/C++
bool is_valid_isbn13(char digits[13])
{
int i, check=0;
for (i=0; i<13; i+=2)
check += digits[i];
for (i=1; i<12; i+=2)
check += 3*digits[i];
return check%10==0;
}
</source>
<source lang="plsql">
-- PL/SQL - for validation in Oracle database
function validate_isbn_13(isbn varchar2) return integer is
    checksum integer;
    weight integer;
    modular integer;
    valid integer;
    reminder integer;
begin
    valid := -1;
    checksum := 0;
    for i in 1 .. 12 loop
        if mod( i, 2) = 0 then
            weight := 3;
        else
            weight := 1;
        end if;
        checksum := checksum + weight * to_number( substr( isbn, i, 1 ) );
    end loop;
    modular := mod( checksum, 10 );
 
    if modular = 0 then
        reminder := 0;
    else
        reminder := 10 - modular;
    end if;
 
    if to_char( reminder ) = substr(isbn, 13, 1 ) then
        valid := 0;
    end if;
 
    return valid;
end validate_isbn_13;
</source>
<source lang="bash">
# Bourne-Again Shell
function is_valid_isbn13 () {
declare ISBN="${1//[^[:digit:]]}"
declare -i CheckDigit=0
 
  for i in $(seq 0 12); do
    CheckDigit+=$((${ISBN:$i:1}*(1 + 2*(i % 2))))
  done
  return $((CheckDigit % 10))
}
</source>
<source lang="bash">
/* Maxima one-liner */
check_isbn13([x]):= is(mod(sum(x[2*i+1],i,0,6)+3*sum(x[2*i],i,1,6),10)=0)$
</source>
 
===ISBN-10 to ISBN-13 conversion===
The conversion is quite simple as one only needs to prepend the prefix "978" and calculate the new checksum using the ISBN-13 algorithm.
<source lang="javascript">
function isbn10ToIsbn13(isbn10) {
isbn13 = "978" + isbn10;
return isbn13.substr(0, isbn13.length-1) + getIsbn13CheckSum(isbn13);
}</source>
 
===Errors in usage===
Publishers and [[library|libraries]] have varied policies about the use of the ISBN check digit. Publishers sometimes fail to check the correspondence of a book title and its ISBN before publishing it; that failure causes book identification problems for libraries, booksellers, and readers.<ref>Lorimer, Rowland; Shoichet, Jillian; Maxwell, John W. (2005). ''Book Publishing I.'' CCSP Press. p. 299. ISBN 978-0-9738727-0-5.</ref>
 
Most libraries and booksellers display the book record for an invalid ISBN issued by the publisher. The [[Library of Congress]] catalogue contains books published with invalid ISBNs, which it usually tags with the phrase "Cancelled ISBN".<ref>[http://www.loc.gov/marc/bibliographic/bd020.html 020 - International Standard Book Number (R) &ndash; MARC 21 Bibliographic - Full]. Library of Congress.</ref> However, book-ordering systems such as [[Amazon.com]] will not search for a book if an invalid ISBN is entered to its search engine.{{Citation needed|date=March 2012}}
 
=== eISBN ===
There are no e-ISBN or eISBN numbers. Only the term ISBN should be used.<ref>[http://www.isbn.org/standards/home/about/faqs7.html isbn.org, Retrieved, August 29, 2013]</ref><ref>[http://www.sellbox.com/myth-eisbn-every-ebook-edition-needs-unique-number www.sellbox.com, Retrieved, August 29, 2013]</ref>
 
==EAN format used in barcodes, and upgrading==
Currently the [[barcode]]s on a book's back cover (or inside a mass-market [[paperback]] book's front cover) are [[European Article Number|EAN-13]]; they may have a separate barcode encoding five digits for the [[currency]] and the [[recommended retail price]].<ref>[http://www.barcodeisland.com/ean13.phtml EAN-13Methodology] — including a detailed description of the EAN13 format.</ref> For 10 digit ISBNs, the number "978", the [[Bookland]] "country code", is prefixed to the ISBN in the barcode data, and the check digit is recalculated according to the EAN13 formula (modulo 10, 1x and 3x weighting on alternate digits).
 
Partly because of an expected shortage in certain ISBN categories, the [[International Organization for Standardization]] (ISO) decided to migrate to a thirteen-digit ISBN (ISBN-13). The process began 1 January 2005 and was planned to conclude 1 January 2007.<ref>There is a [http://www.collectionscanada.ca/iso/tc46sc9/isbn.htm FAQ document] about this migration.</ref>  As of 2011, all the 13-digit ISBNs begin with 978.  As the 978 ISBN supply is exhausted, the 979 prefix will be introduced. Part of the 979 prefix is reserved for use with the [[Bookland|Musicland]] code for [[Sheet music|musical scores]] with an [[ISMN]]. 10 digit ISMN codes differed visually as they began with an "M" letter; the bar code represents the "M" as a zero (0), and for checksum purposes it counted as a 3. All ISMNs are now 13 digits commencing 979-0; 979-1 to 979-9 will be used by ISBN.
 
Publisher identification code numbers are unlikely to be the same in the 978 and 979 ISBNs, likewise, there is no guarantee that language area code numbers will be the same. Moreover, the ten-digit ISBN check digit generally is not the same as the thirteen-digit ISBN check digit. Because the EAN/UCC-13 is part of the [[Global Trade Item Number]] (GTIN) system (that includes the EAN/UCC-14, the UPC-12, and the EAN-8), it is expected that ISBN-generating [[software]] should accommodate fourteen-digit ISBNs.<ref>[http://www.isbn.org/standards/home/isbn/transition.asp Are You Ready for ISBN-13?] at isbn.org.</ref>
 
Barcode format compatibility is maintained, because (aside from the group breaks) the ISBN-13 barcode format is identical to the EAN barcode format of existing ISBN-10s. So, migration to an EAN-based system allows booksellers the use of a single numbering system for both books and non-book products that is compatible with existing ISBN-based data, with only minimal changes to [[information technology]] systems. Hence, many [[bookstore|booksellers]] (e.g., [[Barnes & Noble]]) migrated to EAN barcodes as early as March 2005. Although many American and Canadian booksellers were able to read EAN-13 barcodes before 2005, most general retailers could not read them. The upgrading of the [[Universal Product Code|UPC]] [[barcode system]] to full EAN-13, in 2005, eased migration to the ISBN-13 in [[North America]].
 
==See also==
* [[Amazon Standard Identification Number|ASIN]] (Amazon Standard Identification Number)
* [[CODEN]] (serial publication identifier currently used by libraries; replaced by the ISSN for new works)
* [[Digital Object Identifier|DOI]] (Digital Object Identifier)
* [[English Short Title Catalogue|ESTC]] (English Short Title Catalogue)
* [[ETTN]] (Electronic Textbook Track Number)
* [[International Standard Audiovisual Number|ISAN]] (International Standard Audiovisual Number)
* [[International Standard Music Number|ISMN]] (International Standard Music Number)
* [[International Standard Musical Work Code|ISWC]] (International Standard Musical Work Code)
* [[International Standard Recording Code|ISRC]] (International Standard Recording Code)
* [[International Standard Serial Number|ISSN]] (International Standard Serial Number)
* [[International Standard Text Code|ISTC]] (International Standard Text Code)
* [[ISWN]] (International Standard Wine Number)
* [[Library of Congress Control Number|LCCN]] (Library of Congress Control Number)
* [[List of group-0 ISBN publisher codes]]
* [[List of group-1 ISBN publisher codes]]
* [[Online Computer Library Center|OCLC]] number (Online Computer Library Center number<ref>{{cite web|url=http://xisbn.worldcat.org/xisbnadmin/xoclcnum/index.htm |title=WorldCat Web service: xISBN [OCLC - WorldCat Affiliate tools&#93;: xOCLCNUM |publisher=Xisbn.worldcat.org |date= |accessdate=2013-05-27}}</ref>)
* [[Registration authority]]
* [[Serial Item and Contribution Identifier|SICI]] (Serial Item and Contribution Identifier)
* [[Special:Booksources]], Wikipedia's ISBN search page
* [[VD 16]] (Verzeichnis der im deutschen Sprachbereich erschienenen Drucke des 16. Jahrhunderts)(in English: ''Bibliography of Books Printed in the German Speaking Countries of the Sixteenth Century'')
* [[VD 17]] (Verzeichnis der im deutschen Sprachraum erschienenen Drucke des 17. Jahrhunderts)(in English: ''Bibliography of Books Printed in the German Speaking Countries of the Seventeenth Century'')
 
==Notes and references==
{{Reflist|colwidth=30em}}
 
==External links==
<!-- ============================== NoMoreLinks ===============-->
<!-- DO NOT ADD MORE LINKS TO THIS ARTICLE. WIKIPEDIA IS NOT A COLLECTION OF LINKS -->
<!-- If you think that your link might be useful,  instead of placing it here, put -->
<!-- it on this article's discussion page first. Links that have not been verified -->
<!-- WILL BE DELETED.  See WP:WPSPAM for motivation.        -->
<!-- ====================================================== -->
*[http://www.iso.org/iso/en/CatalogueDetailPage.CatalogueDetail?CSNUMBER=36563&ICS1=1&ICS2=140&ICS3=20 ISO 2108:2005] at [http://www.iso.org www.iso.org]
* {{cite web|title=Are You Ready for ISBN-13?|url=http://www.isbn.org/standards/home/isbn/transition.asp transition|publisher=R.R. Bowker LLC}}
* [http://www.bookweb.org/education/6865.html Description of the ISBN to EAN upgrade process] at bookweb.org
* [http://www.isbn-international.org International ISBN Agency]—coordinates and supervises the worldwide use of the ISBN system.
* [http://www.isbn-international.org/page/ranges Numerical List of Group Identifiers] List of language/region prefixes
* [http://www.isbn.org/converterpub.asp Free conversion tool: ISBN-10 to ISBN-13 & ISBN-13 to ISBN-10] from the [http://www.isbn.org/ ISBN agency]. Also shows correct hyphenation & verifies if ISBNs are valid or not.
* RFC 3187 <!-- should be automatically linked by Wikipedia --> Using International Standard Book Numbers as [[Uniform Resource Name]]s (URN)
* {{PDFlink|[http://isbn-international.org/en/download/implementation-guidelines-04.pdf Implementation guidelines]|51.0&nbsp;KB}} for the 13-digit ISBN code.
{{Audiovisual works|state=uncollapsed}}
{{ISO standards}}
 
[[Category:1966 introductions]]
[[Category:Book publishing]]
[[Category:Bookselling]]
[[Category:Book terminology]]
[[Category:Checksum algorithms]]
[[Category:Identifiers]]
[[Category:ISO standards]]
[[Category:Library science]]
[[Category:Universal identifiers]]
I

Revision as of 23:18, 4 March 2014


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