Editing Check digit (section)

=== <nowiki>ISBN</nowiki> 13 ===
{{Further|International Standard Book Number#ISBN-13 check digit calculation}}
<nowiki>ISBN</nowiki> 13 (in use January 2007) is equal to the [[EAN-13]] code found underneath a book's barcode. Its check digit is generated in a similar way to the UPC.<ref name=ISBNINTERNATIONAL>{{cite web |url=https://www.isbn-international.org/content/isbn-users-manual |year=2005 |title=ISBN Users Manual |access-date=2008-05-21 |publisher=International ISBN Agency |archive-date=2014-04-29 |archive-url=https://web.archive.org/web/20140429223601/https://www.isbn-international.org/content/isbn-users-manual |url-status=dead }}</ref>

The check digit is computed as follows:
# Add the digits in the odd-numbered positions from the left (first, third, fifth, etc.—not including the check digit) together.
# Add the digits (up to but not including the check digit) in the even-numbered positions (second, fourth, sixth, etc.) together, and multiply by three, and add this to the result.
# Take the remainder of the result divided by 10 (i.e. the modulo 10 operation). If the remainder is equal to 0 then use 0 as the check digit, and if not 0 subtract the remainder from 10 to derive the check digit.
For example, take the {{ISBN|978-0747532699}}, belonging to ''Harry Potter and the Philosopher's Stone.'' 9 is the check digit here, so the calculations must yield 9 at the end.

# Add the odd number digits: 9+8+7+7+3+6 = 40.
# Add the even number digits: 7+0+4+5+2+9 = 27.
# Multiply the result by 3: 27 x 3 = 81.
# Add the two results together: 40 +81 = 121.
# To calculate the check digit, take the remainder of (121 / 10), which is also known as (121 modulo 10), and if not 0, subtract from 10. Therefore, the check digit value is 9, i.e. (121 / 10) = 12 remainder 1; 10 - 1 = 9.