A check digit is a form of redundancy check used for error detection, the decimal equivalent of a binary checksum. It consists of a single digit computed from the other digits in the message. In telecommunication, a redundancy check is extra data added to a message for the purposes of error detection and error correction. ... In computer science and information theory, error correction consists of using methods to detect and/or correct errors in the transmission or storage of data by the use of some amount of redundant data and (in the case of transmission) the selective retransmission of incorrect segments of the data. ... A checksum is a form of redundancy check, a simple way to protect the integrity of data by detecting errors in data that are sent through space (telecommunications) or time (storage). ...

Examples

UPC

The final digit of a Universal Product Code is a check digit computed as follows:^[1] The Universal Product Code (UPC) is one of a wide variety of bar code languages called symbologies. ...

1. Add the digits (up to but not including the check digit) in the odd-numbered positions (first, third, fifth, etc.) together and multiply by three.
2. Add the digits (up to but not including the check digit) in the even-numbered positions (second, fourth, sixth, etc.) to the result.
3. If the last digit of the result is 0, then the check digit is 0.
4. If the last digit of the result is not zero, then subtract the last digit from 10. The answer must equal the check digit.

For instance, the UPC-A barcode for a box of tissues is "036000291452". The last digit is the check digit "2", and if the other numbers are correct then the check digit calculation must produce 2.

1. We add the odd number digits 0+6+0+2+1+5 = 14, and multiply by 3 to get 14 × 3 = 42.
2. We add the even number digits to this result 42+3

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Headline text

 ast digit is 8, we subtract this from 10 to get 2. 

ISBN 10

The final character of a ten digit International Standard Book Number is a check digit computed so that multiplying each digit by its position in the number (counting from the right) and taking the sum of these products modulo 11 is 0. The last digit (which is multiplied by 1) is the check digit, chosen to make the sum correct. It may need to have the value 10, which is represented as the letter X. For example, take the ISBN 0-201-53082-1. The sum of products is 0×10 + 2×9 + 0×8 + 1×7 + 5×6 + 3×5 + 0×4 + 8×3 + 2×2 = 98 modulo 11 (10) subtracted from 11 ≡ 1. So the ISBN is valid. ISBN redirects here. ... fmod redirects here. ...

While this may seem more complicated than the first scheme, it can be validated very simply by adding all the products together then dividing by 11. If the result is an integer then the ISBN is valid.

ISBN 13

ISBN 13 (in use January, 2007) is equal to the EAN-13 code found underneath a book's barcode. Its check digit is generated the same way as the UPC, except the even digits are multiplied by 3 instead of the odd digits. ^[2] European Article Numbering-Uniform Code Council (EAN-UCC) is the international organization of product barcodes that are printed on almost everything that is sold in stores worldwide. ...

EAN (GLN,GTIN, EAN numbers administered by GS1)

EAN (European Article Number) check digits (administered by GS1) - are calculated by summing the even position numbers and multiplying by 3, then adding the sum of the odd position numbers. The final digit of the result is subtracted from 10 to calculate the check digit (or left as is if already zero). A GS1 check digit calculator and detailed documentation is online at GS1's website. ^[3] A typical EAN-13 barcode A European Article Number (EAN) is a barcoding standard which is a superset of the original 12-digit Universal Product Code (UPC) system developed in North America. ... GS1 is a global organization dedicated to the design and implementation of global standards and solutions to improve the efficiency and visibility of supply and demand chains globally and across multiple sectors. ... GS1 is a global organization dedicated to the design and implementation of global standards and solutions to improve the efficiency and visibility of supply and demand chains globally and across multiple sectors. ...

Other examples of check digits

• The tenth digit of the National Provider Identifier for the healthcare industry more
• The Australian Tax File Number (based on modulo 11)
• The ninth digit of a Canadian Social Insurance Number (SIN)
• The North American CUSIP number
• The International SEDOL number
• The International Securities Identifying Number (ISIN)
• The International CAS registry number's final digit.
• Modulo 10 check digits in credit card account numbers, calculated with the Luhn algorithm.
  • Also used in the Norwegian KID (customer identification number) numbers used in bank giros (credit transfer).
• The final character encoded in a magnetic stripe card is a computed Longitudinal redundancy check
• final digit of a POSTNET code
• final digit of an ISSN code
• final digit of a DUNS number (though this is scheduled to change, such as that the final digit will be chosen freely in new allocations, rather than being a check digit)
• The Spanish fiscal identification number (número de identificación fiscal, NIF), (based on modulo 23).
• The ninth digit of a Vehicle Identification Number (VIN).
• The ninth digit of an Israeli Teudat Zehut (Identity Card) number.
• The 13th digit of Former Yugoslav Unique Master Citizen Number (JMBG)
• Last check digit in EAN/UPC serialisation of Global Trade Identification Number (GTIN). It applies to GTIN-8, GTIN-12, GTIN-13 and GTIN-14.
• The seventh character of a New Zealand NHI Number.
• The last digit of 11-digit Turkish Identification Number (TC Kimlik Numarası).

Compare to check bit. A National Provider Identifier or NPI is a unique 10-digit identification number issued to health care providers in the United States by the Centers for Medicare and Medicaid Services (CMS). ... Tax File Number (TFN) is an 8 or 9 digit number issued by the Australian Taxation Office (ATO) to each taxpayer (individual, company, superannuation fund, partnership or trust) to identify their Australian tax dealings. ... A sample SIN card. ... The acronym CUSIP typically refers to both the Committee on Uniform Security Identification Procedures and the 9-digit alphanumeric security identifiers that they distribute for all North American security issues for the purposes of facilitating clearing and settlement of trades. ... SEDOL stands for Stock Exchange Daily Official List, a list of security identifiers used in the United Kingdom and Ireland for clearing purposes. ... An International Securities Identifying Number (ISIN) uniquely identifies a security. ... CAS registry numbers are unique numerical identifiers for chemical compounds, polymers, biological sequences, mixtures and alloys. ... This article is about the payment system. ... The Luhn algorithm or Luhn formula, also known as the modulus 10 or mod 10 algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers and Canadian Social Insurance Numbers. ... A magnetic stripe card is a type of card capable of storing data by modifying the magnetism of tiny iron-based magnetic particles on a band of magnetic material on the card. ... In telecommunication, a longitudinal redundancy check (LRC) or horizontal redundancy check is a form of redundancy check based on the formation of a block check following preset rules: The block check formation rules are applied in the same manner to each character. ... This page may meet Wikipedia’s criteria for speedy deletion. ... ISSN, or International Standard Serial Number, is the unique eight-digit number applied to a periodical publication including electronic serials. ... The Data Universal Numbering System, abbreviated as DUNS or D-U-N-S is a system developed and regulated by Dun & Bradstreet (D&B) which assigns a unique numeric identifier to a single business entity. ... NIF may refer to: the National Islamic Front of Sudan the National Ignition Facility at Lawrence Livermore National Laboratory in the United States the Nationalist and Integrationist Front of Ituri, Democratic Republic of the Congo the New Imperial Federation, a Star Wars Role Playing network [1] in which characters play... VIN redirects here. ... Israeli identity card Teudat Zehut (תעודת ×–הות) is the Israeli compulsory identity document, as prescribed in the Identity Card Carrying and Displaying Act of 1982: [1] // Criminal offence carries a 5,000 NIS fine for not carrying an identity card or for misuse of the document. ... The Socialist Federal Republic of Yugoslavia was a Balkan state that existed from 1945 to 1992. ... Unique Master Citizen Number (Serbo-Croatian: Jedinstveni Matični Broj GraÄ‘ana / Јединствени Матични Број Грађана, acronym JMBG / ЈМБГ, Macedonian: Единствен матичен број на граѓанинот, acronym ЕМБГ, Slovene: Enotna matična Å¡tevilka občana, acronym EMÅ O) was a unique identification number that was assigned at birth to every citizen of former Yugoslavia. ... European Article Numbering-Uniform Code Council (EAN-UCC) is the international organization of product barcodes that are printed on almost everything that is sold in stores worldwide. ... The National Health Index (NHI) number is the unique person identifier used within the New Zealand health system. ... A check bit is a single bit that is added to a byte or string as a part of an error detection (or sometimes error_correction) system. ...

External links

• Identification numbers and check digit schemes (a mathematical explanation of various check digit schemes)

• [1] (GS1 check digit calculator)

References