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 very simple measure for protecting the integrity of data by detecting errors in data that is sent through space (telecommunications) or time (storage). ...

[edit] Examples

[edit] UPC

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

1. Add the digits in the odd-numbered positions (first, third, fifth, etc.) together and multiply by three.
2. Add the digits in the even-numbered positions (second, fourth, sixth, etc.) to the result.
3. Subtract the result from the next-higher multiple of ten. The answer is the check digit.

For instance, a UPC-A barcode (In this case, a UPC for a box of tissues) "03600029145X" where X is the check digit, X can be calculated by adding the odd-numbered digits (0+6+0+2+1+5 = 14), multiplying by three (14 × 3 = 42), adding the even-numbered digits (42+3+0+0+9+4 = 58) and subtracting from the next-highest multiple of ten (60 - 58 = 2). The check digit is thus 2.

[edit] 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. The barcode of an ISBN . ... In computing, the modulo operation finds the remainder of division of one number by another. ...

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 (in use January, 2007) generates its check digit the same way as the UPC.

[edit] 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).
• 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)

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. ... 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 England and Ireland for clearing purposes. ... An International Securities Identifying Number (ISIN) uniquely identifies a fungible security, its structure is defined in ISO 6166. ... CAS registry numbers are unique numerical identifiers for chemical compounds, polymers, biological sequences, mixtures and alloys. ... Credit cards A credit card is a system of payment named after the small plastic card issued to users of the 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. ... POSTNET is a barcode symbology that is used by the United States Postal Service to assist in directing mail. ... 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... Vehicle Identification Numbers (VINs) are used to uniquely identify motor vehicles. ... The Teudat Zehut (תעודת ×–הות) is the Israeli compulsory identity document, as prescribed in the Identity Card Carrying and Displaying Act of 1982: // Law and common practice The criminal offence carries a 5,000 NIS fine (about $1,000). ... 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. ... 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. ...

[edit] External links

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

• NPI check digit tool for the health care industry