Check digit

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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.

With a check digit, one can detect simple errors in the input of a series of digits, such as a single mistyped digit, or the permutation of two successive digits.

Examples

UPC

The final digit of a Universal Product Code is a check digit computed as follows:^[1]

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. The check digit will be the smallest number required to round the Sum up to the nearest multiple of 10.

For instance, the UPC-A barcode for a box of tissues is "036000241457". The last digit is the check digit "7", and if the other numbers are correct then the check digit calculation must produce 7.

1. We add the odd number digits: 0+6+0+2+1+5 = 14
2. Multiply the result by 3: 14 × 3 = 42
3. We add the even number digits: 3+0+0+4+4 = 11
4. We add the two results together: 42 + 11 = 53
5. 60 (the next highest multiple of 10) modulo 53 is 7. Therefore, 7 is the check digit.^[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 + 1×1 = 99 ≡ 0 modulo 11. So the ISBN is valid.

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. The sum can be computed without any multiplications by initializing two variables, t and sum, to 0 and repeatedly performing t = t + digit; sum = sum + t; (which can be expressed in C as sum += t += digit;). If the final sum is a multiple of 11, 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. ^[3]

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. ^[4]

Other examples of check digits

• The tenth digit of the National Provider Identifier for the US healthcare industry more
• The Australian Tax File Number (based on modulo 11)
• The Guatemalan Tax Number (NIT - Número de Identificación Tributaria) 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 on a New Zealand locomotive's Traffic Monitoring System (TMS) number.
• The last two digits of the 11-digit Turkish Identification Number (Turkish: TC Kimlik Numarası).
• The third and fourth digits in an International Bank Account Number (Modulo 97 check).
• The ninth character in an EU cattle passport number (cycles from 1 to 7: see British Cattle Movement Service).

Compare to check bit.

• Modulo 97 check digits in a Belgian and Serbian bank account numbers.
• A Verhoeff algorithm check digit can be calculated for a series of decimal numbers.
• Mayo Clinic patient identification numbers include a trailing check digit ^{Needs verification or sourcing}

External links

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

• [1] (GS1 check digit calculator)

• Check identity numbers by check digits.

References