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A check digit is a form of redundancy check used for error detection, the decimal equivalent of a binary checksum. In Mathematics, Computer science, Telecommunication, and Information theory, error detection and correction has great practical importance in In Mathematics, Computer science, Telecommunication, and Information theory, error detection and correction has great practical importance in 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 It consists of a single digit computed from the other digits in the message.

Contents

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. The Universal Product Code ( UPC) is a barcode symbology (ie a specific type of Barcode) that is widely used in the United States and ) 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+0+0+9+4 = 58.
  3. The last 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.

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. A European Article Number ( EAN) is a barcoding standard which is a Superset of the original 12-digit Universal Product Code (UPC system 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]

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. A European Article Number ( EAN) is a barcoding standard which is a Superset of the original 12-digit Universal Product Code (UPC system 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 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. 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 [3]

Other examples of check digits

Compare to check bit. In Mathematics, Computer science, Telecommunication, and Information theory, error detection and correction has great practical importance in

External links

References

  1. ^ GS1 Check Digit Calculator. GS1 US (2006). Retrieved on 2008-05-21. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 878 - Syracuse Italy is captured by the Muslim sultan of Sicily.
  2. ^ ISBN Users Manual. International ISBN Agency (2005). Retrieved on 2008-05-21. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 878 - Syracuse Italy is captured by the Muslim sultan of Sicily.
  3. ^ Check Digit Calculator. GS1 (2005). Retrieved on 2008-05-21. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 878 - Syracuse Italy is captured by the Muslim sultan of Sicily.
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