1. Check Digit https://store.theartofservice.com/the-check-digit-toolkit.html

2. International Standard Book Number Check digits 1 A check digit is a form of redundancy check used for error detection, the decimal equivalent of a binary check bit. It consists of a single digit computed from the other digits in the message. https://store.theartofservice.com/the-check-digit-toolkit.html

3. International Standard Book Number ISBN-10 check digits 1 The 2001 edition of the official manual of the International ISBN Agency says that the ISBN-10 check digit – which is the last digit of the ten-digit ISBN – must range from 0 to 10 (the symbol X is used for 10), and must be such that the sum of all the ten digits, each multiplied by its (integer) weight, descending from 10 to 1, is a multiple of 11. https://store.theartofservice.com/the-check-digit-toolkit.html

4. International Standard Book Number ISBN-10 check digits 1 Formally, using modular arithmetic, we can say: https://store.theartofservice.com/the-check-digit-toolkit.html

5. International Standard Book Number ISBN-10 check digits 1 It is also true for ISBN-10's that the sum of all the ten digits, each multiplied by its weight in ascending order from 1 to 10, is a multiple of 11. For this example: https://store.theartofservice.com/the-check-digit-toolkit.html

6. International Standard Book Number ISBN-10 check digits 1 The two most common errors in handling an ISBN (e.g., typing or writing it) are a single altered digit or the transposition of adjacent digits. It can be proved that all possible valid ISBN-10's have at least two digits different from each other. It can also be proved that there are no pairs of valid ISBN-10's with eight identical digits and two transposed digits. (These are true only because the ISBN is less than 11 digits long, and because 11 is prime.) https://store.theartofservice.com/the-check-digit-toolkit.html

7. International Standard Book Number ISBN-10 check digits 1 The ISBN check digit method therefore ensures that it will always be possible to detect these two most common types of error, i.e. if either of these types of error has occurred, the result will never be a valid ISBN - the sum of the digits multiplied by their weights will never be a multiple of 11. However, if the error occurs in the publishing house and goes undetected, the book will be issued with an invalid ISBN. https://store.theartofservice.com/the-check-digit-toolkit.html

8. International Standard Book Number ISBN-10 check digits 1 In contrast, it is possible for other types of error, such as two altered non-transposed digits, or three altered digits, to result in a valid ISBN number (although it is still unlikely). https://store.theartofservice.com/the-check-digit-toolkit.html

9. International Standard Book Number ISBN-10 check digit calculation 1 Modular arithmetic is convenient for calculating the check digit using modulus 11. Each of the first nine digits of the ten-digit ISBN – excluding the check digit, itself – is multiplied by a number in a sequence from 10 to 2, and the remainder of the sum, with respect to 11, is computed. The resulting remainder, plus the check digit, must equal 11; therefore, the check digit is 11 minus the remainder of the sum of the products. https://store.theartofservice.com/the-check-digit-toolkit.html

10. International Standard Book Number ISBN-10 check digit calculation 1 For example, the check digit for an ISBN-10 of 0- 306-40615-? is calculated as follows: https://store.theartofservice.com/the-check-digit-toolkit.html

11. International Standard Book Number ISBN-10 check digit calculation 1 Thus the check digit is 2, and the complete sequence is ISBN 0-306-40615-2. The value required to satisfy this condition might be 10; if so, an 'X' should be used. https://store.theartofservice.com/the-check-digit-toolkit.html

12. International Standard Book Number ISBN-13 check digit calculation 1 The 2005 edition of the International ISBN Agency's official manual describes how the 13-digit ISBN check digit is calculated. https://store.theartofservice.com/the-check-digit-toolkit.html

13. International Standard Book Number ISBN-13 check digit calculation 1 The calculation of an ISBN-13 check digit begins with the first 12 digits of the thirteen-digit ISBN (thus excluding the check digit itself). Each digit, from left to right, is alternately multiplied by 1 or 3, then those products are summed modulo 10 to give a value ranging from 0 to 9. Subtracted from 10, that leaves a result from 1 to 10. A zero (0) replaces a ten (10), so, in all cases, a single check digit results. https://store.theartofservice.com/the-check-digit-toolkit.html

14. International Standard Book Number ISBN-13 check digit calculation 1 For example, the ISBN-13 check digit of 978-0-306- 40615-? is calculated as follows: https://store.theartofservice.com/the-check-digit-toolkit.html

15. International Standard Book Number ISBN-13 check digit calculation 1 Thus, the check digit is 7, and the complete sequence is ISBN 978-0-306-40615-7. https://store.theartofservice.com/the-check-digit-toolkit.html

16. International Standard Book Number ISBN-13 check digit calculation 1 Formally, the ISBN-13 check digit calculation is: https://store.theartofservice.com/the-check-digit-toolkit.html

17. International Standard Book Number ISBN-13 check digit calculation 1 The ISBN-10 formula uses the prime modulus 11 which avoids this blind spot, but requires more than the digits 0-9 to express the check digit. https://store.theartofservice.com/the-check-digit-toolkit.html

18. International Standard Book Number ISBN-13 check digit calculation 1 Additionally, if the sum of the 2nd, 4th, 6th, 8th, 10th, and 12th digits is tripled then added to the remaining digits (1st, 3rd, 5th, 7th, 9th, 11th, and 13th), the total will always be divisible by 10 (i.e., end in 0). https://store.theartofservice.com/the-check-digit-toolkit.html

19. International Standard Book Number ISBN-13 check digit calculation 1 public static boolean isISBN13Valid(String isbn) { https://store.theartofservice.com/the-check-digit-toolkit.html

20. International Standard Book Number ISBN-13 check digit calculation 1 check += Integer.valueOf(isbn.su bstring(i, i + 1)); https://store.theartofservice.com/the-check-digit-toolkit.html

21. International Standard Book Number ISBN-13 check digit calculation 1 function isValidISBN13(ISBNumber) { https://store.theartofservice.com/the-check-digit-toolkit.html

22. International Standard Book Number ISBN-13 check digit calculation 1 sum = transformed_digits.red uce(:+) https://store.theartofservice.com/the-check-digit-toolkit.html

23. International Standard Book Number ISBN-13 check digit calculation 1 check = (10 - (sum(int(digit) * (3 if idx % 2 else 1) for idx, digit in enumerate(isbn[:12])) % 10)) % 10 https://store.theartofservice.com/the-check-digit-toolkit.html

24. International Standard Book Number ISBN-13 check digit calculation 1 FUNCTION validate_isbn_13(isbn VARCHAR2) RETURN INTEGER IS https://store.theartofservice.com/the-check-digit-toolkit.html

25. International Standard Book Number ISBN-13 check digit calculation 1 modular INTEGER; https://store.theartofservice.com/the-check-digit-toolkit.html

26. International Standard Book Number ISBN-13 check digit calculation 1 IF modular = 0 THEN https://store.theartofservice.com/the-check-digit-toolkit.html

27. International Standard Book Number ISBN-13 check digit calculation 1 reminder := 10 - modular; https://store.theartofservice.com/the-check-digit-toolkit.html

28. International Standard Book Number ISBN-13 check digit calculation 1 IF TO_CHAR( reminder ) = SUBSTR(isbn, 13, 1 ) THEN https://store.theartofservice.com/the-check-digit-toolkit.html

29. International Standard Book Number ISBN-13 check digit calculation 1 # Bourne-Again Shell https://store.theartofservice.com/the-check-digit-toolkit.html

30. International Standard Music Number - Check digit 1 To calculate the check digit, each digit of the ISMN is multiplied by a weight, alternating 1 and 3 left to right. These weighted digits are added together. The check digit is the integer between 0 and 9 that makes the sum a multiple of 10. https://store.theartofservice.com/the-check-digit-toolkit.html

31. ISO/IEC 7812 - Check digit 1 The final digit is a check digit which is calculated using the Luhn algorithm, defined in Annex B of ISO/IEC 7812-1. https://store.theartofservice.com/the-check-digit-toolkit.html

32. ISO 6346 - Check Digit 1 The check digit consists of one numeric digit providing a means of validating the recording and transmission accuracies of the owner code and serial number. https://store.theartofservice.com/the-check-digit-toolkit.html

33. International Bank Account Number - Generating IBAN check digits 1 According to the ECBS "generation of the IBAN shall be the exclusive responsibility of the bank/branch servicing the account". The ECBS document replicates part of the ISO/IEC 7064:2003 standard as a method for generating check digits in the range 02 to 98. Check digits in the ranges 00 to 96, 01 to 97, and 03 to 99 will also provide validation of an IBAN, but the standard is silent as to whether or not these ranges may be used. https://store.theartofservice.com/the-check-digit-toolkit.html

34. International Bank Account Number - Generating IBAN check digits 1 Check that the total IBAN length is correct as per the country. If not, the IBAN is invalid https://store.theartofservice.com/the-check-digit-toolkit.html

35. International Bank Account Number - Generating IBAN check digits 1 Replace the two check digits by 00 (e.g. GB00 for the UK) https://store.theartofservice.com/the-check-digit-toolkit.html

36. International Bank Account Number - Generating IBAN check digits 1 Move the four initial characters to the end of the string https://store.theartofservice.com/the-check-digit-toolkit.html

37. International Bank Account Number - Generating IBAN check digits 1 Replace the letters in the string with digits, expanding the string as necessary, such that A or a = 10, B or b = 11, and Z or z = 35. Each alphabetic character is therefore replaced by 2 digits https://store.theartofservice.com/the-check-digit-toolkit.html

38. International Bank Account Number - Generating IBAN check digits 1 Calculate mod-97 of the new number, which results in the remainder https://store.theartofservice.com/the-check-digit-toolkit.html

39. International Bank Account Number - Generating IBAN check digits 1 Subtract the remainder from 98, and use the result for the two check digits. If the result is a single digit number, pad it with a leading 0 to make a two-digit number https://store.theartofservice.com/the-check-digit-toolkit.html

40. Codabar - Check digit 1 Because Codabar is self-checking, most standards do not define a check digit.http://mdn.morovia.com/manuals/bax 3/shared.bartech.php#Symbology.Codaba r https://store.theartofservice.com/the-check-digit-toolkit.html

41. Codabar - Check digit 1 Some standards that use Codabar will define a check digit, but the algorithm is not universal. For purely numerical data, such as the library barcode pictured above, the Luhn algorithm is popular.http://www.makebarcode.com/spe cs/codabar.html https://store.theartofservice.com/the-check-digit-toolkit.html

42. Codabar - Check digit 1 When all 16 symbols are possible, a simple modulo-16 checksum is used.http://www.barcodesymbols.com/cod abar.htm The values 10 through 19 are assigned to the symbols –$:/+.ABCD, respectively. https://store.theartofservice.com/the-check-digit-toolkit.html

43. Universal Product Code - Check digits 1 In the UPC-A system, the check digit is calculated as follows: https://store.theartofservice.com/the-check-digit-toolkit.html

44. Universal Product Code - Check digits 1 # Add the digits in the Even and odd numbers|odd-numbered positions (first, third, fifth, etc.) together and multiply by three. https://store.theartofservice.com/the-check-digit-toolkit.html

45. Universal Product Code - Check digits 1 # Add the digits in the even and odd numbers|even-numbered positions (second, fourth, sixth, etc.) to the result. https://store.theartofservice.com/the-check-digit-toolkit.html

46. Universal Product Code - Check digits 1 # Find the result modulo operation|modulo 10 (i.e. the remainder when divided by 10.. 10 goes into 58 5 times with 8 leftover). https://store.theartofservice.com/the-check-digit-toolkit.html

47. Universal Product Code - Check digits 1 # If the result is not zero, subtract the result from ten. https://store.theartofservice.com/the-check-digit-toolkit.html

48. Universal Product Code - Check digits 1 For example, in a UPC-A barcode 03600029145'x' where 'x' is the unknown check digit, 'x' can be calculated by https://store.theartofservice.com/the-check-digit-toolkit.html

49. Universal Product Code - Check digits 1 *adding the odd- numbered digits (0+6+0+2+1+5 = 14), https://store.theartofservice.com/the-check-digit-toolkit.html

50. Universal Product Code - Check digits 1 *calculating modulo ten (58mod10 = 8), https://store.theartofservice.com/the-check-digit-toolkit.html

51. Universal Product Code - Check digits 1 *subtracting from ten (10minus;8 = 2). https://store.theartofservice.com/the-check-digit-toolkit.html

52. Universal Product Code - Check digits 1 This should not be confused with the numeral X which stands for a value of 10 in modulo 11, commonly seen in the International Standard Book Number|ISBN check digit. https://store.theartofservice.com/the-check-digit-toolkit.html

53. Code 128 - Check digit calculation 1 The remainder of the division is the check digit's 'value' which is then converted into a character (following the instructions given Code 128#Conversion to char|below) and appended to the end of the barcode. https://store.theartofservice.com/the-check-digit-toolkit.html

54. Code 128 - Check digit calculation 1 For example, in the following table, the code 128 variant A checksum value is calculated for the alphanumeric string PJJ123C https://store.theartofservice.com/the-check-digit-toolkit.html

55. Code 128 - Calculating check digit with multiple variants 1 As Code 128 allows multiple variants, as well as switching between variants within a single barcode, it is important to remember that the absolute Code 128 value of a character is completely independent of its value within a given variant. For instance the Variant C value 33 and the Variant B value A are both considered to be a Code 128 value of 33, and the check digit would be computed based on the value of 33 times the character's position within the barcode. https://store.theartofservice.com/the-check-digit-toolkit.html

56. British Cattle Movement Service - Check Digit 1 The check digit for a cow’s ear tag is calculated by dividing the number obtained from the herd mark and animal number by 7 and adding one to the remainder. Take UK herd number 303565 cow number 01234. We work out the check digit as follows: https://store.theartofservice.com/the-check-digit-toolkit.html

57. MSI Barcode - Check digit calculation 1 The MSI barcode uses one of five possible schemes for calculating a check digit: https://store.theartofservice.com/the-check-digit-toolkit.html

58. MSI Barcode - Check digit calculation 1 * Modulo operation|Mod 10 (most common) https://store.theartofservice.com/the-check-digit-toolkit.html

59. MSI Barcode - Mod 10 Check Digit 1 When using the Mod 10 check digit algorithm, a string to be encoded 1234567 will be printed with a check digit of 4: https://store.theartofservice.com/the-check-digit-toolkit.html

60. MSI Barcode - Mod 10 Check Digit 1 [http://publib.boulder.ibm.com/infocenter/pr inter/v1r1/index.jsp?topic=/com.ibm.printer s.afpproducts/com.ibm.printers.ppfaug/ib6 p8mst334.htm IBM Printing Systems Information Center - Check Digit Calculation Method], IBM. https://store.theartofservice.com/the-check-digit-toolkit.html

61. MSI Barcode - Mod 10 Check Digit 1 uses the Luhn algorithm. https://store.theartofservice.com/the-check-digit-toolkit.html

62. MSI Barcode - Mod 11 Check Digit 1212 https://store.theartofservice.com/the-check-digit-toolkit.html

63. MSI Barcode - Mod 11 Check Digit 1 This example is using the IBM modulo 11 algorithm with a weighting pattern of (2,3,4,5,6,7) https://store.theartofservice.com/the-check-digit-toolkit.html

64. MSI Barcode - Mod 11 Check Digit 1 Let X = the final product of the string to encode. https://store.theartofservice.com/the-check-digit-toolkit.html

65. MSI Barcode - Mod 11 Check Digit 1 3. Mod the sum by 11, subtract the result from 11, and then apply the mod 11 function again. https://store.theartofservice.com/the-check-digit-toolkit.html

66. MSI Barcode - Mod 1010 check digit 1 Simply calculate the Mod 10 check digit the first time and then calculate it again with the previous result and append the result of the second Mod 10 Calculation to the string to be encoded. https://store.theartofservice.com/the-check-digit-toolkit.html

67. MSI Barcode - Mod 1110 check digit 1 Same as Mod 1010 but the first calculation should be a Mod 11 Check digit. https://store.theartofservice.com/the-check-digit-toolkit.html

68. International Mobile Equipment Identity - Check digit computation 1 The last number of the IMEI is a check digit calculated using the Luhn algorithm. https://store.theartofservice.com/the-check-digit-toolkit.html

69. International Mobile Equipment Identity - Check digit computation 1 According to the [http://www.gsma.com/documents/ts-06-6- 0-imei-allocation-and-approval- guidelines/20164/ IMEI Allocation and Approval Guidelines], https://store.theartofservice.com/the-check-digit-toolkit.html

70. International Mobile Equipment Identity - Check digit computation 1 The Check Digit shall be calculated according to Luhn algorithm|Luhn formula (ISO/IEC 7812). (See GSM 02.16 / 3GPP 22.016). The Check Digit is a function of all other digits in the IMEI. The Software Version Number (SVN) of a mobile is not included in the calculation. https://store.theartofservice.com/the-check-digit-toolkit.html

71. International Mobile Equipment Identity - Check digit computation 1 The purpose of the Check Digit is to help guard against the possibility of incorrect entries to the CEIR and EIR equipment. https://store.theartofservice.com/the-check-digit-toolkit.html

72. International Mobile Equipment Identity - Check digit computation 1 The presentation of the Check Digit both electronically and in printed form on the label and packaging is very important. Logistics (using bar-code reader) and EIR/CEIR administration cannot use the Check Digit unless it is printed outside of the packaging, and on the ME IMEI/Type Accreditation label. https://store.theartofservice.com/the-check-digit-toolkit.html

73. International Mobile Equipment Identity - Check digit computation 1 The check digit is not transmitted over the radio interface, nor is it stored in the EIR database at any point. Therefore, all references to the last three or six digits of an IMEI refer to the actual IMEI number, to which the check digit does not belong. https://store.theartofservice.com/the-check-digit-toolkit.html

74. International Mobile Equipment Identity - Check digit computation 1 # Starting from the right, double every other digit (e.g., 7 → 14). https://store.theartofservice.com/the-check-digit-toolkit.html

75. International Mobile Equipment Identity - Check digit computation 1 Conversely, one can calculate the IMEI by choosing the check digit that would give a sum divisible by 10. For the example IMEI 49015420323751?, https://store.theartofservice.com/the-check-digit-toolkit.html

76. International Mobile Equipment Identity - Check digit computation 1 To make the sum divisible by 10, we set ? = 8, so the IMEI is 490154203237518. https://store.theartofservice.com/the-check-digit-toolkit.html

77. Check digit 1 A 'check digit' is a form of redundancy check used for Error detection and correction|error detection on identification numbers (e.g. bank account numbers) which have been input manually. It is analogous to a binary parity bit used to check for errors in computer-generated data. It consists of a single digit (sometimes more than one) computed by an algorithm from the other digits (or letters) in the sequence input. https://store.theartofservice.com/the-check-digit-toolkit.html

78. Check digit 1 With a check digit, one can detect simple errors in the input of a series of characters (usually digits) such as a single mistyped digit or some permutations of two successive digits. https://store.theartofservice.com/the-check-digit-toolkit.html

79. Check digit - Design 1 Check digit algorithms are generally designed to capture human transcription errors. In order of complexity, these include the following: https://store.theartofservice.com/the-check-digit-toolkit.html

80. Check digit - Design 1 * single digit errors, such as 1 → 2 https://store.theartofservice.com/the-check-digit-toolkit.html

81. Check digit - Design 1 * transposition errors, such as 12 → 21 https://store.theartofservice.com/the-check-digit-toolkit.html

82. Check digit - Design 1 * twin errors, such as 11 → 22 https://store.theartofservice.com/the-check-digit-toolkit.html

83. Check digit - Design 1 * jump transpositions errors, such as 132 → 231 https://store.theartofservice.com/the-check-digit-toolkit.html

84. Check digit - Design 1 * jump twin errors, such as 131 → 232 https://store.theartofservice.com/the-check-digit-toolkit.html

85. Check digit - Design 1 * phonetic errors, such as 60 → 16 (sixty to sixteen) https://store.theartofservice.com/the-check-digit-toolkit.html

86. Check digit - Design 1 In choosing a system, a high probability of catching errors is traded off against implementation difficulty; simple check digit systems are easily understood and implemented by humans but do not catch as many errors as complex ones, which require sophisticated programs to implement. https://store.theartofservice.com/the-check-digit-toolkit.html

87. Check digit - Design 1 A desirable feature is that left-padding with zeros should not change the check digit. This allows variable length digits to be used and the length to be changed. https://store.theartofservice.com/the-check-digit-toolkit.html

88. Check digit - Design 1 If there is a single check digit added to the original number, the system will not always capture multiple errors, such as two replacement errors (12 → 34) though, typically, double errors will be caught 90% of the time (both changes would need to change the output by offsetting amounts). https://store.theartofservice.com/the-check-digit-toolkit.html

89. Check digit - Design 1 A very simple check digit method would be to take the sum of all digits (digital root|digital sum) modulo operation|modulo 10. This would catch any single-digit error, as such an error would always change the sum, but does not catch any transposition errors (switching two digits) as re-ordering does not change the sum. https://store.theartofservice.com/the-check-digit-toolkit.html

90. Check digit - Design 1 A slightly more complex method is to take the weighted sum of the digits, modulo 10, with different weights for each number position. https://store.theartofservice.com/the-check-digit-toolkit.html

91. Check digit - Design 1 To illustrate this, for example if the weights for a four digit number were 5, 3, 2, 7 and the number to be coded was 4871, then one would take 5×4 + 3×8 + 2×7 + 7×1 = 65, i.e. 5 modulo 10, and the check digit would be 5, giving 48715. https://store.theartofservice.com/the-check-digit-toolkit.html

92. Check digit - Design 1 Using different weights on neighboring numbers means that most transpositions change the check digit; however, because all weights differ by an even number, this does not catch transpositions of two digits that differ by 5, (0 and 5, 1 and 6, 2 and 7, 3 and 8, 4 and 9), since the 2 and 5 multiply to yield 10. https://store.theartofservice.com/the-check-digit-toolkit.html

93. Check digit - Design 1 The code instead uses modulo 11, which is prime, and all the number positions have different weights 1,2,\dots,10. This system thus detects all single digit substitution and transposition errors (including jump transpositions), but at the cost of the check digit possibly being 10, represented by X. (An alternative is simply to avoid using the serial numbers which result in an X check digit.) instead uses the GS1 algorithm used in EAN numbers. https://store.theartofservice.com/the-check-digit-toolkit.html

94. Check digit - Design 1 To reduce this failure rate, it is necessary to use more than one check digit (for example, the modulo 97 check referred to below, which uses two check digits - for the algorithm, see International Bank Account Number) and/or to use a wider range of characters in the check digit, for example letters plus numbers. https://store.theartofservice.com/the-check-digit-toolkit.html

95. Check digit - UPC 1 The final digit of a Universal Product Code is a check digit computed as follows: https://store.theartofservice.com/the-check-digit-toolkit.html

96. Check digit - UPC 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. https://store.theartofservice.com/the-check-digit-toolkit.html

97. Check digit - UPC 1 # Add the digits (up to but not including the check digit) in the even-numbered positions (second, fourth, sixth, etc.) to the result. https://store.theartofservice.com/the-check-digit-toolkit.html

98. Check digit - UPC 1 # Take the remainder of the result divided by 10 (modulo operation) and subtract this from 10 to derive the check digit. https://store.theartofservice.com/the-check-digit-toolkit.html

99. Check digit - UPC 1 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. https://store.theartofservice.com/the-check-digit-toolkit.html

100. Check digit - UPC 1 # Add the odd number digits: 0+6+0+2+1+5 = 14 https://store.theartofservice.com/the-check-digit-toolkit.html

101. Check digit - UPC 1 # To calculate the check digit, take the remainder of (53 / 10), which is also known as (53 modulo 10), and subtract from 10. Therefore, the check digit value is 7. https://store.theartofservice.com/the-check-digit-toolkit.html

102. Check digit - UPC 1 Another example: to calculate the check digit for the following food item 01010101010. https://store.theartofservice.com/the-check-digit-toolkit.html

103. Check digit - UPC 1 # To calculate the check digit, take the remainder of (5 / 10), which is also known as (5 modulo 10), and subtract from 10 i.e. (10 - 5 modulo 10) = 5. Therefore, the check digit value is 5. https://store.theartofservice.com/the-check-digit-toolkit.html

104. Check digit - UPC 1 # If the remainder is 0, subtracting from 10 would give 10. In that case, use 0 as the check digit. https://store.theartofservice.com/the-check-digit-toolkit.html

105. Check digit - ISBN 10 1 The digit the farthest to the right (which is multiplied by 1) is the check digit, chosen to make the sum correct https://store.theartofservice.com/the-check-digit-toolkit.html

106. Check digit - ISBN 10 1 While this may seem more complicated than the first scheme, it can be validated 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 (programming language)|C as sum += t += digit;). If the final sum is a multiple of 11, the ISBN is valid. https://store.theartofservice.com/the-check-digit-toolkit.html

107. Check digit - ISBN 13 1 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 that the even digits are multiplied by 3 instead of the odd digits. https://store.theartofservice.com/the-check-digit-toolkit.html

108. Check digit - EAN (GLN,GTIN, EAN numbers administered by GS1) 1 EAN (European Article Number) check digits (administered by GS1) are calculated by summing the odd position numbers and multiplying by 3 and then by adding the sum of the even position numbers. Numbers are examined going from right to left, so the first odd position is the last digit in the code. The final digit of the result is subtracted from 10 to calculate the check digit (or left as-is if already zero). https://store.theartofservice.com/the-check-digit-toolkit.html

109. Check digit - EAN (GLN,GTIN, EAN numbers administered by GS1) 1 A GS1 check digit calculator and detailed documentation is online at GS1's website. https://store.theartofservice.com/the-check-digit-toolkit.html

110. Check digit - EAN (GLN,GTIN, EAN numbers administered by GS1) 1 Another official calculator page shows that the mechanism for GTIN-13 is the same for Global Location Number/GLN. https://store.theartofservice.com/the-check-digit-toolkit.html

111. Check digit - International 1 * The International SEDOL number. https://store.theartofservice.com/the-check-digit-toolkit.html

112. Check digit - International 1 * The final digit of an ISSN code or IMO Number. https://store.theartofservice.com/the-check-digit-toolkit.html

113. Check digit - International 1 * The International Securities Identifying Number (ISIN). https://store.theartofservice.com/the-check-digit-toolkit.html

114. Check digit - International 1 * The International CAS registry number's final digit. https://store.theartofservice.com/the-check-digit-toolkit.html

115. Check digit - International 1 * Modulo 10 check digits in credit card account numbers, calculated by the Luhn algorithm. https://store.theartofservice.com/the-check-digit-toolkit.html

116. Check digit - International 1 **Also used in the Norwegian KID (customer identification number) numbers used in bank giros (credit transfer). https://store.theartofservice.com/the-check-digit-toolkit.html

117. Check digit - International 1 * 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. https://store.theartofservice.com/the-check-digit-toolkit.html

118. Check digit - International 1 * The final digit of a Data Universal Numbering System|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). https://store.theartofservice.com/the-check-digit-toolkit.html

119. Check digit - International 1 * The third and fourth digits in an International Bank Account Number (Modulo 97 check). https://store.theartofservice.com/the-check-digit-toolkit.html

120. Check digit - International 1 * The final character encoded in a magnetic stripe card is a computed Longitudinal redundancy check. https://store.theartofservice.com/the-check-digit-toolkit.html

121. Check digit - In the USA 1 * The tenth digit of the National Provider Identifier for the US healthcare industry. https://store.theartofservice.com/the-check-digit-toolkit.html

122. Check digit - In the USA 1 * The North American CUSIP number. https://store.theartofservice.com/the-check-digit-toolkit.html

123. Check digit - In the USA 1 * The final (ninth) digit of the routing transit number, a bank code used in the United States. https://store.theartofservice.com/the-check-digit-toolkit.html

124. Check digit - In the USA 1 * The ninth digit of a Vehicle identification number|Vehicle Identification Number (VIN). https://store.theartofservice.com/the-check-digit-toolkit.html

125. Check digit - In the USA 1 * Mayo Clinic patient identification numbers used in Arizona and Florida include a trailing check digit. https://store.theartofservice.com/the-check-digit-toolkit.html

126. Check digit - In Central America 1 * The Guatemalan Tax Number (NIT - Número de Identificación Tributaria) based on modulo operator|modulo 11. https://store.theartofservice.com/the-check-digit-toolkit.html

127. Check digit - In Eurasia 1 * The Spanish fiscal identification number (número de identificación fiscal, NIF), (based on modulo 23). https://store.theartofservice.com/the-check-digit-toolkit.html

128. Check digit - In Eurasia 1 * The ninth digit of an Israeli Teudat Zehut (Identity Card) number. https://store.theartofservice.com/the-check-digit-toolkit.html

129. Check digit - In Eurasia 1 * The 13th digit of the Serbian and SFRY|Former Yugoslav Unique Master Citizen Number|Unique Master Citizen Number (JMBG). https://store.theartofservice.com/the-check-digit-toolkit.html

130. Check digit - In Eurasia 1 * The last two digits of the 11-digit Turkish Identification Number (). https://store.theartofservice.com/the-check-digit-toolkit.html

131. Check digit - In Eurasia 1 * The ninth character in the 14-character European Union|EU cattle passport number (cycles from 1 to 7: see British Cattle Movement Service#Ear tag number|British Cattle Movement Service). https://store.theartofservice.com/the-check-digit-toolkit.html

132. Check digit - In Eurasia 1 * The ninth digit in an Icelandic Kennitala (national ID number). https://store.theartofservice.com/the-check-digit-toolkit.html

133. Check digit - In Eurasia 1 * Modulo 97 check digits in a Belgium|Belgian and Serbian bank account numbers. https://store.theartofservice.com/the-check-digit-toolkit.html

134. Check digit - In Eurasia 1 * The ninth digit in a Hungary|Hungarian TAJ number (social insurance number). https://store.theartofservice.com/the-check-digit-toolkit.html

135. Check digit - In Eurasia 1 * For the residents of India, the unique identity number named AADHAAR#Salient features of AADHAAR|Aadhaar has a trailing 12th digit that is calculated with the Verhoeff algorithm. https://store.theartofservice.com/the-check-digit-toolkit.html

136. Check digit - In Eurasia 1 * The Intellectual Property Office of Singapore|Intellectual Property Office of Singapore (IPOS) has confirmed a new format for application numbers of registrable Intellectual Property (IP, e.g., Trademark|trade marks, patents, Industrial design right|registered designs). It will include a check character calculated with the Damm algorithm. https://store.theartofservice.com/the-check-digit-toolkit.html

137. Check digit - In Oceania 1 * The Australian Tax File Number (based on modulo operator|modulo 11). https://store.theartofservice.com/the-check-digit-toolkit.html

138. Check digit - In Oceania 1 * The seventh character of a New Zealand NHI Number. https://store.theartofservice.com/the-check-digit-toolkit.html

139. Check digit - In Oceania 1 * The last digit in a Locomotives of New Zealand|New Zealand locomotive's Traffic Monitoring System (TMS) number. https://store.theartofservice.com/the-check-digit-toolkit.html

140. Check digit - Algorithms 1 Notable algorithms include: https://store.theartofservice.com/the-check-digit-toolkit.html

141. Luhn algorithm - Verification of the check digit 1 digits = digits_of(card_number) https://store.theartofservice.com/the-check-digit-toolkit.html

142. Luhn algorithm - Calculation of the check digit 1 The algorithm above checks the validity of an input with a check digit. Calculating the check digit requires only a slight adaptation of the algorithm—namely: https://store.theartofservice.com/the-check-digit-toolkit.html

143. Luhn algorithm - Calculation of the check digit 1 # Append a zero check digit to the partial number and calculate checksum https://store.theartofservice.com/the-check-digit-toolkit.html

144. ISBN - ISBN-10 check digits 1 The 2001 edition of the official manual of the [http://www.isbn-international.org/ International ISBN Agency] says that the ISBN-10 check digit– which is the last digit of the ten-digit ISBN– must range from 0 to 10 (the symbol X is used for 10), and must be such that the sum of all the ten digits, each multiplied by its (integer) weight, descending from 10 to 1, is a multiple of 11 (number)|11. https://store.theartofservice.com/the-check-digit-toolkit.html

145. ISBN - ISBN-10 check digits 1 The two most common errors in handling an ISBN (e.g., typing or writing it) are a single altered digit or the transposition of adjacent digits. It can be mathematical proof|proved that all possible valid ISBN-10's have at least two digits different from each other. It can also be proved that there are no pairs of valid ISBN-10's with eight identical digits and two transposed digits. (These are true only because the ISBN is less than 11 digits long, and because 11 is a prime number.) https://store.theartofservice.com/the-check-digit-toolkit.html

146. ISBN - ISBN-10 check digits 1 The ISBN check digit method therefore ensures that it will always be possible to detect these two most common types of error, i.e https://store.theartofservice.com/the-check-digit-toolkit.html

147. ISBN - ISBN-10 check digit calculation 1 The resulting remainder, plus the check digit, must equal 11; therefore, the check digit is (11 minus the remainder of the sum of the products modulo 11) modulo 11 https://store.theartofservice.com/the-check-digit-toolkit.html

148. ISBN - ISBN-10 check digit calculation 1 The value x_ required to satisfy this condition might be 10; if so, an 'X' should be used. https://store.theartofservice.com/the-check-digit-toolkit.html

149. ISBN - ISBN-13 check digit calculation 1 The 2005 edition of the International ISBN Agency's official manual describes how the 13-digit ISBN check digit is calculated. The ISBN-13 check digit, which is the last digit of the ISBN, must range from 0 to 9 and must be such that the sum of all the thirteen digits, each multiplied by its (integer) weight, alternating between 1 and 3, is a multiple of 10 (number)|10. https://store.theartofservice.com/the-check-digit-toolkit.html

150. ISBN - ISBN-13 check digit calculation 1 The ISBN-10 formula uses the prime number|prime modulus 11 which avoids this blind spot, but requires more than the digits 0-9 to express the check digit. https://store.theartofservice.com/the-check-digit-toolkit.html

151. Routing transit number - Check digit 1 The ninth, check digit provides a checksum test using a position-weighted sum of each of the digits. High-speed check-sorting equipment will typically verify the checksum and if it fails, route the item to a reject pocket for manual examination, repair, and re-sorting. Mis- routings to an incorrect bank are thus greatly reduced. https://store.theartofservice.com/the-check-digit-toolkit.html

152. Routing transit number - Check digit 1 : (Modulo operation|Mod or modulo is the remainder of a division operation.) https://store.theartofservice.com/the-check-digit-toolkit.html

153. Routing transit number - Check digit 1 In terms of weights, this is 371 371 371 https://store.theartofservice.com/the-check-digit-toolkit.html

154. Routing transit number - Check digit 1 As an example, consider 111000025 (which is a valid routing number of Bank of America in Virginia). Applying the formula, we get: https://store.theartofservice.com/the-check-digit-toolkit.html

155. Routing transit number - Check digit 1 The following formula can be used to generate the ninth digit in the checksum: https://store.theartofservice.com/the-check-digit-toolkit.html

156. Routing transit number - Check digit 1 This is just moving all terms other than d_9 to the right hand side of the equation, which inverts the coefficients with respect to 10 (3 \mapsto (10-3) = 7; 7 \mapsto (10- 7) = 3; 1 \mapsto (10-1) = 9). https://store.theartofservice.com/the-check-digit-toolkit.html

157. Routing transit number - Check digit 1 Following the above example for the Bank of America routing number 111000025, https://store.theartofservice.com/the-check-digit-toolkit.html

158. Routing transit number - Check digit 1 This checksum is very easy to represent in computer programming languages. The following Python (programming language)|Python example will print True when the checksum is valid: https://store.theartofservice.com/the-check-digit-toolkit.html

159. Damm algorithm - Validating a number against the included check digit 1 #Set up an interim digit and initialize it to 0. https://store.theartofservice.com/the-check-digit-toolkit.html

160. Damm algorithm - Validating a number against the included check digit 1 #Process the number digit by digit: Use the number's digit as column index and the interim digit as row index, take the table entry and replace the interim digit with it. https://store.theartofservice.com/the-check-digit-toolkit.html

161. Damm algorithm - Validating a number against the included check digit 1 #The number is valid if and only if the resulting interim digit has the value of 0. https://store.theartofservice.com/the-check-digit-toolkit.html

162. Damm algorithm - Calculating the check digit 1 The resulting interim digit is '4'. This is the calculated check digit. We append it to the number and obtain '5724'. https://store.theartofservice.com/the-check-digit-toolkit.html

163. UPC code - Check digits 1 # Adding the odd-numbered digits (0+6+0+2+1+5 = 14) https://store.theartofservice.com/the-check-digit-toolkit.html

164. UPC code - Check digits 1 # Calculating modulo ten (58mod10 = 8) https://store.theartofservice.com/the-check-digit-toolkit.html

165. UPC code - Check digits 1 # Subtracting from ten (10minus;8 = 2) https://store.theartofservice.com/the-check-digit-toolkit.html

166. Base 11 - ISBN check digit 1 The check digit for ISBN|ISBN-10 is found as the result of taking modular arithmetic|modulo 11. Since this could give 11 possible results, the digit X, not A, is used in place of 10. Remember that X (disambiguation)|X is the Roman numeral for ten. (The newer ISBN-13 standard uses modulo 10, so no extra digits are required.) https://store.theartofservice.com/the-check-digit-toolkit.html

167. Code 128 - Check digit calculation 1 The remainder of the division is the check digit's 'value' which is then converted into a character (following the instructions given Code 128#Conversion to char|below) and appended to the end of the barcode. https://store.theartofservice.com/the-check-digit-toolkit.html

168. Code 128 - Calculating check digit with multiple variants 1 As Code 128 allows multiple variants, as well as switching between variants within a single barcode, the absolute Code 128 value of a character is completely independent of its value within a given variant. For instance the Variant C value 33 and the Variant B value A are both considered to be a Code 128 value of 33, and the check digit would be computed based on the value of 33 times the character's position within the barcode. https://store.theartofservice.com/the-check-digit-toolkit.html

169. For More Information, Visit: https://store.theartofservice.co m/the-check-digit-toolkit.html https://store.theartofservice.co m/the-check-digit-toolkit.html The Art of Service https://store.theartofservice.com