48:
219:(2004), that too detects all single-digit errors and all adjacent transposition errors. These three methods use a single check digit and will therefore fail to capture around 10% of more complex errors. 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
356:: 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 (mod 11). So the ISBN is valid. Positions can also be counted from left, in which case the check digit is multiplied by 10, to check validity: 0×1 + 2×2 + 0×3 + 1×4 + 5×5 + 3×6 + 0×7 + 8×8 + 2×9 + 1×10 = 143 ≡ 0 (mod 11).
402:
characters, which are alphanumerics minus vowels and the letter 'l' (ell). This restriction helps when generating opaque strings that are unlikely to form words by accident and will not contain both O and 0, or l and 1. Having a prime radix of R=29, the betanumeric repertoire permits the algorithm to
195:
with 10, so changing any digit changes the check digit; using a coefficient that is divisible by 2 or 5 would lose information (because 5×0 = 5×2 = 5×4 = 5×6 = 5×8 = 0 modulo 10) and thus not catch some single-digit errors. Using different weights on neighboring numbers means that most transpositions
199:
The ISBN-10 code instead uses modulo 11, which is prime, and all the number positions have different weights 1, 2, ... 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,
403:
guarantee detection of single-character and transposition errors for strings less than R=29 characters in length (beyond which it provides a slightly weaker check). The algorithm generalizes to any character repertoire with a prime radix R and strings less than R characters in length.
145:
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.
149:
A desirable feature is that left-padding with zeros should not change the check digit. This allows variable length numbers to be used and the length to be changed. If there is a single check digit added to the original number, the system will not always capture
734:
The last digit of
Chinese citizen ID number (second generation) is calculated by modulo 11-2 as specified in Chinese GuoBiao (aka national standard) GB11643-1999 which adopts ISO 7064:1983. 'X' is used if the calculated checking digit is
175:
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. 65 modulo 10, and the check digit would be 5, giving 48715.
196:
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.
347:
11 is 0. The digit the farthest to the right (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
290:
To calculate the check digit, take the remainder of (53 / 10), which is also known as (53 modulo 10), and if not 0, subtract from 10. Therefore, the check digit value is 7. i.e. (53 / 10) = 5 remainder 3; 10 - 3 =
262:
Take the remainder of the result divided by 10 (i.e. the modulo 10 operation). If the remainder is equal to 0 then use 0 as the check digit, and if not 0 subtract the remainder from 10 to derive the check
317:
To calculate the check digit, take the remainder of (5 / 10), which is also known as (5 modulo 10), and if not 0, subtract from 10: i.e. (5 / 10) = 0 remainder 5; (10 - 5) = 5. Therefore, the check digit
165:
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.
274:
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.
34:
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.
154:
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).
31:
used to check for errors in computer-generated data. It consists of one or more digits (or letters) computed by an algorithm from the other digits (or letters) in the sequence input.
200:
represented by "X". (An alternative is simply to avoid using the serial numbers which result in an "X" check digit.) ISBN-13 instead uses the GS1 algorithm used in EAN numbers.
1125:
27:
on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It is analogous to a binary
267:
A GS1 check digit calculator and detailed documentation is online at GS1's website. Another official calculator page shows that the mechanism for GTIN-13 is the same for
365:
343:
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
486:
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).
256:
Add the digits in the odd-numbered positions from the left (first, third, fifth, etc.—not including the check digit) together and multiply by three.
911:
179:
Systems with weights of 1, 3, 7, or 9, with the weights on neighboring numbers being different, are widely used: for example, 31 31 weights in
211:(1969), which catches all single-digit substitution and transposition errors, and many (but not all) more complex errors. Similar is another
334:
996:
971:
432:
1089:
1133:
708:
259:
Add the digits (up to but not including the check digit) in the even-numbered positions (second, fourth, sixth, etc.) to the result.
749:
1177:
467:
658:
191:. This system detects all single-digit errors and around 90% of transposition errors. 1, 3, 7, and 9 are used because they are
207:(1954), which captures 98% of single-digit transposition errors (it does not detect 90 ↔ 09) and the still more sophisticated
1110:
895:
608:
340:
1030:
490:
353:
220:
95:
77:
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483:
386:
and works with variable length strings of letters and digits, called extended digits. It is widely used with the
567:
73:
24:
639:
554:
508:
463:
Also used in the
Norwegian KID (customer identification number) numbers used in bank giros (credit transfer),
632:
522:
241:
69:
1158:
Identification numbers and check digit schemes (a mathematical explanation of various check digit schemes)
784:
543:
188:
1068:
915:
601:
The
Spanish fiscal identification number (número de identificación fiscal, NIF) (based on modulo 23).
395:
249:
58:
936:
223:) and/or to use a wider range of characters in the check digit, for example letters plus numbers.
724:
184:
62:
1000:
268:
245:
237:
180:
975:
374:
code found underneath a book's barcode. Its check digit is generated the same way as the UPC.
950:
712:
697:
383:
1100:
885:
504:
563:
patient identification numbers used in
Arizona and Florida include a trailing check digit.
8:
446:
382:
The NOID Check Digit
Algorithm (NCDA), in use since 2004, is designed for application in
116:
857:
1050:
David
Bressoud, Stan Wagon, "Computational Number Theory", 2000, Key College Publishing
806:
701:
208:
295:
Another example: to calculate the check digit for the following food item "01010101010
891:
830:
349:
890:. Classroom Resource Materials. Mathematical Association of America. pp. 4–6.
767:
643:
344:
212:
192:
162:
399:
881:
763:
682:
bank account numbers. Serbia sometimes also uses modulo 11, for reference number.
581:
475:
Last check digit in EAN/UPC serialisation of Global Trade
Identification Number (
187:
numbers (GS1 algorithm), and the 371 371 371 weights used in United States bank
812:
800:
728:
654:
580:
The
Guatemalan Tax Number (NIT – Número de Identificación Tributaria) based on
457:
387:
216:
204:
1171:
391:
1022:
618:
172:
of the digits, modulo 10, with different weights for each number position.
169:
158:
774:
711:(IPOS) has confirmed a new format for application numbers of registrable
605:
560:
453:
366:
International
Standard Book Number § ISBN-13 check digit calculation
157:
A very simple check digit method would be to take the sum of all digits (
777:
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28:
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109:
47:
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231:
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529:
720:
679:
625:
615:
371:
1061:"OpenFIGI: Unlock the Power of Efficiency with Open Symbology"
335:
International
Standard Book Number § ISBN-10 check digits
693:
635:(JMBG). (but not all of them, due to errors or non-residency)
536:
1060:
629:
476:
439:
421:
1126:"New Format for Singapore IP Application Numbers at IPOS"
727:). It will include a check character calculated with the
611:(BSN) (national identifier) uses the modulo 11 algorithm.
141:
phonetic errors, such as 60 → 16 ("sixty" to "sixteen")
119:. In order of complexity, these include the following:
700:
has a trailing 12th digit that is calculated with the
479:). It applies to GTIN-8, GTIN-12, GTIN-13 and GTIN-14.
989:
858:"What is Check Digit? - Definition from Techopedia"
390:scheme and somewhat used with schemes, such as the
1023:"noid - Nice Opaque Identifier Generator commands"
999:. International ISBN Agency. 2005. Archived from
972:"Check Digit Calculator, at GS1 US official site"
406:
1169:
874:
657:cattle passport number (cycles from 1 to 7: see
232:UPC, EAN, GLN, GTIN, numbers administered by GS1
1123:
887:Identification Numbers and Check Digit Schemes
370:ISBN 13 (in use January 2007) is equal to the
168:A slightly more complex method is to take the
1117:
1082:
135:jump transpositions errors, such as 132 → 231
964:
278:Add the odd number digits: 0+6+0+2+1+5 = 14.
1161:UPC, EAN, and SCC-14 check digit calculator
433:International Securities Identifying Number
305:Add the odd number digits: 0+0+0+0+0+0 = 0.
287:Add the two results together: 42 + 11 = 53.
284:Add the even number digits: 3+0+0+4+4 = 11.
123:letter/digit errors, such as l → 1 or O → 0
76:. Unsourced material may be challenged and
787:'s Traffic Monitoring System (TMS) number.
16:Error detection for identification numbers
1099:. Autumn 2011. p. 16. Archived from
937:"How to calculate a check digit manually"
709:Intellectual Property Office of Singapore
96:Learn how and when to remove this message
904:
880:
750:vehicle registration plates of Singapore
653:The ninth character in the 14-character
314:Add the two results together: 0 + 5 = 5.
311:Add the even number digits: 1+1+1+1+1=5.
203:More complicated algorithms include the
23:is a form of redundancy check used for
1170:
398:. An extended digit is constrained to
281:Multiply the result by 3: 14 × 3 = 42.
252:is a check digit computed as follows:
689:TAJ number (social insurance number).
574:
129:transposition errors, such as 12 → 21
638:The last two digits of the 11-digit
308:Multiply the result by 3: 0 x 3 = 0.
74:adding citations to reliable sources
41:
696:, the unique identity number named
456:account numbers, calculated by the
339:The final character of a ten-digit
138:jump twin errors, such as 131 → 232
13:
1124:Chong-Yee Khoo (20 January 2014).
943:
489:The third and fourth digits in an
341:International Standard Book Number
126:single-digit errors, such as 1 → 2
112:are generally designed to capture
14:
1189:
1152:
1020:
503:The final character encoded in a
491:International Bank Account Number
221:International Bank Account Number
498:International Standard Text Code
411:
46:
1071:from the original on 2022-08-09
1053:
1033:from the original on 2022-05-22
745:(Personal Identification Code).
659:British Cattle Movement Service
568:Customs & Border Protection
542:The final (ninth) digit of the
525:for the US healthcare industry.
417:The International SEDOL number.
1178:Error detection and correction
1044:
1014:
929:
914:. GS1 US. 2006. Archived from
850:
407:Other examples of check digits
1:
843:
791:
756:
640:Turkish Identification Number
598:uses the modulo 11 algorithm.
588:
555:Vehicle Identification Number
509:Longitudinal redundancy check
1090:"Unique Identification Card"
912:"GS1 Check Digit Calculator"
796:Notable algorithms include:
674:Modulo 97 check digits in a
633:Unique Master Citizen Number
523:National Provider Identifier
515:
242:International Article Number
132:twin errors, such as 11 → 22
7:
1132:. Cantab IP. Archived from
833:– similar modular sum check
819:
773:The seventh character of a
226:
10:
1194:
1164:GS1 check digit calculator
550:used in the United States.
544:ABA routing transit number
452:Modulo 10 check digits in
363:
359:
332:
328:
37:
974:. GS1 US. Archived from
951:"Check Digit Calculator"
566:The eleventh digit of a
438:Object Management Group
250:Global Trade Item Number
183:codes, 13 13 weights in
621:(Identity Card) number.
521:The tenth digit of the
377:
189:routing transit numbers
785:New Zealand locomotive
664:The ninth digit in an
647:
624:The 13th digit of the
614:The ninth digit of an
496:The final digit in an
420:The final digit of an
384:persistent identifiers
269:Global Location Number
246:Global Location Number
238:Universal Product Code
1130:Singapore Patent Blog
713:intellectual property
692:For the residents of
685:The ninth digit in a
671:(national ID number).
553:The ninth digit of a
528:The final digit of a
482:The final digit of a
442:standard final digit.
364:Further information:
333:Further information:
236:The final digit of a
783:The last digit in a
505:magnetic stripe card
117:transcription errors
70:improve this section
997:"ISBN Users Manual"
839:– binary equivalent
748:The last letter on
609:Burgerservicenummer
535:The North American
447:CAS registry number
215:-based method, the
807:Verhoeff algorithm
738:The 11th digit of
725:registered designs
702:Verhoeff algorithm
648:TC Kimlik Numarası
575:In Central America
493:(Modulo 97 check).
445:The International
209:Verhoeff algorithm
897:978-0-88385-720-5
831:Casting out nines
470:of mobile phones.
106:
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764:tax file number
762:The Australian
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630:Former Yugoslav
591:
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449:'s final digit.
414:
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368:
362:
337:
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102:
91:
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67:
51:
40:
25:error detection
17:
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5:
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1153:External links
1151:
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1106:on 2014-06-26.
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862:Techopedia.com
848:
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813:Damm algorithm
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801:Luhn algorithm
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458:Luhn algorithm
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205:Luhn algorithm
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1003:on 2014-04-29
1002:
998:
992:
978:on 2016-11-21
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354:0-201-53082-1
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55:This section
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32:
30:
26:
22:
1138:. Retrieved
1134:the original
1129:
1119:
1101:the original
1097:Geek Gazette
1096:
1084:
1073:. Retrieved
1064:
1055:
1046:
1035:. Retrieved
1027:metacpan.org
1026:
1016:
1005:. Retrieved
1001:the original
991:
980:. Retrieved
976:the original
966:
955:. Retrieved
945:
931:
920:. Retrieved
916:the original
906:
886:
876:
865:. Retrieved
861:
852:
795:
619:Teudat Zehut
381:
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273:
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178:
174:
170:weighted sum
167:
156:
151:
148:
144:
113:
108:Check digit
107:
92:
83:
68:Please help
56:
33:
20:
18:
953:. GS1. 2005
775:New Zealand
715:(IP, e.g.,
561:Mayo Clinic
454:credit card
400:betanumeric
324:value is 5.
159:digital sum
21:check digit
1075:2022-10-15
1037:2022-10-15
1007:2008-05-21
982:2012-08-09
957:2008-05-21
922:2008-05-21
867:2022-03-16
844:References
792:Algorithms
778:NHI Number
766:(based on
757:In Oceania
717:trademarks
596:NHS Number
589:In Eurasia
426:IMO Number
110:algorithms
86:April 2010
29:parity bit
837:Check bit
743:Isikukood
687:Hungarian
669:Kennitala
666:Icelandic
548:bank code
516:In the US
57:does not
1172:Category
1069:Archived
1065:OpenFIGI
1031:Archived
884:(2001).
826:Checksum
820:See also
740:Estonian
466:Used in
424:code or
227:Examples
152:multiple
721:patents
698:Aadhaar
680:Serbian
676:Belgian
644:Turkish
626:Serbian
616:Israeli
594:The UK
539:number.
530:POSTNET
435:(ISIN).
360:ISBN 13
329:ISBN 10
193:coprime
78:removed
63:sources
1140:6 July
939:. GS1.
894:
815:(2004)
809:(1969)
803:(1954)
768:modulo
582:modulo
557:(VIN).
372:EAN-13
352:
345:modulo
271:/GLN.
263:digit.
163:modulo
38:Design
1104:(PDF)
1093:(PDF)
694:India
606:Dutch
537:CUSIP
532:code.
114:human
1142:2014
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