893:, whichever direction they are read), the scanner will first see odd parity digits, if scanning left-to-right, or even parity digits, if scanning right-to-left. With the parity/direction information, an upside-down symbol will not confuse the scanner. When confronted with an upside-down symbol, the scanner may simply ignore it (many scanners alternate left-to-right and right-to-left scans, so they will read the symbol on a subsequent pass) or recognize the digits and put them in the right order. There is another property in the digit encoding. The right-hand side digits are the optical inverse of the left-hand side digits, i.e. black bars are turned into white spaces and vice versa. For example, the left-hand side "4" is
333:, the location where IBM would develop the scanner. During the presentation, Crouse gave a lab demonstration where he read UPC-like labels with his ring wand. In addition to reading regular labels, he read the large two-page centerfold label in the proposal booklet. He then turned to a page showing a photo of labeled items sitting on a table. The labels were small and flawed due to the resolution of the printed photo but the wand read many of them. This demonstration showed the robustness of the pure Delta C code. The proposal was accepted.
5647:
2615:, i.e. UPC-E barcode follows the pattern SDDDDDDE. The way in which a 6-digit UPC-E relates to a 12-digit UPC-A, is determined by UPC-E numerical pattern and UPC-E parity pattern. It can only correspond to UPC-A number system 0 or 1, the value of which, along with the UPC-A check digit, determines the UPC-E parity pattern of the encoding. With the manufacturer code digits represented by M's, and product code digits by P's, then:
5627:
4535:
33:
1027:
5637:
4545:
3184:
3175:
3166:
3157:
3148:
3139:
3130:
3121:
3112:
3103:
3094:
3085:
3076:
3067:
3058:
3049:
3040:
3031:
3022:
3013:
557:(1, 2, 3, or 4 units) of each bar (space). Since the guard patterns each include two bars, and each of the 12 digits of the UPC-A barcode consists of two bars and two spaces, all UPC-A barcodes consist of exactly (3 × 2) + (12 × 2) = 30 bars, of which 6 represent guard patterns and 24 represent numerical digits.
102:
85:(GTINs) and follow the global GS1 specification, which is based on international standards. Some retailers, such as clothing and furniture, do not use the GS1 system, instead using other barcode symbologies or article number systems. Some retailers use the EAN/UPC barcode symbology, but do not use a GTIN for products sold only in their own stores.
4243:
866:
859:
852:
845:
838:
831:
824:
817:
810:
803:
789:
782:
775:
768:
761:
754:
747:
740:
733:
726:
3193:
3006:
880:
873:
796:
719:
712:
1125:
488:, characters or other content of any kind may appear on a UPC-A barcode. There is a one-to-one correspondence between 12-digit number and strip of black bars and white spaces, i.e. there is only one way to represent each 12-digit number visually and there is only one way to represent each strip of black bars and white spaces numerically.
4227:
1202:. The LLLLL digits are digits 2-6 of the product's UPC prefix, the next three RRR are a family code (set by manufacturer or supplied by the coupon clearing house), and the next two RR are a value code (according to the GS1 value code table), which determines the amount of the discount. These coupons can be doubled or tripled.
300:
4046:
918:
577:
The UPC-A barcode is visually represented by strips of bars and spaces that encode the UPC-A 12-digit number. Each digit is represented by a unique pattern of 2 bars and 2 spaces. The bars and spaces are variable width, i.e. 1, 2, 3, or 4 modules wide. The total width for a digit is always 7 modules;
556:
UPC-A barcodes can be printed at various densities to accommodate a variety of printing and scanning processes. The significant dimensional parameter is called x-dimension (width of single module element). The width of each bar (space) is determined by multiplying the x-dimension and the module width
318:
Laurer's first attempt with a bar code used Delta B. The resulting label size was about six inches by three inches which was too large. Crouse suggested that Laurer use his Delta C bar code and provided a copy of his patent that had a sample alphanumeric character set and rules to generate other size
311:
These two proposals reduced the area from the bull's eye by one third and then one sixth. The image to the right shows the label proposed by
Baumeister. He did not specify any specific bar code as that was well understood. Except for the bar coding and ten digits the UPC label today is his proposal.
307:
In the spring of 1972, Baumeister announced a breakthrough. He proposed a label with bars that were slightly longer than the distance across all bars that needed to be read in a single pass. This label could be scanned with a simple "X" scanner only slightly more complex than the straight line laser
287:
Delta C achieved its higher performance by only using leading to leading or trailing to trailing edges which was unaffected by uniform ink spread. The code provided best performance when it had a defined character set with a fixed reference distance that spanned most or preferably all the character.
3238:
of UPC-A, adding an extra digit to the beginning of every UPC-A number. This expanded the number of unique values theoretically possible by ten times to 1 trillion. EAN-13 barcodes also indicate the country in which the company that sells the product is based (which may or may not be the same as the
888:
The UPC-A's left-hand side digits (the digits to the left of the M (middle) guard pattern) have odd parity, which means the total width of the black bars is an odd number of modules. On the contrary, the right-hand side digits have even parity. Consequently, a UPC scanner can determine whether it is
373:
Requiring every bit width to be read precisely basically nullified the Delta C advantage except for the Delta C reference measurement. Only the strange character set and the size of the label remains as a shadow of the Delta C code. The size was still that calculated for pure Delta C. If the label
369:
Then they decided to add odd/even parity to the number of units filled with bars in each side. Odd/even parity is a technique used to detect any odd number of bit errors in a bit stream. They decided to use odd on one half and even on the other. This would provide additional indication of which half
322:
Later Laurer asked Crouse for assistance in how the scanner could detect a label. Together they defined guard bars and a definition of how to detect the label. The guard bars also provided identification for half label discrimination and training bars for the scanner threshold circuits. Laurer had a
295:
Although Litton
Industries proposed a bull's eye symbol cut in half to reduce the area, it was still too large and presented the same ink smear printing problems as the RCA symbol. The redundancy and checking ability were removed completely. They were also aware of the many proposals from around the
1168:
Reserved for local use (store/warehouse), for items sold by variable weight. Variable-weight items, such as meats, fresh fruits, or vegetables, are assigned an item number by the store, if they are packaged there. In this case, the LLLLL is the item number, and the RRRRR is either the weight or the
377:
Mechanical engineering and electronic circuit design commonly require worst case designs using known tolerances. Many engineers working with bar codes had little experience with such things and used somewhat intuitive methods. This was the cause of the poor performance of the Delta B code and quite
357:
Laurer did not apply
Baumeister's equations to this set. He felt just one bar width measurement would not be too serious. As it turned out it would have required over fifty percent increase in width and height for an area increase of more than double. Laurer later admitted these four characters in
349:
Since eighteen characters were not enough Laurer tried adding one unit to the character set. This yielded twenty-six Delta C characters which could provide the two sets of decimal characters but it also added fourteen percent to the width of the label and thereby the height. This would be a thirty
345:
It was decided that the two halves of the label should have a different set of numeric characters. The character set Laurer derived from the Delta C patent used seven printable increments or units where two bars and two spaces would be printed. This yielded twenty combinations of characters, but
3767:
After graduating from
Maryland in 1951, George Laurer joined IBM as a junior engineer and worked up the ranks to senior engineer. In 1969, he returned to the technical side of engineering and was later assigned the monumental task of designing a code and symbol for product identification for the
2610:
To allow the use of UPC barcodes on smaller packages, where a full 12-digit barcode may not fit, a zero-suppressed version of UPC was developed, called UPC-E, in which the number system digit, all trailing zeros in the manufacturer code, and all leading zeros in the product code, are suppressed
353:
Laurer returned to the original character set with twenty characters but four of those were two pairs with the same Delta C reading. He decided to use them all. To distinguish between the pairs he would measure one bar width in each of the pairs to distinguish them from each other. For each pair
560:
The x-dimension for the UPC-A at the nominal size is 0.33 mm (0.013"). Nominal symbol height for UPC-A is 25.9 mm (1.02"). The bars forming the S (start), M (middle), and E (end) guard patterns, are extended downwards by 5 times x-dimension, with a resulting nominal symbol height of
342:, makers of handheld printing devices insisted that the code be character independent, so that handheld printing devices could produce the bar code in store if the items were not bar-coded by the manufacturers. Dymo's proposal was accepted by IBM and incorporated in IBM's latest proposal.
4033:
3405:
1036:
1462:
4019:
291:
In August 1971, Crouse joined the scanner effort. After several months they had made no progress. They were aware of the RCA bull's eye label that could be scanned with a simple straight line laser scanner, but a readable label was far too large.
585:
A complete UPC-A is 95 modules wide: 84 modules for the digits (L and R sections) combined with 11 modules for the S (start), M (middle), and E (end) guard patterns. The S (start) and E (end) guard patterns are 3 modules wide and use the pattern
4006:
499:
E, where S (start), M (middle), and E (end) guard patterns are represented the same way on every UPC-A barcode and the L (left) and R (right) sections collectively represent the 12 numerical digits that make each UPC-A unique. The first digit
361:
David Savir, a mathematician, was given the task of proving the symbol could be printed and would meet the reliability requirements, and was most likely unaware of
Baumeister's equations. He and Laurer added two more digits to the ten for
276:
to determine how to make a supermarket scanner and label. In late 1970, Heard
Baumeister provided equations to calculate characters-per-inch achievable by two IBM bar codes, Delta A and Delta B. In February 1971, Baumeister joined Laurer.
3693:
1022:{\displaystyle {\begin{aligned}{\text{(possible values per left digit)}}^{\text{(left digits)}}&\times {\text{(possible values per right digit)}}^{\text{(5 right digits)}}\\=10^{6}&\times 10^{5}=100,000,000,000.\end{aligned}}}
2462:
65:
The chosen symbology has bars (or spaces) of exactly 1, 2, 3, or 4 units wide each; each decimal digit to be encoded consists of two bars and two spaces chosen to have a total width of 7 units, in both an "even" and an "odd"
564:
A quiet zone, with a width of at least 9 times the x-dimension, must be present on each side of the scannable area of the UPC-A barcode. For a GTIN-12 number encoded in a UPC-A barcode, the first and last digits of the
280:
Delta B compared bar widths to space width to code bits. This was extremely sensitive to ink spread, where improper levels of ink or pressure would cause both edges of a bar to spread outward or shrink in.
1120:{\displaystyle {\begin{aligned}{\text{(possible values per digit)}}^{\text{(digits)}}&\times {\text{(possible parity patterns per UPC-E number)}}\\=10^{6}&\times 2=2,000,000.\end{aligned}}}
235:
cash register rang up 67 cents. The shopping cart also contained other barcoded items but the gum was the first one picked up at the checkout. A facsimile of the gum packet went on display at the
4044:, Crouse, William G. & Jones, John E., "Method and Device for Reading and Decoding a High Density Self-Clocking Bar Code", published 28 June 1971, issued 27 March 1973
1041:
923:
594:, where each bar and space is also one module wide. In addition, a UPC-A symbol requires a quiet zone (extra space of 9 modules wide) before the S (start) and after the E (end) guard patterns.
3685:
256:, he helped "select a symbol that would endure the inevitable rush of technology that lay ahead." He chose the font, and he came up with the idea to add numbers to the bottom, which is a
1248:
2005:
1740:
1823:
209:/Data General, put forward alternative proposals for symbol representations to the council. The Symbol Selection Committee finally chose to implement the IBM proposal designed by
1898:
3853:
3768:
Uniform
Grocery Product Code Council. His solution—the Universal Product Code—radically changed the retail world. Since then, he has enhanced the code by adding a 13th digit.
1633:
UPC-A can detect about 89% of transposition errors. Specifically, if and only if the difference between two adjacent digits is 5, the UPC-A can't detect their transposition.
315:
Laurer proceeded to define the details of the label and write a proposal. N.J. Woodland was assigned as planner for the project and aided Laurer with writing his proposal.
561:
27.55 mm (1.08"). This also applies to the bars of the first and last numerical digit of UPC-A barcode. UPC-A can be reduced or magnified anywhere from 80% to 200%.
3270:
In North
America, the EAN adds 30% more codes, mainly by adding digits 10 through 12 to the UPC digits 00 through 09. This is a powerful incentive to phase out the UPC.
4812:
2776:
For example, a UPC-E 654321 may correspond to the UPC-A 065100004327 or 165100004324, depending on the UPC-E parity pattern of the encoded digits, as described next:
1236:
3811:
2611:(omitted). This symbology differs from UPC-A in that it only uses a 6-digit code, does not use M (middle) guard pattern, and the E (end) guard pattern is formed as
515:, that allows some errors to be detected in scanning or manual entry. The guard patterns separate the two groups of six numerical digits and establish the timing.
1617:
can be any other value in {1, 2, 3, 4, 5, 6, 7, 8, 9}. If the error digit is in an odd position (weight 1), the left hand side of check digit equation changes by
5591:
4031:, Shields, Charles B. & Stapelfeldt, Roelif, "Automatic car identification system", published 17 August 1967, issued 2 November 1971
3537:
889:
scanning a symbol from left-to-right or from right-to-left (the symbol is upside-down). After seeing a S (start) or E (end) guard pattern (they are the same,
4616:
70:
form, which enables being scanned in either direction. Special "guard patterns" (3 or 5 units wide, not encoding a digit) are intermixed to help decoding.
2362:
370:
ticket was being read. This meant that every bar width had to be read accurately to provide a good reading. It also meant every space would also be known.
336:
One month later, 1 January 1973 Crouse transferred back to IBM's
Advanced Technology group, and Laurer remained with the full responsibility for the label.
1183:
are scanned at point of sale, NDC-based UPCs are used on prescription drug packages and surgical products and, in this case, are commonly called UPN Codes.
4837:
88:
Research indicates that the adoption and diffusion of the UPC stimulated innovation and contributed to the growth of international retail supply chains.
3478:
3452:
326:
Previously Crouse had an idea for a simple wand worn like a ring and bracelet. He decided to develop that wand to provide a demonstration of the label.
374:
size had been properly recalculated, taking into account the required bar width measurements the label would have been far too large to be acceptable.
4969:
4947:
3905:
547:
UPC-A 042100005264 is equivalent to UPC-E 425261 with the "EOEEOO" parity pattern, which is defined by UPC-A number system 0 and UPC-A check digit 4.
3576:
4611:
4301:
3660:
Twenty-Five Years Behind Bars: The
Proceedings of the Twenty-Fifth Anniversary of the U.P.C. at the Smithsonian Institution, September 30, 1999
5083:
3668:
253:
350:
percent increase in area or a label of 1.7 in × 1.03 in (43 mm × 26 mm). Laurer felt this was not acceptable.
3243:. Every UPC-A code can be easily converted to the equivalent EAN-13 code by prepending 0 digit to the UPC-A code. This does not change the
3606:
4827:
3635:
3510:
569:
are always placed outside the symbol in order to indicate the quiet zones that are necessary for UPC barcode scanners to work properly.
240:
3789:
5690:
5580:
4104:
3746:
284:
In mid 1971, William "Bill" Crouse invented a new bar code called Delta C. It achieved four times the characters per inch as Delta B.
183:
78:
3430:
3213:
5314:
4889:
2586:
UPC-D is a variable length code (12 digits or more) with the 12th digit being the check digit. These versions are not in common use.
1605:
A single digit error means exactly one digit is wrong. Let the difference modulo 10 of the erroneous digit and the correct digit be
5228:
3845:
3724:
3374:
5743:
5738:
5160:
3883:
1621:
and the equivalence is no longer zero. If the error digit is in an even position (weight 3), then the left hand side changes by
308:
scanner. The next day Baumeister suggested if the label were split into two halves the bar lengths could be cut nearly in half.
5670:
5660:
5650:
5187:
252:
was a consultant on the team that created the Universal Product Code barcode. As Chairman of a committee of scientists at the
5665:
5360:
5350:
5248:
4479:
3305:
531:
509:
363:
3264:
All products marked with an EAN will be accepted in North America currently, in addition to those already marked with a UPC.
538:
484:
Each UPC-A barcode consists of a scannable strip of black bars and white spaces above a sequence of 12 numerical digits. No
5553:
5319:
4581:
566:
5723:
5718:
5680:
5675:
5284:
4157:
4079:
GS1 three-digit prefix list indicating country of origin of company in UPC code (not necessarily country of manufacture)
3231:
3225:
2350:-transpositions, therefore the proportion of non-detectable transposition errors is (ignoring the transpositions where
1457:{\displaystyle (3x_{1}+x_{2}+3x_{3}+x_{4}+3x_{5}+x_{6}+3x_{7}+x_{8}+3x_{9}+x_{10}+3x_{11}+x_{12})\equiv 0{\pmod {10}}.}
1179:(NDC) number. Pharmaceuticals in the U.S. use the middle 10 digits of the UPC as their NDC number. Though usually only
197:, defined the numerical format that formed the basis of the Uniform Product Code. Technology firms including Charegon,
5733:
5177:
5069:
4437:
3527:
123:
3968:
73:
A UPC (technically, a UPC-A) consists of 12 digits that are uniquely assigned to each trade item. The international
5548:
5532:
5074:
5029:
4957:
4276:
1211:
The UPC includes a check digit to detect common data entry errors. For example, UPC-A codes choose the check digit
590:, where each bar and space is one module wide. The M (middle) guard pattern is 5 modules wide and uses the pattern
3239:
country in which the good is manufactured). The three leading digits of the code determine this, according to the
4662:
4392:
3946:
3240:
2580:
and National Health Related Items Code. It has 11 digits plus a 1-digit product code, and is not in common use.
5685:
5466:
5274:
5129:
4296:
1951:
1552:
Add the even-numbered digits (42 + (3 + 0 + 0 + 9 + 4) = 58).
319:
alphabets. This reduced the label size to about 1.5 in × 0.9 in (38 mm × 23 mm).
82:
5107:
3913:
3486:
3464:
1135:
Below is a description of all possible number systems with the corresponding 12-digit UPC-A numbering scheme
5527:
5233:
4500:
4407:
3205:
1-1-1 4-1-1-1 1-2-3-1 2-3-1-1 1-4-1-1 2-2-1-2 2-2-2-1 1-1-1-1-1-1.
236:
127:
1665:
1658:
is the difference between the two digits. If the digits were in their correct order, they would contribute
1546:
Sum the odd-numbered digits (0 + 6 + 0 + 2 + 1 + 5 = 14).
5558:
5145:
4847:
4097:
1751:
269:
160:
5574:
5539:
5165:
5124:
4755:
3572:
1180:
4060:
4017:, Brainerd, H. B., "Identification System", published 2 July 1959, issued 18 April 1964
1835:
194:
4041:
4028:
4014:
4001:
3396:
5728:
5394:
5304:
5258:
5253:
5059:
4857:
4802:
4785:
4628:
4510:
4343:
3831:
1485:
1475:
330:
5568:
5430:
5365:
5170:
5113:
5079:
4548:
4505:
4004:, Bilgutay, Ilhan M., "Bar Code Font", published 11 May 1972, issued 27 August 1974
3658:
2589:
UPC-E is a 6-digit code, that has its equivalent in UPC-A 12-digit code with number system 0 or 1.
1908:
modulo 10, then the change will not be detected. Consequently, only when the character difference
5543:
5518:
5418:
5400:
5064:
4271:
4172:
3366:
2577:
1176:
224:
381:
The following table shows the workable labels, available in the early 1970s, with their sizes.
216:
The first UPC-marked item ever to be scanned at a retail checkout was a 10-pack (50 sticks) of
5713:
5655:
5602:
5496:
5491:
5355:
5279:
4874:
4842:
4750:
4682:
4667:
4574:
4538:
4167:
4090:
3805:
3664:
3598:
3506:
3358:
3286:
164:
3629:
5585:
5388:
5380:
5309:
5211:
5139:
4740:
4697:
4692:
3781:
3557:
3552:
3532:
3350:
2595:
is a 2-digit supplement to the UPC used to indicate the edition of a magazine or periodical.
1746:
to the left hand side of the check digit equation. In the transposed order, they contribute
1214:
339:
273:
244:
210:
206:
3754:
5563:
5476:
5299:
5238:
4884:
4807:
4677:
4458:
4453:
4064:
3422:
1628:, but that change is also nonzero modulo 10, so the check digit equation is not satisfied.
232:
131:
111:
909:
The number of UPC-A and UPC-E barcodes are limited by the standards used to create them.
346:
there were two pairs that when read by Delta C rules yielded the same code for the pair.
182:, but this system was eventually abandoned and replaced with a radio-based system called
4076:
1594:
The check digit equation is selected to have reasonable error detection properties (see
504:
indicates a particular number system to be used by the following digits. The last digit
5612:
5486:
5481:
5442:
5370:
5324:
5243:
4952:
4832:
4606:
4598:
4515:
4463:
4397:
3716:
3400:
3338:
1595:
171:
156:
3875:
2457:{\displaystyle {\frac {10}{18+16+14+12+10+8+6+4+2}}={\frac {10}{90}}=11.111\ldots \%.}
5707:
5461:
5436:
5406:
5192:
4913:
4852:
4760:
4735:
4650:
4182:
3370:
3248:
2601:
is a 5-digit supplement to the UPC used to indicate suggested retail price for books.
329:
On 1 December 1972, IBM presented Laurer's proposal to the Super Market Committee in
5630:
5424:
5412:
5017:
5012:
4991:
4567:
4372:
4202:
3201:
UPC-E 654321 with "EOEOEO" parity pattern (UPC-A 065100004327) would be encoded as
1190:
179:
152:
50:
3503:
Punched Cards to Bar Codes: A 200 Year Journey with Descriptions of over 260 Codes
3315:
2583:
UPC-C is a 12-digit code with a product code and a check digit; not in common use.
1830:
to the LHS. Subtracting the two contributions gives how much they change the LHS:
476:
This is assuming a bull's eye with the same information and reliable readability.
217:
32:
3825:
3686:"Murray Eden, a biomedical engineer with a love of singing, dies in Tucson at 99"
1158:
For most products. The LLLLL digits are the manufacturer code (assigned by local
5501:
5471:
5294:
5182:
4906:
4901:
4672:
4357:
4327:
4322:
4187:
4162:
3244:
1467:
If an entered code does not satisfy the equation, then it is not a valid UPC-A.
512:
249:
220:
5223:
5216:
5150:
4896:
4717:
4707:
4352:
4197:
4192:
3969:"UPC-A Symbology – UPC-E background information and UPC-A to UPC-E conversion"
228:
59:
3362:
67:
4981:
4974:
4790:
4712:
4702:
4317:
257:
189:
In 1973, a group of trade associations from the grocery industry formed the
130:
to the section by replacing the section with a link and a summary or by
3939:"Bar Code 1: A Web Of Information About Bar Code UPC and EAN Bar Code Page"
3339:"Upstream, Downstream: Diffusion and Impacts of the Universal Product Code"
303:
The UPC Label showing the general characteristics of Baumeister's proposals
193:(UPCC) which, with the help of consultants Larry Russell and Tom Wilson of
3976:
3212:
2576:
UPC-B is a 12-digit version of UPC with no check digit, developed for the
5640:
5597:
5345:
5289:
5054:
5039:
5022:
4867:
4795:
4765:
4421:
4416:
4382:
4377:
4361:
4250:
4147:
485:
213:, but with a slight modification to the font in the human readable area.
3663:. Harvard University Wertheim Publications Committee. pp. 74, 108.
167:, developed a bull's-eye-style code and applied for the patent in 1949.
5607:
5049:
5044:
4986:
4817:
4745:
4387:
4367:
4286:
4281:
4207:
4152:
4142:
4137:
4132:
4127:
4113:
1904:
An error will be detected as long as the modular change is nonzero; if
175:
117:
55:
3938:
3267:
Products with an existing UPC do not have to be re-marked with an EAN.
3183:
3174:
3165:
3156:
3147:
3138:
3129:
3120:
3111:
3102:
3093:
3084:
3075:
3066:
3057:
3048:
3039:
3030:
3021:
3012:
77:
organisation assigns the digits used for both the UPC and the related
5034:
5007:
4964:
4942:
4862:
4520:
4484:
4332:
4291:
4177:
3599:"Oral-History: Murray Eden - Engineering and Technology History Wiki"
3310:
3235:
1492:
1488:-numbered positions (second, fourth, sixth,..., tenth) to the result.
1199:
190:
17:
4242:
4061:
UPC History - ID History Museum - Where the history of the UPC lives
865:
858:
851:
844:
837:
830:
823:
816:
809:
802:
788:
781:
774:
767:
760:
753:
746:
739:
732:
725:
3403:, "Classifying Apparatus and Method", issued 7 October 1952
3354:
3192:
3005:
879:
872:
795:
718:
711:
312:
Shortly after that Baumeister transferred to another area of RTP.
299:
4655:
3254:
2598:
2592:
298:
151:
Wallace Flint proposed an automated checkout system in 1932 using
31:
1506:
is zero, then the check digit is 0; otherwise the check digit is
4879:
4822:
4262:
4226:
3912:. U.S. Department of Health & Human Services. Archived from
537:
530:
4563:
4086:
1636:
If 2 neighboring digits are transposed, then one of the digits
1613:
cannot be zero because that means the digits are the same, but
491:
The scannable area of every UPC-A barcode follows the pattern S
434:
6.0 in × 5.8 in (150 mm × 150 mm)
358:
each set were responsible for most of the scanner read errors.
323:
complete label definition and proceeded to write his proposal.
4590:
3280:
1159:
456:
4.5 in × 2.3 in (114 mm × 58 mm)
445:
6.0 in × 3.0 in (152 mm × 76 mm)
202:
198:
95:
74:
4070:
3631:
Technology Applied to the Food Industry: A Preliminary Report
3628:
National Commission on Productivity and Work Quality (1975).
467:
1.5 in × 0.9 in (38 mm × 23 mm)
260:
system, in case the barcode reader is not working correctly.
3211:
4082:
2569:
UPC in its most common usage technically refers to UPC-A.
1169:
price, with the first R determining which (0 for weight).
1162:
organization), and the RRRRR digits are the product code.
27:
Barcode symbology used for tracking trade items in stores
1495:
10 (i.e. the remainder, when divided by 10) and call it
1478:-numbered positions (first, third, fifth,..., eleventh).
578:
consequently, UPC-A 12-digit number requires a total of
1927:
Next consider how often a transposition has a distance
201:, Litton-Zellweger, Pitney Bowes-Alpex, Plessey-Anker,
4559:
3528:"June 26, 1974: By Gum! There's a New Way to Buy Gum"
2365:
1954:
1838:
1754:
1668:
1555:
Find the result modulo 10 (58 mod 10 = 8 =
1251:
1217:
1039:
921:
3846:"Barcodes for Pharmaceuticals and Surgical Products"
1470:
The UPC-A check digit may be calculated as follows:
1189:
Reserved for local use (store/warehouse), often for
5510:
5452:
5379:
5338:
5267:
5201:
5097:
5000:
4935:
4926:
4778:
4728:
4643:
4636:
4627:
4597:
4493:
4472:
4446:
4430:
4406:
4341:
4310:
4261:
4120:
3283:– International supply-chain standards organization
3753:. The University of Maryland. 2005. Archived from
2915:Encoding table for UPC-E barcode pattern SDDDDDDE
2456:
1999:
1892:
1817:
1734:
1456:
1230:
1119:
1021:
4813:Criminal Reduction Utilising Statistical History
1922:the degenerate "transposition" is not an error).
378:likely the failure of RCA's bull's eye scanner.
81:barcode. UPC data structures are a component of
1602:UPC-A can detect 100% of single digit errors.
4575:
4098:
8:
3906:"NHRIC (National Health Related Items Code)"
3257:is an 8-digit variation of the EAN barcode.
1991:
1961:
1946:Table of d-transpositions for UPC-A barcodes
1549:Multiply the result by 3 (14 × 3 = 42).
1517:For example, in a UPC-A barcode "03600029145
4438:High Capacity Color Barcode (Microsoft Tag)
3810:: CS1 maint: numeric names: authors list (
1640:will be weighted by 1, and the other digit
1065:(possible parity patterns per UPC-E number)
354:those bars would be one or two units wide.
4932:
4640:
4633:
4582:
4568:
4560:
4105:
4091:
4083:
3505:. Peterborough, N.H.: Helmers Publishing.
3479:"Our innovative history – McKinsey firsts"
598:Encoding table for UPC-A barcode pattern S
3933:
3931:
3751:University of Maryland Alumni Association
3417:
3415:
3251:systems can now understand both equally.
2429:
2366:
2364:
2000:{\displaystyle d\in \{0,1,2,\ldots ,9\}:}
1953:
1837:
1753:
1667:
1435:
1420:
1407:
1391:
1378:
1362:
1349:
1333:
1320:
1304:
1291:
1275:
1262:
1250:
1222:
1216:
1079:
1063:
1050:
1045:
1040:
1038:
985:
968:
951:
946:
932:
927:
922:
920:
231:, at 8:01 a.m. on 26 June 1974. The
3399:, Woodland, Norman J. &
2913:
2778:
2617:
2023:
596:
383:
184:Automatic Equipment Identification (AEI)
3297:
1147:denotes the numbering system digit and
897:, meanwhile the right-hand side "4" is
3803:
3684:Casanova, Stephanie (18 August 2020).
3337:Basker, Emek; Simcoe, Timothy (2021).
4948:Center for The Business of Government
3886:from the original on 16 February 2022
3856:from the original on 28 February 2023
3433:from the original on 12 November 2021
1735:{\displaystyle 1a+3b=1a+3(a+d)=4a+3d}
254:Massachusetts Institute of Technology
7:
5636:
4544:
3727:from the original on 21 January 2021
3696:from the original on 14 January 2021
3609:from the original on 21 January 2021
3579:from the original on 9 February 2022
3540:from the original on 24 August 2010.
3423:"UPC - The Transformation of Retail"
1818:{\displaystyle 1b+3a=3a+1(a+d)=4a+d}
296:world, none of which were feasible.
58:that is used worldwide for tracking
3792:from the original on 29 August 2011
3463:(3): 42. March 2010. Archived from
3209:The barcode would look like this:
2029:-transpositions for UPC-A barcodes
1443:
412:12.0 in (300 mm) diameter
174:in North America experimented with
3638:from the original on 19 March 2022
3575:. Smithsonian. 23 September 2015.
2767:0 or 1 + MMMMM-00009 + check digit
2753:0 or 1 + MMMMM-00008 + check digit
2739:0 or 1 + MMMMM-00007 + check digit
2725:0 or 1 + MMMMM-00006 + check digit
2711:0 or 1 + MMMMM-00005 + check digit
2697:0 or 1 + MMMM0-0000P + check digit
2683:0 or 1 + MMM00-000PP + check digit
2669:0 or 1 + MM200-00PPP + check digit
2655:0 or 1 + MM100-00PPP + check digit
2641:0 or 1 + MM000-00PPP + check digit
2448:
1915:will an error be undetected (when
423:9.0 in (230 mm) diameter
79:International Article Number (EAN)
25:
4617:PC business acquisition by Lenovo
3949:from the original on 8 March 2021
3453:"A Brief History of the Bar Code"
2572:Other variants of the UPC exist:
1893:{\displaystyle (4a+3d)-(4a+d)=2d}
948:(possible values per right digit)
899:bar×1 - space×1 - bar×3 - space×2
895:space×1 - bar×1 - space×3 - bar×2
272:(RTP) in North Carolina assigned
5646:
5645:
5635:
5626:
5625:
5315:Sabre airline reservation system
5161:Thomas J. Watson Research Center
4543:
4534:
4533:
4241:
4225:
3782:"Drawing UPC-A Barcodes with C#"
3377:from the original on 17 May 2021
3191:
3182:
3173:
3164:
3155:
3146:
3137:
3128:
3119:
3110:
3101:
3092:
3083:
3074:
3065:
3056:
3047:
3038:
3029:
3020:
3011:
3004:
929:(possible values per left digit)
878:
871:
864:
857:
850:
843:
836:
829:
822:
815:
808:
801:
794:
787:
780:
773:
766:
759:
752:
745:
738:
731:
724:
717:
710:
536:
529:
100:
4828:Information Management Software
3827:UPC Symbol Specification Manual
1436:
415:113.10 in (729.7 cm)
5581:International chess tournament
5361:Globally integrated enterprise
5351:Commercial Processing Workload
3526:Alfred, Randy (26 June 2008).
3314:. 3 April 2013. Archived from
2794:UPC-E parity pattern for UPC-A
2787:UPC-E parity pattern for UPC-A
1878:
1863:
1857:
1839:
1797:
1785:
1711:
1699:
1447:
1437:
1426:
1252:
453:Baumeister 2 halves w/ Delta A
448:18.00 in (116.1 cm)
442:Baumeister 2 halves w/ Delta B
437:34.80 in (224.5 cm)
426:63.62 in (410.5 cm)
364:error detection and correction
223:chewing gum, purchased at the
170:In the 1960s and early 1970s,
165:Drexel Institute of Technology
1:
5320:Scanning tunneling microscope
3747:"Alumni Hall Of Fame Members"
3573:"The History of the Bar Code"
2613:space-bar-space-bar-space-bar
1654:will be weighted by 3, where
567:human-readable interpretation
459:10.35 in (66.8 cm)
4128:Automatic Car Identification
4073:Free online database of UPCs
3715:Roth, Brad (17 April 2020).
3343:Journal of Political Economy
3226:International Article Number
1533:is the unknown check digit,
205:, Scanner Inc., Singer, and
191:Uniform Product Code Council
5188:Canada Head Office Building
5178:Cambridge Scientific Center
5070:Science Research Associates
4838:Mainframe operating systems
4067: (archived 7 July 2019)
3780:rainman_63 (6 April 2005).
1047:(possible values per digit)
470:1.35 in (8.7 cm)
114:the scope of other articles
5760:
5249:Virtual Universe Community
4970:International subsidiaries
4890:Service Automation Manager
4277:Facing Identification Mark
3657:Haberman, Alan L. (2001).
3223:
3002:
2929:
2924:
2630:Available product numbers
708:
630:
620:
398:Bull's eye with Morse Code
163:, a graduate student from
5621:
4529:
4219:
3561:. September–October 2005.
3501:Nelson, Benjamin (1997).
2934:
2919:
1481:Multiply the result by 3.
640:
635:
625:
615:
610:
592:space-bar-space-bar-space
431:Baumeister 1st w/ Delta B
268:Around late 1969, IBM at
83:Global Trade Item Numbers
5275:Automated teller machine
5229:The Great Mind Challenge
4612:Mergers and acquisitions
4297:Intelligent Mail barcode
2578:National Drug Code (NDC)
633:(right numerical digit)
5744:20th-century inventions
5739:Product classifications
5234:Linux Technology Center
4501:Supply chain management
4158:European Article Number
2624:UPC-E numerical pattern
2346:contains the number of
1207:Check digit calculation
623:(left numerical digit)
464:Baumeister with Delta C
420:Bull's eye with Delta A
409:Bull's eye with Delta B
241:American history museum
237:Smithsonian Institution
5559:Dynamic infrastructure
5524:Big Blue sports teams
5330:Universal Product Code
3876:"Barcodes for Coupons"
3485:. 2013. Archived from
3216:
2458:
2001:
1894:
1819:
1736:
1582:Thus, the check digit
1542:may be calculated by:
1458:
1232:
1231:{\displaystyle x_{12}}
1181:over-the-counter drugs
1121:
1023:
580:7×12 = 84 modules
304:
270:Research Triangle Park
195:McKinsey & Company
161:Norman Joseph Woodland
42:Universal Product Code
37:
5691:Vacuum tube computers
5575:IBM and the Holocaust
5540:Common Public License
5425:Louis V. Gerstner Jr.
5208:Academy of Technology
4663:Power microprocessors
4311:2D barcodes (stacked)
3397:US patent 2612994
3215:
2459:
2002:
1895:
1820:
1737:
1484:Add the digit sum at
1459:
1233:
1122:
1024:
302:
132:splitting the content
126:and help introduce a
35:
5305:Magnetic stripe card
5254:World Community Grid
5130:Toronto Software Lab
4786:Carbon Design System
4741:Cell microprocessors
4447:Technological issues
3943:Adams Communications
3832:Uniform Code Council
3605:. 10 November 1999.
3491:(see slide 10 of 18)
2932:(even parity digit)
2363:
1952:
1836:
1752:
1666:
1249:
1240:check digit equation
1215:
1037:
919:
331:Rochester, Minnesota
176:multicolor bar codes
5724:Checksum algorithms
5719:American inventions
5569:GUIDE International
5431:Samuel J. Palmisano
5290:Electronic keypunch
5114:One Atlantic Center
5084:Weather Underground
5080:The Weather Company
4506:Object hyperlinking
3979:on 26 February 2020
3489:on 12 October 2013.
3306:"GS1 BARCODE CHART"
3234:was developed as a
2927:(odd parity digit)
2916:
2030:
1566:is not 0, subtract
1131:Number system digit
607:
134:into a new article.
5734:Unique identifiers
5671:Personal computers
5661:Midrange computers
5651:Navigational boxes
5544:IBM Public License
5519:A Boy and His Atom
5477:Michelle J. Howard
5419:John Fellows Akers
5401:T. Vincent Learson
5108:1250 René-Lévesque
4848:Planning Analytics
4272:CPC Binary Barcode
4173:Interleaved 2 of 5
4077:GS1 company prefix
4024:Railroad bar code.
3880:SimplyBarcodes.com
3690:Arizona Daily Star
3553:"Scanning Species"
3217:
2914:
2454:
2024:
1997:
1890:
1815:
1732:
1576:= 10 − 8 = 2
1474:Sum the digits at
1454:
1228:
1177:National Drug Code
1117:
1115:
1019:
1017:
597:
305:
124:discuss this issue
38:
5701:
5700:
5666:Operating systems
5528:American football
5497:Joseph R. Swedish
5492:Martha E. Pollack
5395:Thomas Watson Jr.
5356:Customer engineer
5280:Cynefin framework
5166:Hakozaki Facility
5125:Rome Software Lab
5093:
5092:
4922:
4921:
4875:Rational Software
4774:
4773:
4756:Personal Computer
4751:Midrange computer
4557:
4556:
4256:
4255:
4168:Industrial 2 of 5
3973:barcodeisland.com
3852:. 24 March 2022.
3670:978-0-674-00657-7
3318:on 7 January 2012
3287:Proof of purchase
3260:UPC usage notes:
3241:GS1 country codes
3199:
3198:
2912:
2911:
2774:
2773:
2437:
2424:
2325:
2324:
1193:or store coupons.
1151:the check digit.
1066:
1053:
1048:
954:
949:
935:
930:
886:
885:
548:
544:
543:
474:
473:
225:Marsh supermarket
149:
148:
56:barcode symbology
16:(Redirected from
5751:
5649:
5648:
5639:
5638:
5629:
5628:
5389:Thomas J. Watson
5310:Relational model
5259:Think conference
5140:330 North Wabash
5060:Microelectronics
4933:
4858:Quantum Platform
4803:Cognos Analytics
4641:
4634:
4584:
4577:
4570:
4561:
4547:
4546:
4537:
4536:
4408:Polar coordinate
4245:
4229:
4222:
4221:
4107:
4100:
4093:
4084:
4050:
4049:
4045:
4037:
4036:
4032:
4023:
4022:
4018:
4010:
4009:
4005:
3989:
3988:
3986:
3984:
3975:. Archived from
3965:
3959:
3958:
3956:
3954:
3945:. 20 June 2013.
3935:
3926:
3925:
3923:
3921:
3902:
3896:
3895:
3893:
3891:
3872:
3866:
3865:
3863:
3861:
3842:
3836:
3835:
3822:
3816:
3815:
3809:
3801:
3799:
3797:
3777:
3771:
3770:
3764:
3762:
3743:
3737:
3736:
3734:
3732:
3712:
3706:
3705:
3703:
3701:
3681:
3675:
3674:
3654:
3648:
3647:
3645:
3643:
3625:
3619:
3618:
3616:
3614:
3595:
3589:
3588:
3586:
3584:
3569:
3563:
3562:
3558:Harvard Magazine
3551:Heller, Nathan.
3548:
3542:
3541:
3523:
3517:
3516:
3498:
3492:
3490:
3475:
3469:
3468:
3449:
3443:
3442:
3440:
3438:
3429:. 7 March 2012.
3419:
3410:
3409:
3408:
3404:
3393:
3387:
3386:
3384:
3382:
3349:(4): 1252–1286.
3334:
3328:
3327:
3325:
3323:
3302:
3195:
3186:
3177:
3168:
3159:
3150:
3141:
3132:
3123:
3114:
3105:
3096:
3087:
3078:
3069:
3060:
3051:
3042:
3033:
3024:
3015:
3008:
2917:
2797:number system 1
2790:number system 0
2779:
2627:UPC-A equivalent
2621:Last UPC-E digit
2618:
2463:
2461:
2460:
2455:
2438:
2430:
2425:
2423:
2367:
2356:
2031:
2006:
2004:
2003:
1998:
1930:
1921:
1914:
1907:
1899:
1897:
1896:
1891:
1824:
1822:
1821:
1816:
1741:
1739:
1738:
1733:
1657:
1653:
1639:
1627:
1620:
1616:
1612:
1608:
1590:
1577:
1569:
1565:
1541:
1532:
1512:
1505:
1498:
1491:Find the result
1463:
1461:
1460:
1455:
1450:
1425:
1424:
1412:
1411:
1396:
1395:
1383:
1382:
1367:
1366:
1354:
1353:
1338:
1337:
1325:
1324:
1309:
1308:
1296:
1295:
1280:
1279:
1267:
1266:
1237:
1235:
1234:
1229:
1227:
1226:
1126:
1124:
1123:
1118:
1116:
1084:
1083:
1067:
1064:
1055:
1054:
1051:
1049:
1046:
1028:
1026:
1025:
1020:
1018:
990:
989:
973:
972:
956:
955:
953:(5 right digits)
952:
950:
947:
937:
936:
933:
931:
928:
900:
896:
882:
875:
868:
861:
854:
847:
840:
833:
826:
819:
812:
805:
798:
791:
784:
777:
770:
763:
756:
749:
742:
735:
728:
721:
714:
608:
581:
546:
540:
533:
518:
517:
390:Label dimensions
384:
245:Washington, D.C.
211:George J. Laurer
144:
141:
135:
104:
103:
96:
21:
5759:
5758:
5754:
5753:
5752:
5750:
5749:
5748:
5704:
5703:
5702:
5697:
5617:
5603:SHARE computing
5564:GlobalFoundries
5506:
5454:
5448:
5375:
5334:
5325:Financial swaps
5300:Hard disk drive
5263:
5197:
5171:Yamato Facility
5089:
4996:
4928:
4918:
4885:Tivoli Software
4770:
4724:
4623:
4593:
4588:
4558:
4553:
4525:
4489:
4473:Other data tags
4468:
4459:Barcode printer
4454:Barcode library
4442:
4426:
4402:
4337:
4306:
4257:
4217:
4121:Linear barcodes
4116:
4111:
4065:Wayback Machine
4057:
4047:
4040:
4034:
4027:
4020:
4013:
4007:
4000:
3997:
3995:Further reading
3992:
3982:
3980:
3967:
3966:
3962:
3952:
3950:
3937:
3936:
3929:
3919:
3917:
3916:on 8 March 2021
3904:
3903:
3899:
3889:
3887:
3874:
3873:
3869:
3859:
3857:
3844:
3843:
3839:
3824:
3823:
3819:
3802:
3795:
3793:
3786:codeproject.com
3779:
3778:
3774:
3760:
3758:
3757:on 23 June 2007
3745:
3744:
3740:
3730:
3728:
3714:
3713:
3709:
3699:
3697:
3683:
3682:
3678:
3671:
3656:
3655:
3651:
3641:
3639:
3627:
3626:
3622:
3612:
3610:
3597:
3596:
3592:
3582:
3580:
3571:
3570:
3566:
3550:
3549:
3545:
3525:
3524:
3520:
3513:
3512:978-091126112-7
3500:
3499:
3495:
3477:
3476:
3472:
3467:on 1 June 2016.
3451:
3450:
3446:
3436:
3434:
3421:
3420:
3413:
3406:
3401:Silver, Bernard
3395:
3394:
3390:
3380:
3378:
3336:
3335:
3331:
3321:
3319:
3304:
3303:
3299:
3295:
3277:
3228:
3222:
3187:
3178:
3169:
3160:
3151:
3142:
3133:
3124:
3115:
3106:
3097:
3088:
3079:
3070:
3061:
3052:
3043:
3034:
3025:
3016:
2936:
2931:
2926:
2921:
2795:
2788:
2783:
2608:
2567:
2371:
2361:
2360:
2351:
2041:
2038:
1950:
1949:
1928:
1916:
1909:
1905:
1834:
1833:
1750:
1749:
1664:
1663:
1655:
1641:
1637:
1622:
1618:
1614:
1610:
1609:. The value of
1606:
1589:
1583:
1571:
1567:
1563:
1540:
1534:
1531:
1525:
1523:
1507:
1503:
1496:
1416:
1403:
1387:
1374:
1358:
1345:
1329:
1316:
1300:
1287:
1271:
1258:
1247:
1246:
1238:to satisfy the
1218:
1213:
1212:
1209:
1133:
1114:
1113:
1085:
1075:
1069:
1068:
1056:
1044:
1035:
1034:
1016:
1015:
981:
974:
964:
958:
957:
945:
938:
926:
917:
916:
907:
898:
894:
642:
637:
632:
627:
622:
617:
612:
579:
575:
554:
510:error detecting
482:
340:Dymo Industries
266:
207:Dymo Industries
145:
139:
136:
121:
118:Barcode#History
116:, specifically
105:
101:
94:
28:
23:
22:
15:
12:
11:
5:
5757:
5755:
5747:
5746:
5741:
5736:
5731:
5726:
5721:
5716:
5706:
5705:
5699:
5698:
5696:
5695:
5694:
5693:
5688:
5683:
5678:
5673:
5668:
5663:
5658:
5643:
5633:
5622:
5619:
5618:
5616:
5615:
5610:
5605:
5600:
5595:
5588:
5586:Lucifer cipher
5583:
5578:
5571:
5566:
5561:
5556:
5551:
5546:
5537:
5536:
5535:
5530:
5522:
5514:
5512:
5508:
5507:
5505:
5504:
5502:Peter R. Voser
5499:
5494:
5489:
5487:Andrew Liveris
5484:
5482:Arvind Krishna
5479:
5474:
5469:
5464:
5458:
5456:
5450:
5449:
5447:
5446:
5443:Arvind Krishna
5440:
5434:
5428:
5422:
5416:
5410:
5404:
5398:
5392:
5385:
5383:
5377:
5376:
5374:
5373:
5368:
5363:
5358:
5353:
5348:
5342:
5340:
5336:
5335:
5333:
5332:
5327:
5322:
5317:
5312:
5307:
5302:
5297:
5292:
5287:
5282:
5277:
5271:
5269:
5265:
5264:
5262:
5261:
5256:
5251:
5246:
5244:Smarter Planet
5241:
5236:
5231:
5226:
5221:
5220:
5219:
5209:
5205:
5203:
5199:
5198:
5196:
5195:
5190:
5185:
5180:
5175:
5174:
5173:
5168:
5163:
5155:
5154:
5153:
5148:
5143:
5136:IBM Buildings
5134:
5133:
5132:
5127:
5121:Software Labs
5119:
5118:
5117:
5111:
5110:, Montreal, QC
5101:
5099:
5095:
5094:
5091:
5090:
5088:
5087:
5077:
5075:Service Bureau
5072:
5067:
5065:Product Center
5062:
5057:
5052:
5047:
5042:
5037:
5032:
5030:Ambra Computer
5027:
5026:
5025:
5020:
5010:
5004:
5002:
4998:
4997:
4995:
4994:
4989:
4984:
4979:
4978:
4977:
4967:
4962:
4961:
4960:
4950:
4945:
4939:
4937:
4930:
4924:
4923:
4920:
4919:
4917:
4916:
4911:
4910:
4909:
4899:
4894:
4893:
4892:
4882:
4877:
4872:
4871:
4870:
4865:
4855:
4850:
4845:
4840:
4835:
4833:Lotus Software
4830:
4825:
4820:
4815:
4810:
4805:
4800:
4799:
4798:
4788:
4782:
4780:
4776:
4775:
4772:
4771:
4769:
4768:
4763:
4758:
4753:
4748:
4743:
4738:
4732:
4730:
4726:
4725:
4723:
4722:
4721:
4720:
4715:
4710:
4705:
4700:
4695:
4687:
4686:
4685:
4680:
4670:
4665:
4660:
4659:
4658:
4647:
4645:
4638:
4631:
4625:
4624:
4622:
4621:
4620:
4619:
4609:
4603:
4601:
4595:
4594:
4589:
4587:
4586:
4579:
4572:
4564:
4555:
4554:
4552:
4551:
4541:
4530:
4527:
4526:
4524:
4523:
4518:
4516:Mobile tagging
4513:
4508:
4503:
4497:
4495:
4494:Related topics
4491:
4490:
4488:
4487:
4482:
4476:
4474:
4470:
4469:
4467:
4466:
4464:Barcode reader
4461:
4456:
4450:
4448:
4444:
4443:
4441:
4440:
4434:
4432:
4428:
4427:
4425:
4424:
4419:
4413:
4411:
4404:
4403:
4401:
4400:
4395:
4390:
4385:
4380:
4375:
4370:
4365:
4355:
4349:
4347:
4339:
4338:
4336:
4335:
4330:
4325:
4320:
4314:
4312:
4308:
4307:
4305:
4304:
4299:
4294:
4289:
4284:
4279:
4274:
4268:
4266:
4259:
4258:
4254:
4253:
4247:
4246:
4238:
4237:
4231:
4230:
4220:
4218:
4216:
4215:
4210:
4205:
4200:
4195:
4190:
4185:
4180:
4175:
4170:
4165:
4160:
4155:
4150:
4145:
4140:
4135:
4130:
4124:
4122:
4118:
4117:
4112:
4110:
4109:
4102:
4095:
4087:
4081:
4080:
4074:
4071:UPC-Search.org
4068:
4056:
4055:External links
4053:
4052:
4051:
4038:
4025:
4011:
3996:
3993:
3991:
3990:
3960:
3927:
3897:
3867:
3837:
3817:
3772:
3738:
3707:
3676:
3669:
3649:
3634:. p. 15.
3620:
3590:
3564:
3543:
3518:
3511:
3493:
3470:
3444:
3411:
3388:
3355:10.1086/712762
3329:
3296:
3294:
3291:
3290:
3289:
3284:
3276:
3273:
3272:
3271:
3268:
3265:
3224:Main article:
3221:
3218:
3207:
3206:
3197:
3196:
3189:
3180:
3171:
3162:
3153:
3144:
3135:
3126:
3117:
3108:
3099:
3090:
3081:
3072:
3063:
3054:
3045:
3036:
3027:
3018:
3009:
3001:
3000:
2997:
2994:
2991:
2988:
2985:
2982:
2979:
2976:
2973:
2970:
2967:
2964:
2961:
2958:
2955:
2952:
2949:
2946:
2943:
2939:
2938:
2933:
2928:
2923:
2910:
2909:
2906:
2903:
2899:
2898:
2895:
2892:
2888:
2887:
2884:
2881:
2877:
2876:
2873:
2870:
2866:
2865:
2862:
2859:
2855:
2854:
2851:
2848:
2844:
2843:
2840:
2837:
2833:
2832:
2829:
2826:
2822:
2821:
2818:
2815:
2811:
2810:
2807:
2804:
2800:
2799:
2792:
2785:
2772:
2771:
2768:
2765:
2762:
2758:
2757:
2754:
2751:
2748:
2744:
2743:
2740:
2737:
2734:
2730:
2729:
2726:
2723:
2720:
2716:
2715:
2712:
2709:
2706:
2702:
2701:
2698:
2695:
2692:
2688:
2687:
2684:
2681:
2678:
2674:
2673:
2672:PPP = 000-999
2670:
2667:
2664:
2660:
2659:
2658:PPP = 000-999
2656:
2653:
2650:
2646:
2645:
2644:PPP = 000-999
2642:
2639:
2636:
2632:
2631:
2628:
2625:
2622:
2607:
2604:
2603:
2602:
2596:
2590:
2587:
2584:
2581:
2566:
2563:
2562:
2561:
2560:
2559:
2558:
2557:
2556:
2555:
2554:
2553:
2552:
2551:
2550:
2549:
2548:
2547:
2546:
2545:
2544:
2543:
2542:
2541:
2540:
2539:
2538:
2537:
2536:
2535:
2534:
2533:
2532:
2531:
2530:
2529:
2528:
2527:
2526:
2525:
2524:
2523:
2522:
2521:
2520:
2519:
2518:
2517:
2516:
2515:
2514:
2513:
2512:
2511:
2510:
2509:
2453:
2450:
2447:
2444:
2441:
2436:
2433:
2428:
2422:
2419:
2416:
2413:
2410:
2407:
2404:
2401:
2398:
2395:
2392:
2389:
2386:
2383:
2380:
2377:
2374:
2370:
2333:
2332:
2331:
2330:
2329:
2328:
2327:
2326:
2323:
2322:
2319:
2316:
2313:
2310:
2307:
2304:
2301:
2298:
2295:
2292:
2288:
2287:
2284:
2280:
2279:
2276:
2273:
2269:
2268:
2265:
2262:
2259:
2255:
2254:
2251:
2248:
2245:
2242:
2238:
2237:
2234:
2231:
2228:
2225:
2222:
2218:
2217:
2214:
2211:
2208:
2205:
2202:
2199:
2195:
2194:
2191:
2188:
2185:
2182:
2179:
2176:
2173:
2169:
2168:
2165:
2162:
2159:
2156:
2153:
2150:
2147:
2144:
2140:
2139:
2136:
2133:
2130:
2127:
2124:
2121:
2118:
2115:
2112:
2108:
2107:
2104:
2101:
2098:
2095:
2092:
2089:
2086:
2083:
2080:
2077:
2073:
2072:
2069:
2066:
2063:
2060:
2057:
2054:
2051:
2048:
2045:
2042:
2039:
2034:
2014:
2013:
2012:
2011:
2010:
2009:
2008:
2007:
1996:
1993:
1990:
1987:
1984:
1981:
1978:
1975:
1972:
1969:
1966:
1963:
1960:
1957:
1935:
1934:
1933:
1932:
1925:
1924:
1923:
1902:
1901:
1900:
1889:
1886:
1883:
1880:
1877:
1874:
1871:
1868:
1865:
1862:
1859:
1856:
1853:
1850:
1847:
1844:
1841:
1828:
1827:
1826:
1814:
1811:
1808:
1805:
1802:
1799:
1796:
1793:
1790:
1787:
1784:
1781:
1778:
1775:
1772:
1769:
1766:
1763:
1760:
1757:
1744:
1743:
1742:
1731:
1728:
1725:
1722:
1719:
1716:
1713:
1710:
1707:
1704:
1701:
1698:
1695:
1692:
1689:
1686:
1683:
1680:
1677:
1674:
1671:
1631:
1630:
1629:
1596:Luhn algorithm
1587:
1580:
1579:
1560:
1553:
1550:
1547:
1538:
1529:
1521:
1515:
1514:
1500:
1489:
1482:
1479:
1465:
1464:
1453:
1449:
1446:
1442:
1439:
1434:
1431:
1428:
1423:
1419:
1415:
1410:
1406:
1402:
1399:
1394:
1390:
1386:
1381:
1377:
1373:
1370:
1365:
1361:
1357:
1352:
1348:
1344:
1341:
1336:
1332:
1328:
1323:
1319:
1315:
1312:
1307:
1303:
1299:
1294:
1290:
1286:
1283:
1278:
1274:
1270:
1265:
1261:
1257:
1254:
1225:
1221:
1208:
1205:
1204:
1203:
1197:
1194:
1187:
1184:
1173:
1170:
1166:
1163:
1156:
1132:
1129:
1128:
1127:
1112:
1109:
1106:
1103:
1100:
1097:
1094:
1091:
1088:
1086:
1082:
1078:
1074:
1071:
1070:
1062:
1059:
1057:
1043:
1042:
1032:
1029:
1014:
1011:
1008:
1005:
1002:
999:
996:
993:
988:
984:
980:
977:
975:
971:
967:
963:
960:
959:
944:
941:
939:
925:
924:
914:
906:
903:
884:
883:
876:
869:
862:
855:
848:
841:
834:
827:
820:
813:
806:
799:
792:
785:
778:
771:
764:
757:
750:
743:
736:
729:
722:
715:
707:
706:
703:
700:
697:
694:
691:
688:
685:
682:
679:
676:
673:
670:
667:
664:
661:
658:
655:
652:
649:
645:
644:
639:
634:
629:
624:
619:
614:
574:
571:
553:
550:
542:
541:
534:
526:
525:
522:
481:
478:
472:
471:
468:
465:
461:
460:
457:
454:
450:
449:
446:
443:
439:
438:
435:
432:
428:
427:
424:
421:
417:
416:
413:
410:
406:
405:
402:
399:
395:
394:
391:
388:
265:
262:
157:Bernard Silver
147:
146:
108:
106:
99:
93:
90:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5756:
5745:
5742:
5740:
5737:
5735:
5732:
5730:
5727:
5725:
5722:
5720:
5717:
5715:
5712:
5711:
5709:
5692:
5689:
5687:
5684:
5682:
5679:
5677:
5674:
5672:
5669:
5667:
5664:
5662:
5659:
5657:
5654:
5653:
5652:
5644:
5642:
5634:
5632:
5624:
5623:
5620:
5614:
5611:
5609:
5606:
5604:
5601:
5599:
5596:
5594:
5593:
5589:
5587:
5584:
5582:
5579:
5577:
5576:
5572:
5570:
5567:
5565:
5562:
5560:
5557:
5555:
5552:
5550:
5547:
5545:
5541:
5538:
5534:
5531:
5529:
5526:
5525:
5523:
5521:
5520:
5516:
5515:
5513:
5509:
5503:
5500:
5498:
5495:
5493:
5490:
5488:
5485:
5483:
5480:
5478:
5475:
5473:
5470:
5468:
5465:
5463:
5462:Thomas Buberl
5460:
5459:
5457:
5451:
5444:
5441:
5438:
5437:Ginni Rometty
5435:
5432:
5429:
5426:
5423:
5420:
5417:
5414:
5411:
5408:
5407:Frank T. Cary
5405:
5402:
5399:
5396:
5393:
5390:
5387:
5386:
5384:
5382:
5378:
5372:
5369:
5367:
5364:
5362:
5359:
5357:
5354:
5352:
5349:
5347:
5344:
5343:
5341:
5337:
5331:
5328:
5326:
5323:
5321:
5318:
5316:
5313:
5311:
5308:
5306:
5303:
5301:
5298:
5296:
5293:
5291:
5288:
5286:
5283:
5281:
5278:
5276:
5273:
5272:
5270:
5266:
5260:
5257:
5255:
5252:
5250:
5247:
5245:
5242:
5240:
5237:
5235:
5232:
5230:
5227:
5225:
5222:
5218:
5215:
5214:
5213:
5210:
5207:
5206:
5204:
5200:
5194:
5193:IBM Rochester
5191:
5189:
5186:
5184:
5181:
5179:
5176:
5172:
5169:
5167:
5164:
5162:
5159:
5158:
5156:
5152:
5149:
5147:
5144:
5142:, Chicago, IL
5141:
5138:
5137:
5135:
5131:
5128:
5126:
5123:
5122:
5120:
5116:, Atlanta, GA
5115:
5112:
5109:
5106:
5105:
5103:
5102:
5100:
5096:
5085:
5081:
5078:
5076:
5073:
5071:
5068:
5066:
5063:
5061:
5058:
5056:
5053:
5051:
5048:
5046:
5043:
5041:
5038:
5036:
5033:
5031:
5028:
5024:
5021:
5019:
5016:
5015:
5014:
5011:
5009:
5006:
5005:
5003:
4999:
4993:
4990:
4988:
4985:
4983:
4980:
4976:
4973:
4972:
4971:
4968:
4966:
4963:
4959:
4956:
4955:
4954:
4951:
4949:
4946:
4944:
4941:
4940:
4938:
4934:
4931:
4925:
4915:
4912:
4908:
4905:
4904:
4903:
4900:
4898:
4895:
4891:
4888:
4887:
4886:
4883:
4881:
4878:
4876:
4873:
4869:
4866:
4864:
4861:
4860:
4859:
4856:
4854:
4851:
4849:
4846:
4844:
4843:Mashup Center
4841:
4839:
4836:
4834:
4831:
4829:
4826:
4824:
4821:
4819:
4816:
4814:
4811:
4809:
4806:
4804:
4801:
4797:
4794:
4793:
4792:
4789:
4787:
4784:
4783:
4781:
4777:
4767:
4764:
4762:
4759:
4757:
4754:
4752:
4749:
4747:
4744:
4742:
4739:
4737:
4734:
4733:
4731:
4727:
4719:
4716:
4714:
4711:
4709:
4706:
4704:
4701:
4699:
4696:
4694:
4691:
4690:
4688:
4684:
4681:
4679:
4676:
4675:
4674:
4671:
4669:
4668:Power Systems
4666:
4664:
4661:
4657:
4654:
4653:
4652:
4649:
4648:
4646:
4642:
4639:
4635:
4632:
4630:
4626:
4618:
4615:
4614:
4613:
4610:
4608:
4605:
4604:
4602:
4600:
4596:
4592:
4585:
4580:
4578:
4573:
4571:
4566:
4565:
4562:
4550:
4542:
4540:
4532:
4531:
4528:
4522:
4519:
4517:
4514:
4512:
4509:
4507:
4504:
4502:
4499:
4498:
4496:
4492:
4486:
4483:
4481:
4478:
4477:
4475:
4471:
4465:
4462:
4460:
4457:
4455:
4452:
4451:
4449:
4445:
4439:
4436:
4435:
4433:
4429:
4423:
4420:
4418:
4415:
4414:
4412:
4409:
4405:
4399:
4396:
4394:
4391:
4389:
4386:
4384:
4381:
4379:
4376:
4374:
4371:
4369:
4366:
4363:
4359:
4356:
4354:
4351:
4350:
4348:
4345:
4342:2D barcodes (
4340:
4334:
4331:
4329:
4326:
4324:
4321:
4319:
4316:
4315:
4313:
4309:
4303:
4300:
4298:
4295:
4293:
4290:
4288:
4285:
4283:
4280:
4278:
4275:
4273:
4270:
4269:
4267:
4264:
4260:
4252:
4249:
4248:
4244:
4240:
4239:
4236:
4233:
4232:
4228:
4224:
4223:
4214:
4211:
4209:
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4186:
4184:
4183:Matrix 2 of 5
4181:
4179:
4176:
4174:
4171:
4169:
4166:
4164:
4161:
4159:
4156:
4154:
4151:
4149:
4146:
4144:
4141:
4139:
4136:
4134:
4131:
4129:
4126:
4125:
4123:
4119:
4115:
4108:
4103:
4101:
4096:
4094:
4089:
4088:
4085:
4078:
4075:
4072:
4069:
4066:
4062:
4059:
4058:
4054:
4043:
4039:
4030:
4026:
4016:
4012:
4003:
3999:
3998:
3994:
3978:
3974:
3970:
3964:
3961:
3948:
3944:
3940:
3934:
3932:
3928:
3915:
3911:
3907:
3901:
3898:
3885:
3881:
3877:
3871:
3868:
3855:
3851:
3847:
3841:
3838:
3833:
3829:
3828:
3821:
3818:
3813:
3807:
3791:
3787:
3783:
3776:
3773:
3769:
3756:
3752:
3748:
3742:
3739:
3726:
3722:
3718:
3717:"Murray Eden"
3711:
3708:
3695:
3691:
3687:
3680:
3677:
3672:
3666:
3662:
3661:
3653:
3650:
3637:
3633:
3632:
3624:
3621:
3608:
3604:
3600:
3594:
3591:
3578:
3574:
3568:
3565:
3560:
3559:
3554:
3547:
3544:
3539:
3535:
3534:
3529:
3522:
3519:
3514:
3508:
3504:
3497:
3494:
3488:
3484:
3480:
3474:
3471:
3466:
3462:
3458:
3454:
3448:
3445:
3432:
3428:
3424:
3418:
3416:
3412:
3402:
3398:
3392:
3389:
3376:
3372:
3368:
3364:
3360:
3356:
3352:
3348:
3344:
3340:
3333:
3330:
3317:
3313:
3312:
3307:
3301:
3298:
3292:
3288:
3285:
3282:
3279:
3278:
3274:
3269:
3266:
3263:
3262:
3261:
3258:
3256:
3252:
3250:
3249:point-of-sale
3246:
3242:
3237:
3233:
3227:
3219:
3214:
3210:
3204:
3203:
3202:
3194:
3190:
3185:
3181:
3176:
3172:
3167:
3163:
3158:
3154:
3149:
3145:
3140:
3136:
3131:
3127:
3122:
3118:
3113:
3109:
3104:
3100:
3095:
3091:
3086:
3082:
3077:
3073:
3068:
3064:
3059:
3055:
3050:
3046:
3041:
3037:
3032:
3028:
3023:
3019:
3014:
3010:
3007:
3003:
2998:
2995:
2992:
2989:
2986:
2983:
2980:
2977:
2974:
2971:
2968:
2965:
2962:
2959:
2956:
2953:
2950:
2947:
2944:
2941:
2940:
2918:
2907:
2904:
2901:
2900:
2896:
2893:
2890:
2889:
2885:
2882:
2879:
2878:
2874:
2871:
2868:
2867:
2863:
2860:
2857:
2856:
2852:
2849:
2846:
2845:
2841:
2838:
2835:
2834:
2830:
2827:
2824:
2823:
2819:
2816:
2813:
2812:
2808:
2805:
2802:
2801:
2798:
2793:
2791:
2786:
2781:
2780:
2777:
2769:
2766:
2763:
2760:
2759:
2755:
2752:
2749:
2746:
2745:
2741:
2738:
2735:
2732:
2731:
2727:
2724:
2721:
2718:
2717:
2713:
2710:
2707:
2704:
2703:
2699:
2696:
2693:
2690:
2689:
2685:
2682:
2679:
2676:
2675:
2671:
2668:
2665:
2662:
2661:
2657:
2654:
2651:
2648:
2647:
2643:
2640:
2637:
2634:
2633:
2629:
2626:
2623:
2620:
2619:
2616:
2614:
2605:
2600:
2597:
2594:
2591:
2588:
2585:
2582:
2579:
2575:
2574:
2573:
2570:
2564:
2507:
2506:
2505:
2504:
2503:
2502:
2501:
2500:
2499:
2498:
2497:
2496:
2495:
2494:
2493:
2492:
2491:
2490:
2489:
2488:
2487:
2486:
2485:
2484:
2483:
2482:
2481:
2480:
2479:
2478:
2477:
2476:
2475:
2474:
2473:
2472:
2471:
2470:
2469:
2468:
2467:
2466:
2465:
2464:
2451:
2445:
2442:
2439:
2434:
2431:
2426:
2420:
2417:
2414:
2411:
2408:
2405:
2402:
2399:
2396:
2393:
2390:
2387:
2384:
2381:
2378:
2375:
2372:
2368:
2359:
2358:
2354:
2349:
2345:
2341:
2340:
2339:
2338:
2337:
2336:
2335:
2334:
2320:
2317:
2314:
2311:
2308:
2305:
2302:
2299:
2296:
2293:
2290:
2289:
2285:
2282:
2281:
2277:
2274:
2271:
2270:
2266:
2263:
2260:
2257:
2256:
2252:
2249:
2246:
2243:
2240:
2239:
2235:
2232:
2229:
2226:
2223:
2220:
2219:
2215:
2212:
2209:
2206:
2203:
2200:
2197:
2196:
2192:
2189:
2186:
2183:
2180:
2177:
2174:
2171:
2170:
2166:
2163:
2160:
2157:
2154:
2151:
2148:
2145:
2142:
2141:
2137:
2134:
2131:
2128:
2125:
2122:
2119:
2116:
2113:
2110:
2109:
2105:
2102:
2099:
2096:
2093:
2090:
2087:
2084:
2081:
2078:
2075:
2074:
2070:
2067:
2064:
2061:
2058:
2055:
2052:
2049:
2046:
2043:
2037:
2033:
2032:
2028:
2022:
2021:
2020:
2019:
2018:
2017:
2016:
2015:
1994:
1988:
1985:
1982:
1979:
1976:
1973:
1970:
1967:
1964:
1958:
1955:
1947:
1943:
1942:
1941:
1940:
1939:
1938:
1937:
1936:
1926:
1919:
1912:
1903:
1887:
1884:
1881:
1875:
1872:
1869:
1866:
1860:
1854:
1851:
1848:
1845:
1842:
1832:
1831:
1829:
1812:
1809:
1806:
1803:
1800:
1794:
1791:
1788:
1782:
1779:
1776:
1773:
1770:
1767:
1764:
1761:
1758:
1755:
1748:
1747:
1745:
1729:
1726:
1723:
1720:
1717:
1714:
1708:
1705:
1702:
1696:
1693:
1690:
1687:
1684:
1681:
1678:
1675:
1672:
1669:
1662:
1661:
1660:
1659:
1652:
1648:
1644:
1635:
1634:
1632:
1626:
1604:
1603:
1601:
1600:
1599:
1597:
1592:
1586:
1575:
1561:
1558:
1554:
1551:
1548:
1545:
1544:
1543:
1537:
1528:
1520:
1511:
1501:
1494:
1490:
1487:
1483:
1480:
1477:
1473:
1472:
1471:
1468:
1451:
1444:
1440:
1432:
1429:
1421:
1417:
1413:
1408:
1404:
1400:
1397:
1392:
1388:
1384:
1379:
1375:
1371:
1368:
1363:
1359:
1355:
1350:
1346:
1342:
1339:
1334:
1330:
1326:
1321:
1317:
1313:
1310:
1305:
1301:
1297:
1292:
1288:
1284:
1281:
1276:
1272:
1268:
1263:
1259:
1255:
1245:
1244:
1243:
1241:
1223:
1219:
1206:
1201:
1198:
1195:
1192:
1191:loyalty cards
1188:
1185:
1182:
1178:
1174:
1171:
1167:
1164:
1161:
1157:
1154:
1153:
1152:
1150:
1146:
1142:
1138:
1130:
1110:
1107:
1104:
1101:
1098:
1095:
1092:
1089:
1087:
1080:
1076:
1072:
1060:
1058:
1033:
1030:
1012:
1009:
1006:
1003:
1000:
997:
994:
991:
986:
982:
978:
976:
969:
965:
961:
942:
940:
934:(left digits)
915:
912:
911:
910:
904:
902:
892:
891:bar-space-bar
881:
877:
874:
870:
867:
863:
860:
856:
853:
849:
846:
842:
839:
835:
832:
828:
825:
821:
818:
814:
811:
807:
804:
800:
797:
793:
790:
786:
783:
779:
776:
772:
769:
765:
762:
758:
755:
751:
748:
744:
741:
737:
734:
730:
727:
723:
720:
716:
713:
709:
704:
701:
698:
695:
692:
689:
686:
683:
680:
677:
674:
671:
668:
665:
662:
659:
656:
653:
650:
647:
646:
609:
605:
601:
595:
593:
589:
588:bar-space-bar
583:
572:
570:
568:
562:
558:
551:
549:
539:
535:
532:
528:
527:
523:
520:
519:
516:
514:
511:
507:
503:
498:
494:
489:
487:
479:
477:
469:
466:
463:
462:
458:
455:
452:
451:
447:
444:
441:
440:
436:
433:
430:
429:
425:
422:
419:
418:
414:
411:
408:
407:
403:
400:
397:
396:
392:
389:
386:
385:
382:
379:
375:
371:
367:
365:
359:
355:
351:
347:
343:
341:
337:
334:
332:
327:
324:
320:
316:
313:
309:
301:
297:
293:
289:
285:
282:
278:
275:
274:George Laurer
271:
263:
261:
259:
255:
251:
247:
246:
242:
238:
234:
230:
226:
222:
219:
214:
212:
208:
204:
200:
196:
192:
187:
185:
181:
178:for tracking
177:
173:
168:
166:
162:
158:
154:
153:punched cards
143:
140:December 2013
133:
129:
128:summary style
125:
119:
115:
113:
109:This section
107:
98:
97:
91:
89:
86:
84:
80:
76:
71:
69:
63:
61:
57:
53:
52:
47:
43:
36:A UPC barcode
34:
30:
19:
5590:
5573:
5554:Deep Thought
5517:
5445:(since 2020)
5413:John R. Opel
5371:Think slogan
5329:
5212:Deep Thunder
5018:Kaleida Labs
5013:AIM alliance
4698:Q System Two
4693:Q System One
4373:Han Xin code
4234:
4212:
3981:. Retrieved
3977:the original
3972:
3963:
3951:. Retrieved
3942:
3918:. Retrieved
3914:the original
3909:
3900:
3888:. Retrieved
3879:
3870:
3858:. Retrieved
3849:
3840:
3826:
3820:
3794:. Retrieved
3785:
3775:
3766:
3759:. Retrieved
3755:the original
3750:
3741:
3729:. Retrieved
3720:
3710:
3698:. Retrieved
3689:
3679:
3659:
3652:
3640:. Retrieved
3630:
3623:
3611:. Retrieved
3602:
3593:
3581:. Retrieved
3567:
3556:
3546:
3531:
3521:
3502:
3496:
3487:the original
3483:mckinsey.com
3482:
3473:
3465:the original
3460:
3456:
3447:
3435:. Retrieved
3426:
3391:
3379:. Retrieved
3346:
3342:
3332:
3320:. Retrieved
3316:the original
3309:
3300:
3259:
3253:
3229:
3208:
3200:
2796:
2789:
2784:check digit
2775:
2612:
2609:
2571:
2568:
2352:
2347:
2343:
2035:
2026:
1945:
1944:Here is the
1917:
1910:
1906:2d ≡ 0
1650:
1646:
1642:
1624:
1593:
1584:
1581:
1573:
1556:
1535:
1526:
1518:
1516:
1509:
1469:
1466:
1239:
1210:
1148:
1144:
1140:
1136:
1134:
908:
890:
887:
603:
599:
591:
587:
584:
576:
563:
559:
555:
545:
505:
501:
496:
492:
490:
483:
475:
380:
376:
372:
368:
360:
356:
352:
348:
344:
338:
335:
328:
325:
321:
317:
314:
310:
306:
294:
290:
286:
283:
279:
267:
264:IBM proposal
248:
215:
188:
169:
150:
137:
110:
87:
72:
64:
49:
45:
41:
39:
29:
5729:Identifiers
5686:Typewriters
5592:Mathematica
5533:Rugby union
5472:Alex Gorsky
5439:(2012–2020)
5433:(2002–2011)
5427:(1993–2002)
5421:(1985–1993)
5415:(1981–1985)
5409:(1973–1981)
5403:(1971–1973)
5397:(1956–1971)
5391:(1914–1956)
5339:Terminology
5295:Floppy disk
5239:SkillsBuild
5202:Initiatives
5183:IBM Hursley
5157:Facilities
4808:Connections
4678:FlashSystem
4358:Data Matrix
4328:MicroPDF417
4323:GS1 DataBar
4263:Post office
4188:MSI Barcode
4163:GS1 DataBar
3890:16 February
3860:28 February
3437:12 November
3245:check digit
2686:PP = 00-99
1572:10 −
1508:10 −
602:LLLLLMRRRRR
513:check digit
495:LLLLLMRRRRR
480:Composition
250:Murray Eden
221:Juicy Fruit
62:in stores.
60:trade items
5708:Categories
5681:System/370
5676:System/360
5467:David Farr
5366:e-business
5268:Inventions
5217:Develothon
5098:Facilities
4958:Promontory
4953:Consulting
4353:Aztec Code
4198:Pharmacode
4193:Patch Code
4042:US 3723710
4029:US 3617707
4015:US 3145291
4002:US 3832686
3983:21 January
3920:12 October
3910:HealthData
3731:14 January
3700:14 January
3642:14 January
3293:References
2565:Variations
1139:LLLLLRRRRR
552:Formatting
387:Label type
229:Troy, Ohio
112:duplicates
5549:Deep Blue
5455:directors
4914:WebSphere
4853:PureQuery
4761:Selectric
4736:Blue Gene
4651:Mainframe
4393:rMQR Code
4318:Codablock
3613:4 January
3583:12 August
3371:229505646
3363:0022-3808
2449:%
2446:…
2025:Table of
1983:…
1959:∈
1920:≡ 0
1913:≡ 5
1861:−
1570:from 10 (
1524:", where
1430:≡
1175:Drugs by
1090:×
1061:×
979:×
943:×
905:Numbering
628:(middle)
258:fail-safe
218:Wrigley's
172:railroads
5714:Barcodes
5631:Category
5598:IBM Plex
5453:Board of
5346:Big Blue
5146:Honolulu
5055:Merative
5040:EduQuest
5023:Taligent
4992:Research
4929:entities
4927:Business
4868:OpenQASM
4796:Cloudant
4766:ThinkPad
4689:Quantum
4637:Hardware
4629:Products
4539:Category
4422:ShotCode
4417:MaxiCode
4410:barcodes
4383:MaxiCode
4378:JAB Code
4362:Semacode
4265:barcodes
4251:MaxiCode
4148:Code 128
4114:Barcodes
3947:Archived
3884:Archived
3854:Archived
3850:UPCs.com
3806:cite web
3790:Archived
3725:Archived
3694:Archived
3636:Archived
3607:Archived
3603:ethw.org
3577:Archived
3538:Archived
3431:Archived
3381:14 March
3375:Archived
3275:See also
3236:superset
2922:(start)
2700:P = 0-9
1948:, where
1155:0–1, 6–9
1143:, where
1052:(digits)
618:(start)
573:Encoding
180:railcars
51:UPC code
5641:Commons
5608:ScicomP
5151:Seattle
5104:Towers
5050:Lexmark
5045:Kyndryl
4987:Red Hat
4936:Current
4907:Granite
4902:Watsonx
4818:Fortran
4746:PowerPC
4673:Storage
4644:Current
4607:History
4599:History
4549:Commons
4388:QR code
4368:DotCode
4287:POSTNET
4282:PostBar
4208:Telepen
4203:Plessey
4153:Codabar
4143:Code 93
4138:Code 39
4133:Code 11
4063:at the
3953:10 July
3834:. 1986.
3761:10 June
3457:Esquire
3188:2-1-1-3
3179:3-1-2-1
3170:2-1-3-1
3161:4-1-1-1
3152:1-3-2-1
3143:2-3-1-1
3134:1-1-4-1
3125:2-2-1-2
3116:1-2-2-2
3107:1-1-2-3
3098:3-1-1-2
3089:1-2-1-3
3080:1-3-1-2
3071:1-1-1-4
3062:1-2-3-1
3053:1-1-3-2
3044:1-4-1-1
3035:2-1-2-2
3026:2-2-2-1
3017:3-2-1-1
2908:OEEOEO
2897:OEOEEO
2886:OEOEOE
2875:OEEEOO
2864:OEEOOE
2853:OEOOEE
2842:OOEEEO
2831:OOEEOE
2820:OOEOEE
2809:OOOEEE
1200:Coupons
486:letters
122:Please
92:History
54:) is a
5613:Unions
5224:Fellow
5035:Cognos
5008:AdStar
5001:Former
4965:Kenexa
4943:Apptio
4897:Watson
4863:Qiskit
4729:Former
4718:Condor
4708:Osprey
4683:DS8000
4521:CueCat
4511:Matrix
4485:Bokode
4398:Boxing
4344:matrix
4333:PDF417
4302:PLANET
4292:RM4SCC
4178:ITF-14
4048:
4035:
4021:
4008:
3796:7 July
3721:Medium
3667:
3509:
3407:
3369:
3361:
3322:7 July
3311:GS1 US
3247:. All
3232:EAN-13
3220:EAN-13
2937:(end)
2905:EOOEOE
2894:EOEOOE
2883:EOEOEO
2872:EOOOEE
2861:EOOEEO
2850:EOEEOO
2839:EEOOOE
2828:EEOOEO
2817:EEOEOO
2806:EEEOOO
2782:UPC-A
2770:9 = P
2764:MMMMM9
2756:8 = P
2750:MMMMM8
2742:7 = P
2736:MMMMM7
2728:6 = P
2722:MMMMM6
2714:5 = P
2708:MMMMM5
2694:MMMMP4
2680:MMMPP3
2666:MMPPP2
2652:MMPPP1
2638:MMPPP0
2443:11.111
1591:is 2.
1493:modulo
638:(end)
524:UPC-E
521:UPC-A
508:is an
404:Large
68:parity
5511:Other
4982:Press
4975:India
4791:Cloud
4779:Other
4713:Heron
4703:Eagle
4656:IBM Z
4431:Other
4235:UPC-A
3533:Wired
3367:S2CID
3255:EAN-8
2606:UPC-E
2599:UPC-5
2593:UPC-2
1931:of 5.
1031:UPC-E
913:UPC-A
643:zone
641:Quiet
613:zone
611:Quiet
401:Large
393:Area
18:UPC-A
5656:FOSS
5381:CEOs
5285:DRAM
4880:SPSS
4823:ILOG
4480:RFID
3985:2013
3955:2019
3922:2015
3892:2022
3862:2023
3812:link
3798:2011
3763:2009
3733:2021
3702:2021
3665:ISBN
3644:2021
3615:2021
3585:2021
3507:ISBN
3439:2021
3383:2021
3359:ISSN
3324:2011
3230:The
2342:Row
2291:Sum
2286:9 9
2278:8 9
2267:7 9
2253:6 9
2236:5 9
2216:4 9
2193:3 9
2167:2 9
2138:1 9
2106:0 9
1598:).
1486:even
1111:000.
1013:000.
159:and
40:The
4591:IBM
4213:UPC
3461:153
3427:IBM
3351:doi
3347:129
3281:GS1
2357:):
2355:= 0
2344:Sum
2283:10
2275:8 8
2264:7 8
2261:7 7
2250:6 8
2247:6 7
2244:6 6
2233:5 8
2230:5 7
2227:5 6
2224:5 5
2213:4 8
2210:4 7
2207:4 6
2204:4 5
2201:4 4
2190:3 8
2187:3 7
2184:3 6
2181:3 5
2178:3 4
2175:3 3
2164:2 8
2161:2 7
2158:2 6
2155:2 5
2152:2 4
2149:2 3
2146:2 2
2135:1 8
2132:1 7
2129:1 6
2126:1 5
2123:1 4
2120:1 3
2117:1 2
2114:1 1
2103:0 8
2100:0 7
2097:0 6
2094:0 5
2091:0 4
2088:0 3
2085:0 2
2082:0 1
2079:0 0
1562:If
1502:If
1476:odd
1441:mod
1160:GS1
1105:000
1007:000
1001:000
995:100
243:in
239:'s
233:NCR
227:in
203:RCA
199:IBM
75:GS1
48:or
46:UPC
5710::
3971:.
3941:.
3930:^
3908:.
3882:.
3878:.
3848:.
3830:.
3808:}}
3804:{{
3788:.
3784:.
3765:.
3749:.
3723:.
3719:.
3692:.
3688:.
3601:.
3555:.
3536:.
3530:.
3481:.
3459:.
3455:.
3425:.
3414:^
3373:.
3365:.
3357:.
3345:.
3341:.
3308:.
2999:9
2435:90
2432:10
2397:10
2391:12
2385:14
2379:16
2373:18
2369:10
2321:2
2309:10
2306:12
2303:14
2300:16
2297:18
2294:10
2272:9
2258:8
2241:7
2221:6
2198:5
2172:4
2143:3
2111:2
2076:1
2071:9
2040:N°
1649:+
1645:=
1588:12
1578:).
1559:).
1539:12
1530:12
1522:12
1445:10
1422:12
1409:11
1393:10
1242::
1224:12
1077:10
983:10
966:10
901:.
705:9
606:E
582:.
366:.
186:.
155:.
5542:/
5086:)
5082:(
4583:e
4576:t
4569:v
4364:)
4360:(
4346:)
4106:e
4099:t
4092:v
3987:.
3957:.
3924:.
3894:.
3864:.
3814:)
3800:.
3735:.
3704:.
3673:.
3646:.
3617:.
3587:.
3515:.
3441:.
3385:.
3353::
3326:.
2996:8
2993:7
2990:6
2987:5
2984:4
2981:3
2978:2
2975:1
2972:0
2969:9
2966:8
2963:7
2960:6
2957:5
2954:4
2951:3
2948:2
2945:1
2942:0
2935:E
2930:E
2925:O
2920:S
2902:9
2891:8
2880:7
2869:6
2858:5
2847:4
2836:3
2825:2
2814:1
2803:0
2761:9
2747:8
2733:7
2719:6
2705:5
2691:4
2677:3
2663:2
2649:1
2635:0
2508:▯
2452:.
2440:=
2427:=
2421:2
2418:+
2415:4
2412:+
2409:6
2406:+
2403:8
2400:+
2394:+
2388:+
2382:+
2376:+
2353:d
2348:d
2318:4
2315:6
2312:8
2068:8
2065:7
2062:6
2059:5
2056:4
2053:3
2050:2
2047:1
2044:0
2036:d
2027:d
1995::
1992:}
1989:9
1986:,
1980:,
1977:2
1974:,
1971:1
1968:,
1965:0
1962:{
1956:d
1929:d
1918:d
1911:d
1888:d
1885:2
1882:=
1879:)
1876:d
1873:+
1870:a
1867:4
1864:(
1858:)
1855:d
1852:3
1849:+
1846:a
1843:4
1840:(
1825:.
1813:d
1810:+
1807:a
1804:4
1801:=
1798:)
1795:d
1792:+
1789:a
1786:(
1783:1
1780:+
1777:a
1774:3
1771:=
1768:a
1765:3
1762:+
1759:b
1756:1
1730:d
1727:3
1724:+
1721:a
1718:4
1715:=
1712:)
1709:d
1706:+
1703:a
1700:(
1697:3
1694:+
1691:a
1688:1
1685:=
1682:b
1679:3
1676:+
1673:a
1670:1
1656:d
1651:d
1647:a
1643:b
1638:a
1625:d
1623:3
1619:d
1615:d
1611:d
1607:d
1585:x
1574:M
1568:M
1564:M
1557:M
1536:x
1527:x
1519:x
1513:.
1510:M
1504:M
1499:.
1497:M
1452:.
1448:)
1438:(
1433:0
1427:)
1418:x
1414:+
1405:x
1401:3
1398:+
1389:x
1385:+
1380:9
1376:x
1372:3
1369:+
1364:8
1360:x
1356:+
1351:7
1347:x
1343:3
1340:+
1335:6
1331:x
1327:+
1322:5
1318:x
1314:3
1311:+
1306:4
1302:x
1298:+
1293:3
1289:x
1285:3
1282:+
1277:2
1273:x
1269:+
1264:1
1260:x
1256:3
1253:(
1220:x
1196:5
1186:4
1172:3
1165:2
1149:R
1145:L
1141:R
1137:L
1108:,
1102:,
1099:2
1096:=
1093:2
1081:6
1073:=
1010:,
1004:,
998:,
992:=
987:5
970:6
962:=
702:8
699:7
696:6
693:5
690:4
687:3
684:2
681:1
678:0
675:9
672:8
669:7
666:6
663:5
660:4
657:3
654:2
651:1
648:0
636:E
631:R
626:M
621:L
616:S
604:R
600:L
506:R
502:L
497:R
493:L
142:)
138:(
120:.
44:(
20:)
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