Universal Product Code - Knowledge (XXG)

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;

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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

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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.

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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

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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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

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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

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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

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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"

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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.

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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.

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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.

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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%.

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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.

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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,

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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.

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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.

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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.

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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.

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Research indicates that the adoption and diffusion of the UPC stimulated innovation and contributed to the growth of international retail supply chains.

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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.

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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.

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Twenty-Five Years Behind Bars: The Proceedings of the Twenty-Fifth Anniversary of the U.P.C. at the Smithsonian Institution, September 30, 1999

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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.

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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

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scanner. The next day Baumeister suggested if the label were split into two halves the bar lengths could be cut nearly in half.

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was a consultant on the team that created the Universal Product Code barcode. As Chairman of a committee of scientists at the

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All products marked with an EAN will be accepted in North America currently, in addition to those already marked with a UPC.

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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

127: 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.

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Add the even-numbered digits (42 + (3 + 0 + 0 + 9 + 4) = 58).

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alphabets. This reduced the label size to about 1.5 in × 0.9 in (38 mm × 23 mm).

82: 5107: 3913: 3486: 3464: 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.

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is the difference between the two digits. If the digits were in their correct order, they would contribute

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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: 1135:

Below is description of all possible number systems with corresponding 12-digit UPC-A numbering schema

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.

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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: 131: 111: 381:

The following table shows the workable labels, available in the early 1970s, with their sizes.

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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.

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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: 909:

The number of UPC-A and UPC-E barcodes are limited by the standards used to create them.

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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

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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.

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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

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UPC-C is a 12-digit code with a product code and a check digit; not in common use.

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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

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to the section by replacing the section with a link and a summary or by

17: 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

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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: 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.

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Wallace Flint proposed an automated checkout system in 1932 using

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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

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cannot be zero because that means the digits are the same, but

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The scannable area of every UPC-A barcode follows the pattern S

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6.0 in × 5.8 in (150 mm × 150 mm)

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each set were responsible for most of the scanner read errors.

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complete label definition and proceeded to write his proposal.

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4.5 in × 2.3 in (114 mm × 58 mm)

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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

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National Commission on Productivity and Work Quality (1975).

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1.5 in × 0.9 in (38 mm × 23 mm)

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system, in case the barcode reader is not working correctly.

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UPC in its most common usage technically refers to UPC-A.

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price, with the first R determining which (0 for weight).

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organization), and the RRRRR digits are the product code.

27:

Barcode symbology used for tracking trade items in stores

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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

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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: 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: 1147:denotes number system digit and 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. 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: 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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: 1151:check digit. 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:. 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