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59-522: SEDOLs are seven characters in length, consisting of two parts: a six-place alphanumeric code and a trailing check digit . SEDOLs issued prior to January 26, 2004 were composed only of numbers. For older SEDOLs, those from Asia and Africa typically begin with 6. Those from the UK and Ireland (until Ireland joined the EU) typically begin with 0 or 3. Those from the rest of Europe typically began with 4, 5, or 7. Those from

118-455: A GTIN for products sold only in their own stores. Research indicates that the adoption and diffusion of the UPC stimulated innovation and contributed to the growth of international retail supply chains. Wallace Flint proposed an automated checkout system in 1932 using punched cards . Bernard Silver and Norman Joseph Woodland , a graduate student from Drexel Institute of Technology , developed

177-440: 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. The scannable area of every UPC-A barcode follows the pattern S L LLLLLMRRRRR R E, where S (start), M (middle), and E (end) guard patterns are represented

236-593: A bull's-eye-style code and applied for the patent in 1949. In the 1960s and early 1970s, railroads in North America experimented with multicolor bar codes for tracking railcars , but this system was eventually abandoned and replaced with a radio-based system called Automatic Equipment Identification (AEI) . In 1973, a group of trade associations from the grocery industry formed the Uniform Product Code Council (UPCC) which, with

295-484: A defined character set with a fixed reference distance that spanned most or preferably all the character. 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. Although Litton Industries proposed a bull's eye symbol cut in half to reduce

354-555: A demonstration of the label. On 1 December 1972, IBM presented Laurer's proposal to the Super Market Committee in Rochester, Minnesota , 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

413-401: A form of redundancy check used for error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It is analogous to a binary parity bit used to check for errors in computer-generated data. It consists of one or more digits (or letters) computed by an algorithm from the other digits (or letters) in

472-415: 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 complete label definition and proceeded to write his proposal. Previously Crouse had an idea for a simple wand worn like a ring and bracelet. He decided to develop that wand to provide

531-473: A multiple of 10. The check digit is computed using a weighted sum of the first six characters. Letters have the value of 9 plus their alphabet position, such that B = 11 and Z = 35. While vowels are never used in SEDOLs, they are not ignored when computing this weighted sum (e.g. H = 17 and J = 19, even though I is not used), simplifying code to compute this sum. The resulting string of numbers is then multiplied by

590-408: 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. One month later, 1 January 1973 Crouse transferred back to IBM's Advanced Technology group, and Laurer remained with the full responsibility for

649-437: A prime radix R and strings less than R characters in length. Notable algorithms include: Universal Product Code The Universal Product Code ( UPC or UPC code ) is a barcode symbology that is used worldwide for tracking trade items in stores. 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

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708-460: A single check digit added to the original number, the system will not always capture multiple errors, such as two replacement errors (12 → 34) though, typically, double errors will be caught 90% of the time (both changes would need to change the output by offsetting amounts). A very simple check digit method would be to take the sum of all digits ( digital sum ) modulo 10. This would catch any single-digit error, as such an error would always change

767-457: A single pass. This label could be scanned with a simple "X" scanner only slightly more complex than the straight line laser scanner. The next day Baumeister suggested if the label were split into two halves the bar lengths could be cut nearly in half. 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

826-404: A total width of 7 units, in both an "even" and an "odd" parity 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. A UPC (technically, a UPC-A) consists of 12 digits that are uniquely assigned to each trade item. The international GS1 organisation assigns the digits used for both the UPC and

885-414: A wider range of characters in the check digit, for example letters plus numbers. The final digit of a Universal Product Code , International Article Number , Global Location Number or Global Trade Item Number is a check digit computed as follows: A GS1 check digit calculator and detailed documentation is online at GS1's website. Another official calculator page shows that the mechanism for GTIN-13

944-506: 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 human-readable interpretation are always placed outside the symbol in order to indicate the quiet zones that are necessary for UPC barcode scanners to work properly. The UPC-A barcode is visually represented by strips of bars and spaces that encode

1003-508: Is 0×10 + 2×9 + 0×8 + 1×7 + 5×6 + 3×5 + 0×4 + 8×3 + 2×2 + 1×1 = 99 ≡ 0 (mod 11). So the ISBN is valid. Positions can also be counted from left, in which case the check digit is multiplied by 10, to check validity: 0×1 + 2×2 + 0×3 + 1×4 + 5×5 + 3×6 + 0×7 + 8×8 + 2×9 + 1×10 = 143 ≡ 0 (mod 11). ISBN 13 (in use January 2007) is equal to the EAN-13 code found underneath a book's barcode. Its check digit

1062-475: Is a check digit computed so that multiplying each digit by its position in the number (counting from the right) and taking the sum of these products modulo 11 is 0. The digit the farthest to the right (which is multiplied by 1) is the check digit, chosen to make the sum correct. It may need to have the value 10, which is represented as the letter X. For example, take the ISBN   0-201-53082-1 : The sum of products

1121-414: 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 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. Requiring every bit width to be read precisely basically nullified

1180-441: Is determined by multiplying the x-dimension and the module width (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. The x-dimension for

1239-576: Is generated the same way as the UPC. The NOID Check Digit Algorithm (NCDA), in use since 2004, is designed for application in persistent identifiers and works with variable length strings of letters and digits, called extended digits. It is widely used with the ARK identifier scheme and somewhat used with schemes, such as the Handle System and DOI . An extended digit is constrained to betanumeric characters, which are alphanumerics minus vowels and

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1298-414: Is the same for Global Location Number /GLN. For instance, the UPC-A barcode for a box of tissues is "036000241457". The last digit is the check digit "7", and if the other numbers are correct then the check digit calculation must produce 7. Another example: to calculate the check digit for the following food item "01010101010 x ". The final character of a ten-digit International Standard Book Number

1357-401: Is traded off against implementation difficulty; simple check digit systems are easily understood and implemented by humans but do not catch as many errors as complex ones, which require sophisticated programs to implement. A desirable feature is that left-padding with zeros should not change the check digit. This allows variable length numbers to be used and the length to be changed. If there is

1416-512: Is upside-down). After seeing a S (start) or E (end) guard pattern (they are the same, bar-space-bar , 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

1475-507: The Damm algorithm (2004), that too detects all single-digit errors and all adjacent transposition errors. These three methods use a single check digit and will therefore fail to capture around 10% of more complex errors. To reduce this failure rate, it is necessary to use more than one check digit (for example, the modulo 97 check referred to below, which uses two check digits—for the algorithm, see International Bank Account Number ) and/or to use

1534-473: The 2 and 5 multiply to yield 10. The ISBN-10 code instead uses modulo 11, which is prime, and all the number positions have different weights 1, 2, ... 10. This system thus detects all single-digit substitution and transposition errors (including jump transpositions), but at the cost of the check digit possibly being 10, represented by "X". (An alternative is simply to avoid using the serial numbers which result in an "X" check digit.) ISBN-13 instead uses

1593-486: The Americas began with 2. After January 26, 2004, SEDOLs were changed to be alpha-numeric and are issued sequentially, beginning with B000009. At each character position numbers precede letters and vowels are never used . All new SEDOLs, therefore, begin with a letter. Ranges beginning with 9 are reserved for end user allocation. The check digit for a SEDOL is chosen to make the total weighted sum of all seven characters

1652-670: 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 size had been properly recalculated, taking into account the required bar width measurements the label would have been far too large to be acceptable. 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

1711-407: 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 there were two pairs that when read by Delta C rules yielded the same code for the pair. 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

1770-566: The GS1 algorithm used in EAN numbers. More complicated algorithms include the Luhn algorithm (1954), which captures 98% of single-digit transposition errors (it does not detect 90 ↔ 09) and the still more sophisticated Verhoeff algorithm (1969), which catches all single-digit substitution and transposition errors, and many (but not all) more complex errors. Similar is another abstract algebra -based method,

1829-598: The IBM proposal designed by George J. Laurer , but with a slight modification to the font in the human readable area. The first UPC-marked item ever to be scanned at a retail checkout was a 10-pack (50 sticks) of Wrigley's Juicy Fruit chewing gum, purchased at the Marsh supermarket in Troy, Ohio , at 8:01 a.m. on 26 June 1974. The NCR cash register rang up 67 cents. The shopping cart also contained other barcoded items but

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1888-425: The S (start) and after the E (end) guard patterns. 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 scanning a symbol from left-to-right or from right-to-left (the symbol

1947-432: 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 bar-space-bar , where each bar and space is one module wide. The M (middle) guard pattern is 5 modules wide and uses the pattern space-bar-space-bar-space , 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

2006-413: 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; consequently, UPC-A 12-digit number requires a total of 7×12 = 84 modules . A complete UPC-A is 95 modules wide: 84 modules for the digits (L and R sections) combined with 11 modules for

2065-464: 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 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%. A quiet zone, with

2124-437: 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 world, none of which were feasible. 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

2183-663: The check digit would be 5, giving 48715. Systems with weights of 1, 3, 7, or 9, with the weights on neighboring numbers being different, are widely used: for example, 31 31 weights in UPC codes, 13 13 weights in EAN numbers (GS1 algorithm), and the 371 371 371 weights used in United States bank routing transit numbers . This system detects all single-digit errors and around 90% of transposition errors. 1, 3, 7, and 9 are used because they are coprime with 10, so changing any digit changes

2242-460: The check digit; using a coefficient that is divisible by 2 or 5 would lose information (because 5×0 = 5×2 = 5×4 = 5×6 = 5×8 = 0 modulo 10) and thus not catch some single-digit errors. Using different weights on neighboring numbers means that most transpositions change the check digit; however, because all weights differ by an even number, this does not catch transpositions of two digits that differ by 5 (0 and 5, 1 and 6, 2 and 7, 3 and 8, 4 and 9), since

2301-450: The country code on the front and the ISIN check digit at the end. JavaScript code for validating SEDOLs Code: Modified from http://rosettacode.org/wiki/SEDOLs BAE Systems : 0263494 The checksum can be calculated by multiplying the first six digits by their weightings: Then summing up the results: The check digit is then calculated by: Check digit A check digit is

2360-701: The gum was the first one picked up at the checkout. A facsimile of the gum packet went on display at the Smithsonian Institution 's American history museum in Washington, D.C. Murray Eden was a consultant on the team that created the Universal Product Code barcode. As Chairman of a committee of scientists at the Massachusetts Institute of Technology , he helped "select a symbol that would endure

2419-532: The help of consultants Larry Russell and Tom Wilson of McKinsey & Company , defined the numerical format that formed the basis of the Uniform Product Code. Technology firms including Charegon, IBM , Litton-Zellweger, Pitney Bowes-Alpex, Plessey-Anker, RCA , Scanner Inc., Singer, and Dymo Industries /Data General, put forward alternative proposals for symbol representations to the council. The Symbol Selection Committee finally chose to implement

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2478-683: 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 fail-safe system, in case the barcode reader is not working correctly. Around late 1969, IBM at Research Triangle Park (RTP) in North Carolina assigned George Laurer 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. Delta B compared bar widths to space width to code bits. This

2537-459: The label. Dymo Industries , 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. It was decided that the two halves of the label should have a different set of numeric characters. The character set Laurer derived from

2596-473: The letter 'l' (ell). This restriction helps when generating opaque strings that are unlikely to form words by accident and will not contain both O and 0, or l and 1. Having a prime radix of R=29, the betanumeric repertoire permits the algorithm to guarantee detection of single-character and transposition errors for strings less than R=29 characters in length (beyond which it provides a slightly weaker check). The algorithm generalizes to any character repertoire with

2655-494: The pairs he would measure one bar width in each of the pairs to distinguish them from each other. For each pair those bars would be one or two units wide. 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 each set were responsible for most of

2714-479: The related International Article Number (EAN) barcode. UPC data structures are a component of Global Trade Item Numbers (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

2773-451: 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 L indicates a particular number system to be used by the following digits. The last digit R is an error detecting check digit , 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

2832-412: The scanner read errors. 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 error detection and correction . Then they decided to add odd/even parity to the number of units filled with bars in each side. Odd/even parity

2891-414: The sequence input. With a check digit, one can detect simple errors in the input of a series of characters (usually digits) such as a single mistyped digit or some permutations of two successive digits. Check digit algorithms are generally designed to capture human transcription errors . In order of complexity, these include the following: In choosing a system, a high probability of catching errors

2950-426: The standards used to create them. Below is a description of all possible number systems with the corresponding 12-digit UPC-A numbering scheme L LLLLLRRRRR R , where L denotes the numbering system digit and R the check digit. The UPC includes a check digit to detect common data entry errors. For example, UPC-A codes choose the check digit x 12 {\displaystyle x_{12}} to satisfy

3009-450: The sum, but does not catch any transposition errors (switching two digits) as re-ordering does not change the sum. A slightly more complex method is to take the weighted sum of the digits, modulo 10, with different weights for each number position. To illustrate this, for example if the weights for a four digit number were 5, 3, 2, 7 and the number to be coded was 4871, then one would take 5×4 + 3×8 + 2×7 + 7×1 = 65, i.e. 65 modulo 10, and

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3068-486: 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 space×1 - bar×1 - space×3 - bar×2 , meanwhile the right-hand side "4" is bar×1 - space×1 - bar×3 - space×2 . The number of UPC-A and UPC-E barcodes are limited by

3127-405: The timing. 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. 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)

3186-468: 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 percent increase in area or a label of 1.7 in × 1.03 in (43 mm × 26 mm). Laurer felt this was not acceptable. 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

3245-413: The weighting factor as follows: The character values are multiplied by the weights. The check digit is chosen to make the total sum, including the check digit, a multiple of 10, which can be calculated from the weighted sum of the first six characters as (10−(weighted sum modulo 10)) modulo 10. For British securities, SEDOLs are converted to ISINs by padding the front with two zeros, then adding

3304-409: 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 alphabets. This reduced the label size to about 1.5 in × 0.9 in (38 mm × 23 mm). Later Laurer asked Crouse for assistance in how the scanner could detect

3363-477: 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. 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. 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

3422-487: Was the cause of the poor performance of the Delta B code and quite likely the failure of RCA's bull's eye scanner. The following table shows the workable labels, available in the early 1970s, with their sizes. This is assuming a bull's eye with the same information and reliable readability. Each UPC-A barcode consists of a scannable strip of black bars and white spaces above a sequence of 12 numerical digits. No letters , characters or other content of any kind may appear on

3481-419: Was well understood. Except for the bar coding and ten digits the UPC label today is his proposal. Shortly after that Baumeister transferred to another area of RTP. 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. Laurer's first attempt with a bar code used Delta B. The resulting label size

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