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ISO 31-0

ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the SI. It is intended for use in all fields of science and technology and is augmented by more specialized conventions defined in other parts of the ISO 31 standard. ISO 31-0 was withdrawn on 17 November 2009. It is superseded by ISO 80000-1. Other parts of ISO 31 have also been withdrawn and replaced by parts of ISO 80000.

Scope

ISO 31 covers only physical quantities used for the quantitative description of physical phenomena. It does not cover conventional scales (e.g., Beaufort scale, Richter scale, colour intensity scales), results of conventional tests, currencies, or information content. The presentation here is only a brief summary of some of the detailed guidelines and examples given in the standard.

Quantities and units

Physical quantities can be grouped into mutually comparable categories. For example, length, width, diameter and wavelength are all in the same category, that is they are all quantities of the same kind. One particular example of such a quantity can be chosen as a reference quantity, called the unit, and then all other quantities in the same category can be expressed in terms of this unit, multiplied by a number called the numerical value. For example, if we write

then "λ" is the symbol for the physical quantity (wavelength), "m" is the symbol for the unit (metre), and "6.982 × 10−7 " is the numerical value of the wavelength in metres.

More generally, we can write

where A is the symbol for the quantity, {A} symbolizes the numerical value of A, and [A] represents the corresponding unit in which A is expressed here. Both the numerical value and the unit symbol are factors, and their product is the quantity. A quantity itself has no inherent particular numerical value or unit; as with any product, there are many different combinations of numerical value and unit that lead to the same quantity (e.g., A = 300 · m = 0.3 · km = ...). This ambiguity makes the {A} and [A] notations useless, unless they are used together.

The value of a quantity is independent of the unit chosen to represent it. It must be distinguished from the numerical value of the quantity that occurs when the quantity is expressed in a particular unit. The above curly-bracket notation could be extended with a unit-symbol index to clarify this dependency, as in {λ} = 6.982 × 10−7 or equivalently {λ} = 698.2. In practice, where it is necessary to refer to the numerical value of a quantity expressed in a particular unit, it is notationally more convenient to simply divide the quantity through that unit, as in

or equivalently

This is a particularly useful and widely used notation for labelling the axes of graphs or for the headings of table columns, where repeating the unit after each numerical value can be typographically inconvenient.

Typographic conventions
Symbols for quantities
  • Quantities are generally represented by a symbol formed from single letters of the Latin or Greek alphabet.
  • Symbols for quantities are set in italic type, independent of the type used in the rest of the text.
  • If in a text different quantities use the same letter symbol, they can be distinguished via subscripts.
  • A subscript is only set in italic type if it consists of a symbol for a quantity or a variable. Other subscripts are set in upright (roman) type. For example, write V for a "nominal volume" (where "n" is just an abbreviation for the word "nominal"), but write V if n is a running index number.
Names and symbols for units
  • If an internationally standardized symbol exists for a unit, then only that symbol should be used. See the SI articles for the list of standard symbols defined by the International System of Units. Note that the distinction between uppercase and lowercase letters is significant for SI unit symbols. For example, "k" is the prefix kilo and "K" stands for the unit kelvin. The symbols of all SI units named after a person or a place start with an uppercase letter, as do the symbols of all prefixes from mega on upwards. All other symbols are lowercase; the only exception is litre, where both l and L are allowed. However, it is stated that the CIPM will examine whether one of the two may be suppressed.
  • Symbols for units should be printed in an upright (roman) typeface.
Numbers

See Sect. 3.3 of the Standard text.

  • Numbers should be printed in upright (roman) type.
  • ISO 31-0 (after Amendment 2) specifies that "the decimal sign is either the comma on the line or the point on the line". This follows resolution 10[1] of the 22nd CGPM, 2003.[2]
  • Numbers consisting of long sequences of digits can be made more readable by separating them into groups, preferably groups of three, separated by a small space. For this reason, ISO 31-0 specifies that such groups of digits should never be separated by a comma or point, as these are reserved for use as the decimal sign.
  • For numbers whose magnitude is less than 1, the decimal sign should be preceded by a zero.
  • The multiplication sign is either a cross or a half-height dot, though the latter should not be used when the dot is the decimal separator.
Expressions
  • Unit symbols follow the numerical value in the expression of a quantity.
  • Numerical value and unit symbol are separated by a space. This rule also applies to the symbol "°C" for degrees Celsius, as in "25 °C". The only exception are the symbols for the units of plane angle degree, minute and second, which follow the numerical value without a space in between (for example "30°").
  • Where quantities are added or subtracted, parenthesis can be used to distribute a unit symbol over several numerical values, as in
P = 100 kW ± 5 kW = (100 ± 5) kW
(but not: 100 ± 5 kW)
d = 12 × (1 ± 10−4 ) m
  • Products can be written as ab, a b, a⋅b, or a×b. The sign for multiplying numbers is a cross (×) or a half-height dot (⋅). The cross should be used adjacent to numbers if a dot on the line is used as the decimal separator, to avoid confusion between a decimal dot and a multiplication dot.
  • Division can be written as a b {\displaystyle {\frac {a}{b}}} , a/b, or by writing the product of a and b−1 , for example a⋅b−1 . Numerator or denominator can themselves be products or quotients, but in this case, a solidus (/) should not be followed by a multiplication sign or division sign on the same line, unless parentheses are used to avoid ambiguity.
Mathematical signs and symbols

A comprehensive list of internationally standardized mathematical symbols and notations can be found in ISO 31-11.

See also
References
  1. "Resolution 10", 22nd General Conference on Weights and Measures, BIPM.
  2. Brief reference to the history, NIST.
Bibliography
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Nominal Pipe Size

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Nominal Pipe Size ( NPS ) is a North American set of standard sizes for pipes used for high or low pressures and temperatures. "Nominal" refers to pipe in non-specific terms and identifies the diameter of the hole with a non-dimensional number (for example – "2-inch nominal steel pipe" consists of many varieties of steel pipe with the only criterion being a 2.375-inch (60.3 mm) outside diameter). Specific pipe is identified by pipe diameter and another non-dimensional number for wall thickness referred to as the Schedule (Sched. or Sch., for example – "2 inch diameter pipe, Schedule 40"). NPS is often incorrectly called National Pipe Size, due to confusion with the American standard for pipe threads, " national pipe straight ", which also abbreviates as "NPS". The European and international designation equivalent to NPS is DN (diamètre nominal/nominal diameter/Durchmesser nach Norm), in which sizes are measured in millimetres, see ISO 6708 . The term NB ( nominal bore ) is also frequently used interchangeab ...more...



ASTM F568M

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ASTM F568M is an ASTM International standard for metric bolts, screws and studs that are used in general engineering applications. It is titled: Standard Specification for Carbon and Alloy Steel Externally Threaded Metric Fasteners. It defines mechanical properties for fasteners that range from M1.6 to 100 in diameter. The standard was withdrawn in 2012. and has been replaced by ISO 898-1 This standard defines property classes, the metric equivalent of a screw grade, that are almost identical to those defined by ISO 898-1 , except for the addition of the 8.8.3 and 10.9.3 classes. These two additional standards are fasteners that have the same mechanical properties as their base property class (i.e. 8.8 and 10.9), but are made from weathering steel . This is a standard set by the standards organization ASTM International , a voluntary standards development organization that sets technical standards for materials, products, systems, and services. Mechanical properties Head markings and mechanical properties H ...more...



ASCII

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ASCII (  (   listen ) ASS -kee ), abbreviated from American Standard Code for Information Interchange , is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment , and other devices. Most modern character-encoding schemes are based on ASCII, although they support many additional characters. ASCII is the traditional name for the encoding system; the Internet Assigned Numbers Authority (IANA) prefers the updated name US-ASCII , which clarifies that this system was developed in the US and based on the typographical symbols predominantly in use there. ASCII is one of a 1963 List of IEEE milestones ASCII chart from a 1972 printer manual (b1 is the least significant bit). Overview ASCII was developed from telegraph code . Its first commercial use was as a seven- bit teleprinter code promoted by Bell data services. Work on the ASCII standard began on October 6, 1960, with the first meeting of the American Standards Association 's (ASA) (now ...more...



Blockchain

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Bitcoin network data A blockchain , originally block chain , is a continuously growing list of records , called blocks, which are linked and secured using cryptography . Each block typically contains a hash pointer as a link to a previous block, a timestamp and transaction data. By design, blockchains are inherently resistant to modification of the data. It is "an open, distributed ledger that can record transactions between two parties efficiently and in a verifiable and permanent way". For use as a distributed ledger, a blockchain is typically managed by a peer-to-peer network collectively adhering to a protocol for validating new blocks. Once recorded, the data in any given block cannot be altered retroactively without the alteration of all subsequent blocks, which requires collusion of the network majority. Blockchains are secure by design and are an example of a distributed computing system with high Byzantine fault tolerance . Decentralized consensus has therefore been achieved with a blockcha ...more...



Radio-frequency identification

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Small RFID chips, here compared to a grain of rice, are incorporated in consumer products, and implanted in pets , for identification purposes Radio-frequency identification ( RFID ) uses electromagnetic fields to automatically identify and track tags attached to objects. The tags contain electronically stored information. Passive tags collect energy from a nearby RFID reader's interrogating radio waves . Active tags have a local power source (such as a battery) and may operate hundreds of meters from the RFID reader. Unlike a barcode , the tag need not be within the line of sight of the reader, so it may be embedded in the tracked object. RFID is one method for Automatic Identification and Data Capture (AIDC). RFID tags are used in many industries, for example, an RFID tag attached to an automobile during production can be used to track its progress through the assembly line; RFID-tagged pharmaceuticals can be tracked through warehouses; and implanting RFID microchips in livestock and pets allows for positiv ...more...



MPEG-1

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MPEG-1 is a standard for lossy compression of video and audio . It is designed to compress VHS -quality raw digital video and CD audio down to 1.5 Mbit/s (26:1 and 6:1 compression ratios respectively) without excessive quality loss, making video CDs , digital cable / satellite TV and digital audio broadcasting (DAB) possible. Today, MPEG-1 has become the most widely compatible lossy audio/video format in the world, and is used in a large number of products and technologies. Perhaps the best-known part of the MPEG-1 standard is the MP3 audio format it introduced. The MPEG-1 standard is published as ISO / IEC 11172 – Information technology—Coding of moving pictures and associated audio for digital storage media at up to about 1.5 Mbit/s. The standard consists of the following five Parts: Systems (storage and synchronization of video, audio, and other data together) Video (compressed video content) Audio (compressed audio content) Conformance testing (testing the correctness of implementations of the standard) ...more...



International Standard Atmosphere

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Comparison of a graph of International Standard Atmosphere temperature and pressure and approximate altitudes of various objects and successful stratospheric jumps The International Standard Atmosphere ( ISA ) is an atmospheric model of how the pressure , temperature , density , and viscosity of the Earth's atmosphere change over a wide range of altitudes or elevations . It has been established to provide a common reference for temperature and pressure and consists of tables of values at various altitudes, plus some formulas by which those values were derived. The International Organization for Standardization (ISO) publishes the ISA as an international standard , ISO 2533:1975. Other standards organizations , such as the International Civil Aviation Organization (ICAO) and the United States Government , publish extensions or subsets of the same atmospheric model under their own standards-making authority. Description The ISA mathematical model divides the atmosphere into layers with an assumed linear distri ...more...



QR code

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QR code for the URL of the English Wikipedia Mobile main page QR code (abbreviated from Quick Response Code ) is the trademark for a type of matrix barcode (or two-dimensional barcode ) first designed for the automotive industry in Japan . A barcode is a machine-readable optical label that contains information about the item to which it is attached. A QR code uses four standardized encoding modes (numeric, alphanumeric, byte/binary, and kanji ) to efficiently store data; extensions may also be used. The QR code system became popular outside the automotive industry due to its fast readability and greater storage capacity compared to standard UPC barcodes . Applications include product tracking, item identification, time tracking, document management, and general marketing. A QR code consists of black squares arranged in a square grid on a white background, which can be read by an imaging device such as a camera, and processed using Reed–Solomon error correction until the image can be appropriately interpreted. ...more...



Orders of magnitude (numbers)

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The logarithmic scale can compactly represent the relationship among variously sized numbers. This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities . Each number is given a name in the short scale , which is used in English-speaking countries, as well as a name in the long scale , which is used in some of the countries that do not have English as their national language. Smaller than 10−100 (one googolth) Mathematics – Numbers: The number zero is a natural, even number which quantifies a count or an amount of null size. Mathematics – Writing: Approximately 10 is a rough first estimate of the probability that a monkey , placed in front of a typewriter , will perfectly type out William Shakespeare's play Hamlet on its first try. However, taking punctuation , capitalization , and spacing into account, the actual probability is far lower: around 10 . Computing: The number 1 × 10 is equal to the smallest positive non-zero value th ...more...



Ash (analytical chemistry)

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In analytical chemistry , ashing or ash content determination is the process of mineralization for preconcentration of trace substances prior to a chemical analysis, such as chromatography , or optical analysis, such as spectroscopy . Overview A crucible and tongs, on a green mat. The residues after a sample is completely burnt - in contrast to the ash remaining after incomplete combustion - consist mostly of metal oxides . Ash is one of the components in the proximate analysis of biological materials, consisting mainly of salty, inorganic constituents. It includes metal salts which are important for processes requiring ions such as Na (Sodium), K (Potassium), and Ca (Calcium). It also includes trace minerals which are required for unique molecules, such as chlorophyll and hemoglobin . A crucible can be used to determine the percentage of ash contained in an otherwise burnable sample of material such as coal , wood , oil , rubber or plastics. The ISO mandates ash content determination for most foodstuffs. ...more...



Code page

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In computing , a code page is a table of values that describes the character set used for encoding a particular set of characters , usually combined with a number of control characters . The term "code page" originated from IBM 's EBCDIC -based mainframe systems, but Microsoft , SAP , and Oracle Corporation are among the few vendors which use this term. The majority of vendors identify their own character sets by a name. In the case when there is a plethora of character sets (like in IBM), identifying character sets through a number is a convenient way to distinguish them. Originally, the code page numbers referred to the page numbers in the IBM standard character set manual, a condition which has not held for a long time. Vendors that use a code page system allocate their own code page number to a character encoding , even if it is better known by another name; for example, UTF-8 has been assigned page numbers 1208 at IBM, 65001 at Microsoft, and 4110 at SAP. Hewlett-Packard uses a similar concept in it ...more...



ISO 10367

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ISO 10367 is character set developed by ISO Character set ISO 10367 _0 _1 _2 _3 _4 _5 _6 _7 _8 _9 _A _B _C _D _E _F   0_   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   1_   16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31   2_   SP 0020 32 ! 0021 33 " 0022 34 # 0023 35 $ 0024 36 % 0025 37 & 0026 38 ' 0027 39 ( 0028 40 ) 0029 41 * 002A 42 + 002B 43 , 002C 44 - 002D 45 . 002E 46 / 002F 47   3_   0 0030 48 1 0031 49 2 0032 50 3 0033 51 4 0034 52 5 0035 53 6 0036 54 7 0037 55 8 0038 56 9 0039 57 : 003A 58 ; 003B 59 003C 60 = 003D 61 > 003E 62 ? 003F 63   4_   @ 0040 64 A 0041 65 B 0042 66 C 0043 67 D 0044 68 E 0045 69 F 0046 70 G 0047 71 H 0048 72 I 0049 73 J 004A 74 K 004B 75 L 004C 76 M 004D 77 N 004E 78 O 004F 79   5_   P 0050 80 Q 0051 81 R 0052 82 S 0053 83 T 0054 84 U 0055 85 V 0056 86 W 0057 87 X 0058 88 Y 0059 89 Z 005A 90 [ 005B 91 \ 005C 92 ] 005D 93 ^ 005E 94 _ 005F 95   6_   ` 0060 96 a 0061 97 b 0062 98 c 0063 99 d 0064 100 e 0065 101 f 0066 102 g 0067 103 h 0068 104 i 0069 105 j 006A 106 k 006B 107 l ...more...



Character encoding

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In computing character encoding is used to represent a repertoire of characters by some kind of encoding system. Depending on the abstraction level and context, corresponding code points and the resulting code space may be regarded as bit patterns , octets , natural numbers , electrical pulses , etc. A character encoding is used in computation , data storage , and transmission of textual data . "Character set", "character map", "codeset" and " code page " are related, but not identical, terms. Early character codes associated with the optical or electrical telegraph could only represent a subset of the characters used in written languages, sometimes restricted to upper case letters, numerals and some punctuation only. The low cost of digital representation of data in modern computer systems allows more elaborate character codes (such as Unicode ) which represent most of the characters used in many written languages. Character encoding using internationally accepted standards permits worldwide interchange of ...more...



Exposure value

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In photography , exposure value ( EV ) is a number that represents a combination of a camera 's shutter speed and f-number , such that all combinations that yield the same exposure have the same EV (for any fixed scene luminance ). Exposure value is also used to indicate an interval on the photographic exposure scale, with a difference of 1 EV corresponding to a standard power-of-2 exposure step, commonly referred to as a stop . The EV concept was developed by the German shutter manufacturer Friedrich Deckel in the 1950s ( Gebele 1958 ; Ray 2000 , 318). Its intent was to simplify choosing among equivalent camera exposure settings by replacing combinations of shutter speed and f-number (e.g., 1/125 s at f/16) with a single number (e.g., 15). On some lenses with leaf shutters , the process was further simplified by allowing the shutter and aperture controls to be linked such that when one was changed, the other was automatically adjusted to maintain the same exposure. This was especially helpful to beginners wi ...more...



Arthur Bigge, 1st Baron Stamfordham

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Lieutenant-Colonel Arthur John Bigge, 1st Baron Stamfordham , GCB , GCIE , GCVO , KCSI , KCMG , ISO , PC (18 June 1849 – 31 March 1931) was a British Army officer and courtier. He was Private Secretary to Queen Victoria during the last few years of her reign, and to George V during most of his reign. He was the maternal grandfather of Lord Adeane , Private Secretary to Elizabeth II from 1953 to 1972. Background and education Bigge was the son of John Frederic Bigge (1814–1885) Vicar of Stamfordham, Northumberland and the grandson of Charles William Bigge (1773–1849) of Benton House, Little Benton, Newcastle on Tyne and Linden Hall, Longhorsley , Northumberland, High Sheriff of Northumberland and a prominent merchant and banker in Newcastle on Tyne. He was educated at Rossall School and the Royal Military Academy and was commissioned into the Royal Artillery in 1869. Career Bigge was appointed Private Secretary to Queen Victoria in 1895 and served until her death in January 1901. A couple of months later he wa ...more...



List of countries and dependencies by population

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World population percentage by country This is a list of countries and dependent territories by population . It includes sovereign states , inhabited dependent territories and, in some cases, constituent countries of sovereign states, with inclusion within the list being primarily based on the ISO standard ISO 3166-1 . For instance, the United Kingdom is considered as a single entity while the constituent countries of the Kingdom of the Netherlands are considered separately. In addition, this list includes certain states with limited recognition not found in ISO 3166-1. The population figures do not reflect the practice of countries that report significantly different populations of citizens domestically and overall. Some countries, notably Thailand , do not report total population, exclusively counting citizens; for total populations an international agency must issue an estimate. Also given in percent is each country's population compared with the population of the world , which the United Nations estimated ...more...



Hazard symbol

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Skull and crossbones , a common symbol for poison and other sources of lethal danger ( GHS hazard pictograms ). Hazard symbols or warning symbols are recognisable symbols designed to warn about hazardous or dangerous materials, locations, or objects, including electric currents, poisons, and radioactivity . The use of hazard symbols is often regulated by law and directed by standards organisations . Hazard symbols may appear with different colors, backgrounds, borders and supplemental information in order to specify the type of hazard and the level of threat (for example, toxicity classes ). Warning symbols are used in many places in lieu of or addition to written warnings as they are quickly recognized (faster than reading a written warning) and more commonly understood (the same symbol can be recognized as having the same meaning to speakers of different languages). List of common symbols Type of hazard Unicode glyph Unicode Image Generic caution ⚠ U+26A0 Poison ☠ U+2620 Ionizing radiation ☢ U+2622 Radiatio ...more...



Tracking number

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Tracking numbers are numbers given to packages when they are shipped. Tracking numbers are useful for knowing the location of time sensitive deliveries. In the United States , some of the companies and organizations that use tracking numbers are UPS , FedEx , and the United States Postal Service . Most Postal Services use the international S10 (UPU standard) , including the United States Postal Service and most European Postal Services. Formats FedEx Ground and Express tracking numbers can be between 12 and 14 digits. Prior to January 2013, Ground tracking numbers were up to 15 digits and Express numbers were up to 12 digits. A UPS tracking number, for domestic packages within the United States, will usually start with "1Z" followed by a 6 character shipper number (numbers and letters), a 2 digit service level indicator (e.g., 03 for GROUND, see UPS Service Codes below), and finally 8 digits identifying the package, for a total of 18 characters. DHL Express supports the carrier-independent ISO standard 154 ...more...



HTML

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Hypertext Markup Language ( HTML ) is the standard markup language for creating web pages and web applications . With Cascading Style Sheets (CSS) and JavaScript it forms a triad of cornerstone technologies for the World Wide Web . Web browsers receive HTML documents from a web server or from local storage and render them into multimedia web pages. HTML describes the structure of a web page semantically and originally included cues for the appearance of the document. HTML elements are the building blocks of HTML pages. With HTML constructs, images and other objects, such as interactive forms, may be embedded into the rendered page. It provides a means to create structured documents by denoting structural semantics for text such as headings, paragraphs, lists, links , quotes and other items. HTML elements are delineated by tags, written using angle brackets . Tags such as and introduce content into the page directly. Others such as ... surround and provide information about document text and may include other ...more...



Ordinal date

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An ordinal date is a calendar date typically consisting of a year and a day of year ranging between 1 and 366 (starting on January 1), though year may sometimes be omitted. The two numbers can be formatted as YYYY-DDD to comply with the ISO 8601 ordinal date format. Calculation Computation of the ordinal date within a year is part of calculating the ordinal date throughout the years from a reference date , such as the Julian date . It is also part of calculating the day of the week , though for this purpose modulo-7 simplifications can be made. For these purposes it is convenient to count January and February as month 13 and 14 of the previous year, for two reasons: the shortness of February and its variable length. In that case the date counted from 1 March is given by which can also be written with m the month number and d the date. The formula reflects the fact that any five consecutive months in the range March–January have a total length of 153 days, due to a fixed pattern 31–30–31–30–31 repeating itself ...more...



Machine-readable passport

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A machine-readable passport ( MRP ) is a machine-readable travel document (MRTD) with the data on the identity page encoded in optical character recognition format. Many countries began to issue machine-readable travel documents in the 1980s. Most travel passports worldwide are MRPs. They are standardized by the ICAO Document 9303 (endorsed by the International Organization for Standardization and the International Electrotechnical Commission as ISO/IEC 7501-1) and have a special machine-readable zone (MRZ), which is usually at the bottom of the identity page at the beginning of a passport. The ICAO Document 9303 describes three types of documents. Usually passport booklets are issued in "Type 3" format, while identity cards and passport cards typically use the "Type 1" format. The machine-readable zone of a Type 3 travel document spans two lines, and each line is 44 characters long. The following information must be provided in the zone: name, passport number, nationality, date of birth, sex, and passport ex ...more...



C standard library

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The C standard library or libc is the standard library for the C programming language , as specified in the ANSI C standard. It was developed at the same time as the C library POSIX specification , which is a superset of it. Since ANSI C was adopted by the International Organization for Standardization , the C standard library is also called the ISO C library . The C standard library provides macros , type definitions and functions for tasks such as string handling, mathematical computations, input/output processing, memory management , and several other operating system services. Application programming interface Header files The application programming interface (API) of the C standard library is declared in a number of header files . Each header file contains one or more function declarations, data type definitions, and macros. After a long period of stability, three new header files ( iso646.h , wchar.h , and wctype.h ) were added with Normative Addendum 1 (NA1), an addition to the C Standard ratified ...more...




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