The multiplication sign ( × ), also known as the times sign or the dimension sign , is a mathematical symbol used to denote the operation of multiplication , which results in a product .
72-462: Multiplication (often denoted by the cross symbol × , by the mid-line dot operator ⋅ , by juxtaposition , or, on computers , by an asterisk * ) is one of the four elementary mathematical operations of arithmetic , with the other ones being addition , subtraction , and division . The result of a multiplication operation is called a product . The multiplication of whole numbers may be thought of as repeated addition ; that is,
144-582: A = sup x ∈ A x {\displaystyle a=\sup _{x\in A}x} and b = sup y ∈ B y , {\displaystyle b=\sup _{y\in B}y,} then a ⋅ b = sup x ∈ A , y ∈ B x ⋅ y . {\displaystyle a\cdot b=\sup _{x\in A,y\in B}x\cdot y.} In particular,
216-402: A byte order mark or escape sequences ; compressing schemes try to minimize the number of bytes used per code unit (such as SCSU and BOCU ). Although UTF-32BE and UTF-32LE are simpler CESes, most systems working with Unicode use either UTF-8 , which is backward compatible with fixed-length ASCII and maps Unicode code points to variable-length sequences of octets, or UTF-16BE , which
288-461: A multiplication table of memorized or consulted products of small numbers (typically any two numbers from 0 to 9). However, one method, the peasant multiplication algorithm, does not. The example below illustrates "long multiplication" (the "standard algorithm", "grade-school multiplication"): In some countries such as Germany , the above multiplication is depicted similarly but with the original product kept horizontal and computation starting with
360-411: A rectangle (for whole numbers) or as finding the area of a rectangle whose sides have some given lengths . The area of a rectangle does not depend on which side is measured first—a consequence of the commutative property. The product of two measurements (or physical quantities ) is a new type of measurement, usually with a derived unit . For example, multiplying the lengths (in meters or feet) of
432-437: A string of the letters "ab̲c𐐀"—that is, a string containing a Unicode combining character ( U+0332 ̲ COMBINING LOW LINE ) as well as a supplementary character ( U+10400 𐐀 DESERET CAPITAL LETTER LONG I ). This string has several Unicode representations which are logically equivalent, yet while each is suited to a diverse set of circumstances or range of requirements: Note in particular that 𐐀
504-575: A list of the first twenty multiples of a certain principal number n : n , 2 n , ..., 20 n ; followed by the multiples of 10 n : 30 n 40 n , and 50 n . Then to compute any sexagesimal product, say 53 n , one only needed to add 50 n and 3 n computed from the table. In the mathematical text Zhoubi Suanjing , dated prior to 300 BC, and the Nine Chapters on the Mathematical Art , multiplication calculations were written out in words, although
576-454: A multiplication sign (such as ⋅ or × ), while the asterisk appeared on every keyboard. This usage originated in the FORTRAN programming language. The numbers to be multiplied are generally called the "factors" (as in factorization ). The number to be multiplied is the "multiplicand", and the number by which it is multiplied is the "multiplier". Usually, the multiplier is placed first, and
648-567: A nonzero natural number, or minus a nonzero natural number. The product of zero and another integer is always zero. The product of two nonzero integers is determined by the product of their positive amounts , combined with the sign derived from the following rule: × + − + + − − − + {\displaystyle {\begin{array}{|c|c c|}\hline \times &+&-\\\hline +&+&-\\-&-&+\\\hline \end{array}}} (This rule
720-420: A particular sequence of bits. Instead, characters would first be mapped to a universal intermediate representation in the form of abstract numbers called code points . Code points would then be represented in a variety of ways and with various default numbers of bits per character (code units) depending on context. To encode code points higher than the length of the code unit, such as above 256 for eight-bit units,
792-499: A professor of mathematics at Princeton University , wrote the following: These place value decimal arithmetic algorithms were introduced to Arab countries by Al Khwarizmi in the early 9th century and popularized in the Western world by Fibonacci in the 13th century. Grid method multiplication , or the box method, is used in primary schools in England and Wales and in some areas of
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#1732852054615864-461: A single glyph . The former simplifies the text handling system, but the latter allows any letter/diacritic combination to be used in text. Ligatures pose similar problems. Exactly how to handle glyph variants is a choice that must be made when constructing a particular character encoding. Some writing systems, such as Arabic and Hebrew, need to accommodate things like graphemes that are joined in different ways in different contexts, but represent
936-546: A single character per code unit. However, due to the emergence of more sophisticated character encodings, the distinction between these terms has become important. "Code page" is a historical name for a coded character set. Originally, a code page referred to a specific page number in the IBM standard character set manual, which would define a particular character encoding. Other vendors, including Microsoft , SAP , and Oracle Corporation , also published their own sets of code pages;
1008-432: A stream of octets (bytes). The purpose of this decomposition is to establish a universal set of characters that can be encoded in a variety of ways. To describe this model precisely, Unicode uses its own set of terminology to describe its process: An abstract character repertoire (ACR) is the full set of abstract characters that a system supports. Unicode has an open repertoire, meaning that new characters will be added to
1080-623: A subset of the characters used in written languages , sometimes restricted to upper case letters , numerals and some punctuation only. The advent of digital computer systems allows more elaborate encodings codes (such as Unicode ) to support hundreds of written languages. The most popular character encoding on the World Wide Web is UTF-8 , which is used in 98.2% of surveyed web sites, as of May 2024. In application programs and operating system tasks, both UTF-8 and UTF-16 are popular options. The history of character codes illustrates
1152-464: A value called b 2 ). This notation is used wherever multiplication should be written explicitly, such as in " ab = a ⋅2 for b = 2 "; this usage is also seen in English-language texts. In some languages, the use of full stop as a multiplication symbol, such as a . b , is common when the symbol for decimal point is comma . Historically, computer language syntax was restricted to
1224-505: A well-defined and extensible encoding system, has replaced most earlier character encodings, but the path of code development to the present is fairly well known. The Baudot code, a five- bit encoding, was created by Émile Baudot in 1870, patented in 1874, modified by Donald Murray in 1901, and standardized by CCITT as International Telegraph Alphabet No. 2 (ITA2) in 1930. The name baudot has been erroneously applied to ITA2 and its many variants. ITA2 suffered from many shortcomings and
1296-473: Is backward compatible with fixed-length UCS-2BE and maps Unicode code points to variable-length sequences of 16-bit words. See comparison of Unicode encodings for a detailed discussion. Finally, there may be a higher-level protocol which supplies additional information to select the particular variant of a Unicode character, particularly where there are regional variants that have been 'unified' in Unicode as
1368-430: Is a consequence of the distributivity of multiplication over addition, and is not an additional rule .) In words: Two fractions can be multiplied by multiplying their numerators and denominators: There are several equivalent ways to define formally the real numbers; see Construction of the real numbers . The definition of multiplication is a part of all these definitions. A fundamental aspect of these definitions
1440-987: Is both a multiple of 3 and a multiple of 5. The product of two numbers or the multiplication between two numbers can be defined for common special cases: natural numbers, integers, rational numbers, real numbers, complex numbers, and quaternions. The product of two natural numbers r , s ∈ N {\displaystyle r,s\in \mathbb {N} } is defined as: r ⋅ s ≡ ∑ i = 1 s r = r + r + ⋯ + r ⏟ s times ≡ ∑ j = 1 r s = s + s + ⋯ + s ⏟ r times . {\displaystyle r\cdot s\equiv \sum _{i=1}^{s}r=\underbrace {r+r+\cdots +r} _{s{\text{ times}}}\equiv \sum _{j=1}^{r}s=\underbrace {s+s+\cdots +s} _{r{\text{ times}}}.} An integer can be either zero,
1512-442: Is defined by a CEF. A character encoding scheme (CES) is the mapping of code units to a sequence of octets to facilitate storage on an octet-based file system or transmission over an octet-based network. Simple character encoding schemes include UTF-8 , UTF-16BE , UTF-32BE , UTF-16LE , and UTF-32LE ; compound character encoding schemes, such as UTF-16 , UTF-32 and ISO/IEC 2022 , switch between several simple schemes by using
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#17328520546151584-444: Is defined by the encoding. Thus, the number of code units required to represent a code point depends on the encoding: Exactly what constitutes a character varies between character encodings. For example, for letters with diacritics , there are two distinct approaches that can be taken to encode them: they can be encoded either as a single unified character (known as a precomposed character), or as separate characters that combine into
1656-490: Is often written using the multiplication sign (either × or × {\displaystyle \times } ) between the terms (that is, in infix notation ). For example, There are other mathematical notations for multiplication: In computer programming , the asterisk (as in 5*2 ) is still the most common notation. This is due to the fact that most computers historically were limited to small character sets (such as ASCII and EBCDIC ) that lacked
1728-430: Is preferred, usually in the larger context of locales. IBM's Character Data Representation Architecture (CDRA) designates entities with coded character set identifiers ( CCSIDs ), each of which is variously called a "charset", "character set", "code page", or "CHARMAP". The code unit size is equivalent to the bit measurement for the particular encoding: A code point is represented by a sequence of code units. The mapping
1800-492: Is represented with either one 32-bit value (UTF-32), two 16-bit values (UTF-16), or four 8-bit values (UTF-8). Although each of those forms uses the same total number of bits (32) to represent the glyph, it is not obvious how the actual numeric byte values are related. As a result of having many character encoding methods in use (and the need for backward compatibility with archived data), many computer programs have been developed to translate data between character encoding schemes,
1872-394: Is that every real number can be approximated to any accuracy by rational numbers . A standard way for expressing this is that every real number is the least upper bound of a set of rational numbers. In particular, every positive real number is the least upper bound of the truncations of its infinite decimal representation ; for example, π {\displaystyle \pi }
1944-421: Is that the magnitudes are multiplied and the arguments are added. The product of two quaternions can be found in the article on quaternions . Note, in this case, that a ⋅ b {\displaystyle a\cdot b} and b ⋅ a {\displaystyle b\cdot a} are in general different. Many common methods for multiplying numbers using pencil and paper require
2016-412: Is the least upper bound of { 3 , 3.1 , 3.14 , 3.141 , … } . {\displaystyle \{3,\;3.1,\;3.14,\;3.141,\ldots \}.} A fundamental property of real numbers is that rational approximations are compatible with arithmetic operations , and, in particular, with multiplication. This means that, if a and b are positive real numbers such that
2088-446: Is the process of assigning numbers to graphical characters , especially the written characters of human language, allowing them to be stored, transmitted, and transformed using computers. The numerical values that make up a character encoding are known as code points and collectively comprise a code space, a code page , or character map . Early character codes associated with the optical or electrical telegraph could only represent
2160-552: Is used by the APL programming language to denote the sign function . The lower-case Latin letter x is sometimes used in place of the multiplication sign. This is considered incorrect in mathematical writing. In algebraic notation, widely used in mathematics, a multiplication symbol is usually omitted wherever it would not cause confusion: " a multiplied by b " can be written as ab or a b . Other symbols can also be used to denote multiplication, often to reduce confusion between
2232-503: The ASCII character set, and the asterisk * became the de facto symbol for the multiplication operator. This selection is reflected in the numeric keypad on English-language keyboards, where the arithmetic operations of addition, subtraction, multiplication and division are represented by the keys + , - , * and / , respectively. Other variants and related characters: Character set Character encoding
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2304-458: The Marchant , automated multiplication of up to 10-digit numbers. Modern electronic computers and calculators have greatly reduced the need for multiplication by hand. Methods of multiplication were documented in the writings of ancient Egyptian , Greek, Indian, and Chinese civilizations. The Ishango bone , dated to about 18,000 to 20,000 BC, may hint at a knowledge of multiplication in
2376-625: The Upper Paleolithic era in Central Africa , but this is speculative. The Egyptian method of multiplication of integers and fractions, which is documented in the Rhind Mathematical Papyrus , was by successive additions and doubling. For instance, to find the product of 13 and 21 one had to double 21 three times, obtaining 2 × 21 = 42 , 4 × 21 = 2 × 42 = 84 , 8 × 21 = 2 × 84 = 168 . The full product could then be found by adding
2448-490: The discrete Fourier transform reduce the computational complexity to O ( n log n log log n ) . In 2016, the factor log log n was replaced by a function that increases much slower, though still not constant. In March 2019, David Harvey and Joris van der Hoeven submitted a paper presenting an integer multiplication algorithm with a complexity of O ( n log n ) . {\displaystyle O(n\log n).} The algorithm, also based on
2520-567: The factors , and 12 is the product . One of the main properties of multiplication is the commutative property , which states in this case that adding 3 copies of 4 gives the same result as adding 4 copies of 3: Thus, the designation of multiplier and multiplicand does not affect the result of the multiplication. Systematic generalizations of this basic definition define the multiplication of integers (including negative numbers), rational numbers (fractions), and real numbers. Multiplication can also be visualized as counting objects arranged in
2592-533: The heavy goods vehicle industry, to calculate the amount of powered wheels. The form is properly a four-fold rotationally symmetric saltire . The multiplication sign × is similar to a lowercase X ( x ) which is not a four-fold rotationally symmetric saltire. The earliest known use of the × symbol to represent multiplication appears in an anonymous appendix to the 1618 edition of John Napier 's Mirifici Logarithmorum Canonis Descriptio . This appendix has been attributed to William Oughtred , who used
2664-482: The 1980s faced the dilemma that, on the one hand, it seemed necessary to add more bits to accommodate additional characters, but on the other hand, for the users of the relatively small character set of the Latin alphabet (who still constituted the majority of computer users), those additional bits were a colossal waste of then-scarce and expensive computing resources (as they would always be zeroed out for such users). In 1985,
2736-509: The Unicode standard is U+0000 to U+10FFFF, inclusive, divided in 17 planes , identified by the numbers 0 to 16. Characters in the range U+0000 to U+FFFF are in plane 0, called the Basic Multilingual Plane (BMP). This plane contains the most commonly-used characters. Characters in the range U+10000 to U+10FFFF in the other planes are called supplementary characters . The following table shows examples of code point values: Consider
2808-507: The United States to help teach an understanding of how multiple digit multiplication works. An example of multiplying 34 by 13 would be to lay the numbers out in a grid as follows: and then add the entries. The classical method of multiplying two n -digit numbers requires n digit multiplications. Multiplication algorithms have been designed that reduce the computation time considerably when multiplying large numbers. Methods based on
2880-425: The adoption of electrical and electro-mechanical techniques these earliest codes were adapted to the new capabilities and limitations of the early machines. The earliest well-known electrically transmitted character code, Morse code , introduced in the 1840s, used a system of four "symbols" (short signal, long signal, short space, long space) to generate codes of variable length. Though some commercial use of Morse code
2952-417: The appropriate terms found in the doubling sequence: The Babylonians used a sexagesimal positional number system , analogous to the modern-day decimal system . Thus, Babylonian multiplication was very similar to modern decimal multiplication. Because of the relative difficulty of remembering 60 × 60 different products, Babylonian mathematicians employed multiplication tables . These tables consisted of
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3024-464: The average personal computer user's hard disk drive could store only about 10 megabytes, and it cost approximately US$ 250 on the wholesale market (and much higher if purchased separately at retail), so it was very important at the time to make every bit count. The compromise solution that was eventually found and developed into Unicode was to break the assumption (dating back to telegraph codes) that each character should always directly correspond to
3096-416: The communication of these hybrid names with a Latin letter "x" is common, when the actual "×" symbol is not readily available. The multiplication sign is also used by historians for an event between two dates . When employed between two dates – for example 1225 and 1232 – the expression "1225×1232" means "no earlier than 1225 and no later than 1232". A monadic × symbol
3168-575: The early Chinese mathematicians employed Rod calculus involving place value addition, subtraction, multiplication, and division. The Chinese were already using a decimal multiplication table by the end of the Warring States period. The modern method of multiplication based on the Hindu–Arabic numeral system was first described by Brahmagupta . Brahmagupta gave rules for addition, subtraction, multiplication, and division. Henry Burchard Fine , then
3240-536: The era had their own character codes, often six-bit, but usually had the ability to read tapes produced on IBM equipment. These BCD encodings were the precursors of IBM's Extended Binary-Coded Decimal Interchange Code (usually abbreviated as EBCDIC), an eight-bit encoding scheme developed in 1963 for the IBM System/360 that featured a larger character set, including lower case letters. In trying to develop universally interchangeable character encodings, researchers in
3312-405: The evolving need for machine-mediated character-based symbolic information over a distance, using once-novel electrical means. The earliest codes were based upon manual and hand-written encoding and cyphering systems, such as Bacon's cipher , Braille , international maritime signal flags , and the 4-digit encoding of Chinese characters for a Chinese telegraph code ( Hans Schjellerup , 1869). With
3384-480: The fast Fourier transform, is conjectured to be asymptotically optimal. The algorithm is not practically useful, as it only becomes faster for multiplying extremely large numbers (having more than 2 bits). One can only meaningfully add or subtract quantities of the same type, but quantities of different types can be multiplied or divided without problems. For example, four bags with three marbles each can be thought of as: When two measurements are multiplied together,
3456-415: The first digit of the multiplier: Multiplying numbers to more than a couple of decimal places by hand is tedious and error-prone. Common logarithms were invented to simplify such calculations, since adding logarithms is equivalent to multiplying. The slide rule allowed numbers to be quickly multiplied to about three places of accuracy. Beginning in the early 20th century, mechanical calculators , such as
3528-413: The fundamental idea of multiplication. The product of a sequence, vector multiplication , complex numbers , and matrices are all examples where this can be seen. These more advanced constructs tend to affect the basic properties in their own ways, such as becoming noncommutative in matrices and some forms of vector multiplication or changing the sign of complex numbers. In arithmetic , multiplication
3600-475: The most well-known code page suites are " Windows " (based on Windows-1252) and "IBM"/"DOS" (based on code page 437 ). Despite no longer referring to specific page numbers in a standard, many character encodings are still referred to by their code page number; likewise, the term "code page" is often still used to refer to character encodings in general. The term "code page" is not used in Unix or Linux, where "charmap"
3672-417: The multiplicand is placed second; however, sometimes the first factor is considered the multiplicand and the second the multiplier. Also, as the result of multiplication does not depend on the order of the factors, the distinction between "multiplicand" and "multiplier" is useful only at a very elementary level and in some multiplication algorithms , such as the long multiplication . Therefore, in some sources,
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#17328520546153744-473: The multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand , as the quantity of the other one, the multiplier ; both numbers can be referred to as factors . For example, the expression 3 × 4 {\displaystyle 3\times 4} , phrased as "3 times 4" or "3 multiplied by 4", can be evaluated by adding 3 copies of 4 together: Here, 3 (the multiplier ) and 4 (the multiplicand ) are
3816-444: The multiplication sign × and the common variable x . In some countries, such as Germany , the primary symbol for multiplication is the " dot operator " ⋅ (as in a⋅b ). This symbol is also used in compound units of measurement , e.g., N⋅m (see International System of Units#Lexicographic conventions ). In algebra, it is a notation to resolve ambiguity (for instance, "b times 2" may be written as b ⋅2 , to avoid being confused with
3888-514: The original influence for John Napier's more general usage. Two even earlier uses of a ✕ notation have been identified, but do not stand critical examination. In mathematics , the symbol × has a number of uses, including In biology , the multiplication sign is used in a botanical hybrid name , for instance Ceanothus papillosus × impressus (a hybrid between C. papillosus and C. impressus ) or Crocosmia × crocosmiiflora (a hybrid between two other species of Crocosmia ). However,
3960-399: The others. Thus, 2 × π {\displaystyle 2\times \pi } is a multiple of π {\displaystyle \pi } , as is 5133 × 486 × π {\displaystyle 5133\times 486\times \pi } . A product of integers is a multiple of each factor; for example, 15 is the product of 3 and 5 and
4032-442: The product is of a type depending on the types of measurements. The general theory is given by dimensional analysis . This analysis is routinely applied in physics, but it also has applications in finance and other applied fields. A common example in physics is the fact that multiplying speed by time gives distance . For example: Multiplication sign The symbol is also used in botany , in botanical hybrid names and
4104-416: The product of two positive real numbers is the least upper bound of the term-by-term products of the sequences of their decimal representations. As changing the signs transforms least upper bounds into greatest lower bounds, the simplest way to deal with a multiplication involving one or two negative numbers, is to use the rule of signs described above in § Product of two integers . The construction of
4176-412: The punched card code then in use only allowed digits, upper-case English letters and a few special characters, six bits were sufficient. These BCD encodings extended existing simple four-bit numeric encoding to include alphabetic and special characters, mapping them easily to punch-card encoding which was already in widespread use. IBM's codes were used primarily with IBM equipment; other computer vendors of
4248-505: The real numbers through Cauchy sequences is often preferred in order to avoid consideration of the four possible sign configurations. Two complex numbers can be multiplied by the distributive law and the fact that i 2 = − 1 {\displaystyle i^{2}=-1} , as follows: The geometric meaning of complex multiplication can be understood by rewriting complex numbers in polar coordinates : Furthermore, from which one obtains The geometric meaning
4320-460: The repertoire over time. A coded character set (CCS) is a function that maps characters to code points (each code point represents one character). For example, in a given repertoire, the capital letter "A" in the Latin alphabet might be represented by the code point 65, the character "B" by 66, and so on. Multiple coded character sets may share the same character repertoire; for example ISO/IEC 8859-1 and IBM code pages 037 and 500 all cover
4392-491: The same character. An example is the XML attribute xml:lang. The Unicode model uses the term "character map" for other systems which directly assign a sequence of characters to a sequence of bytes, covering all of the CCS, CEF and CES layers. In Unicode, a character can be referred to as 'U+' followed by its codepoint value in hexadecimal. The range of valid code points (the codespace) for
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#17328520546154464-537: The same repertoire but map them to different code points. A character encoding form (CEF) is the mapping of code points to code units to facilitate storage in a system that represents numbers as bit sequences of fixed length (i.e. practically any computer system). For example, a system that stores numeric information in 16-bit units can only directly represent code points 0 to 65,535 in each unit, but larger code points (say, 65,536 to 1.4 million) could be represented by using multiple 16-bit units. This correspondence
4536-522: The same semantic character. Unicode and its parallel standard, the ISO/IEC 10646 Universal Character Set , together constitute a unified standard for character encoding. Rather than mapping characters directly to bytes , Unicode separately defines a coded character set that maps characters to unique natural numbers ( code points ), how those code points are mapped to a series of fixed-size natural numbers (code units), and finally how those units are encoded as
4608-556: The same symbol in his 1631 algebra text, Clavis Mathematicae , stating: Multiplication of species [i.e. unknowns] connects both proposed magnitudes with the symbol 'in' or × : or ordinarily without the symbol if the magnitudes be denoted with one letter. An earlier use of the symbol from the 1500s appears in The Ground of Arts , where it is used in the context of a mental arithmetic method for computing simple, single-digit multiplications. Rob Eastaway theorizes that this may have been
4680-433: The solution was to implement variable-length encodings where an escape sequence would signal that subsequent bits should be parsed as a higher code point. Informally, the terms "character encoding", "character map", "character set" and "code page" are often used interchangeably. Historically, the same standard would specify a repertoire of characters and how they were to be encoded into a stream of code units — usually with
4752-404: The term "multiplicand" is regarded as a synonym for "factor". In algebra, a number that is the multiplier of a variable or expression (e.g., the 3 in 3 x y 2 {\displaystyle 3xy^{2}} ) is called a coefficient . The result of a multiplication is called a product . When one factor is an integer, the product is a multiple of the other or of the product of
4824-454: The two sides of a rectangle gives its area (in square meters or square feet). Such a product is the subject of dimensional analysis . The inverse operation of multiplication is division . For example, since 4 multiplied by 3 equals 12, 12 divided by 3 equals 4. Indeed, multiplication by 3, followed by division by 3, yields the original number. The division of a number other than 0 by itself equals 1. Several mathematical concepts expand upon
4896-504: Was adopted fairly widely. ASCII67's American-centric nature was somewhat addressed in the European ECMA-6 standard. Herman Hollerith invented punch card data encoding in the late 19th century to analyze census data. Initially, each hole position represented a different data element, but later, numeric information was encoded by numbering the lower rows 0 to 9, with a punch in a column representing its row number. Later alphabetic data
4968-667: Was encoded by allowing more than one punch per column. Electromechanical tabulating machines represented date internally by the timing of pulses relative to the motion of the cards through the machine. When IBM went to electronic processing, starting with the IBM 603 Electronic Multiplier, it used a variety of binary encoding schemes that were tied to the punch card code. IBM used several Binary Coded Decimal ( BCD ) six-bit character encoding schemes, starting as early as 1953 in its 702 and 704 computers, and in its later 7000 Series and 1400 series , as well as in associated peripherals. Since
5040-409: Was often improved by many equipment manufacturers, sometimes creating compatibility issues. In 1959 the U.S. military defined its Fieldata code, a six-or seven-bit code, introduced by the U.S. Army Signal Corps. While Fieldata addressed many of the then-modern issues (e.g. letter and digit codes arranged for machine collation), it fell short of its goals and was short-lived. In 1963 the first ASCII code
5112-582: Was released (X3.4-1963) by the ASCII committee (which contained at least one member of the Fieldata committee, W. F. Leubbert), which addressed most of the shortcomings of Fieldata, using a simpler code. Many of the changes were subtle, such as collatable character sets within certain numeric ranges. ASCII63 was a success, widely adopted by industry, and with the follow-up issue of the 1967 ASCII code (which added lower-case letters and fixed some "control code" issues) ASCII67
5184-576: Was via machinery, it was often used as a manual code, generated by hand on a telegraph key and decipherable by ear, and persists in amateur radio and aeronautical use. Most codes are of fixed per-character length or variable-length sequences of fixed-length codes (e.g. Unicode ). Common examples of character encoding systems include Morse code, the Baudot code , the American Standard Code for Information Interchange (ASCII) and Unicode. Unicode,
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