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Octal
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. This is to say that 10octal represents eight and 100octal represents sixty-four. However, English, like most languages, uses a base-10 number system, hence a true octal system might use different vocabulary. In the decimal system, each place is a power of ten. For example: : \mathbf_ = \mathbf \times 10^1 + \mathbf \times 10^0 In the octal system, each place is a power of eight. For example: : \mathbf_8 = \mathbf \times 8^2 + \mathbf \times 8^1 + \mathbf \times 8^0 By performing the calculation above in the familiar decimal system, we see why 112 in octal is equal to 64+8+2=74 in decimal. Octal numerals can be easily converted from binary representations (similar to a quaternary numeral system) by grouping consecutive binary digits into groups of three (starting from the right, for integers). For example, the binary representation for decimal 74 is 1001010. Two zeroes ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quaternary Numeral System
A quaternary numeral system is base-. It uses the digits 0, 1, 2 and 3 to represent any real number. Conversion from binary is straightforward. Four is the largest number within the subitizing range and one of two numbers that is both a square and a highly composite number (the other being 36), making quaternary a convenient choice for a base at this scale. Despite being twice as large, its radix economy is equal to that of binary. However, it fares no better in the localization of prime numbers (the smallest better base being the primorial base six, senary). Quaternary shares with all fixed- radix numeral systems many properties, such as the ability to represent any real number with a canonical representation (almost unique) and the characteristics of the representations of rational numbers and irrational numbers. See decimal and binary for a discussion of these properties. Relation to other positional number systems Relation to binary and hexadecimal As wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Numeral System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" ( zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was spec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems In the system with radix 13, for example, a string of digits such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bagua
The bagua or pakua (八卦) are a set of eight symbols that originated in China, used in Taoist cosmology to represent the fundamental principles of reality, seen as a range of eight interrelated concepts. Each consists of three lines, each line either "broken" or "unbroken", respectively representing yin or yang. Due to their tripartite structure, they are often referred to as Eight Trigrams in English. The trigrams are related to Taiji philosophy, Taijiquan and the Wuxing, or "five elements". The relationships between the trigrams are represented in two arrangements: the ''Primordial'' (), "Earlier Heaven", or "Fu Xi" bagua () and the ''Manifested'' (), "Later Heaven", or "King Wen" bagua. The trigrams have correspondences in astronomy, astrology, geography, geomancy, anatomy, the family, martial arts, Chinese medicine and elsewhere. The ancient Chinese classic, I Ching (Pinyin: Yi Jing), consists of the 64 pairwise permutations of trigrams, referred to as "hexagrams", ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugh Jones (reverend)
The Reverend Hugh Jones (1691–1760) is the most famous and accomplished of a sometimes confusing array of Anglican clergymen of the same name from the American colonies of Virginia and Maryland. Jones is best known for his authorship of The Present State of Virginia, and a short view of Maryland and North Carolina' (London, 1724). For several years he taught mathematics at The College of William and Mary, in Williamsburg, Virginia, wherJones Hallis named for him. Birth and education He appears to have been born in Herefordshire, England, just east of Wales, in the parish of Little Dewchurch. Alumni records at Oxford University list his matriculation to Jesus College in March 1708, age 17, placing his birth around 1691. He received the B.A. in 1712, according to these records, and the M.A. in 1716. In a deposition given at age 49 (1740), he said "That he learnt Arithmetick at School, studied Geometry, Geography and Astronomy in the University of Oxford;" that he there took th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base 10
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A ''decimal numeral'' (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , where is an integer, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles XII Of Sweden
Charles XII, sometimes Carl XII ( sv, Karl XII) or Carolus Rex (17 June 1682 – 30 November 1718 O.S.), was King of Sweden (including current Finland) from 1697 to 1718. He belonged to the House of Palatinate-Zweibrücken, a branch line of the House of Wittelsbach. Charles was the only surviving son of Charles XI and Ulrika Eleonora the Elder. He assumed power, after a seven-month caretaker government, at the age of fifteen. In 1700, a triple alliance of Denmark–Norway, Saxony– Poland–Lithuania and Russia launched a threefold attack on the Swedish protectorate of Holstein-Gottorp and provinces of Livonia and Ingria, aiming to draw advantage as the Swedish Empire was unaligned and ruled by a young and inexperienced king, thus initiating the Great Northern War. Leading the Swedish army against the alliance, Charles won multiple victories despite being usually significantly outnumbered. A major victory over a Russian army some three times the size in 1700, at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms". He is the author of the multi-volume work ''The Art of Computer Programming'' and contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar, Knuth created the WEB and CWEB computer programming systems designed to encou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Art Of Computer Programming
''The Art of Computer Programming'' (''TAOCP'') is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. Volumes 1–5 are intended to represent the central core of computer programming for sequential machines. When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. Work began in earnest on Volume 4 in 1973, but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2. Writing of the final copy of Volume 4A began in longhand in 2001, and the first online pre-fascicle, 2A, appeared later in 2001. The first published installment of Volume 4 appeared in paperback as Fascicle 2 in 2005. The hardback Volume 4A, combining Volume 4, Fascicles 0–4, was published in 2011. Volume 4, Fascicle 6 ("Satisfiability") was r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Gentleman's Magazine
''The Gentleman's Magazine'' was a monthly magazine founded in London, England, by Edward Cave in January 1731. It ran uninterrupted for almost 200 years, until 1922. It was the first to use the term '' magazine'' (from the French ''magazine'', meaning "storehouse") for a periodical. Samuel Johnson's first regular employment as a writer was with ''The Gentleman's Magazine''. History The original complete title was ''The Gentleman's Magazine: or, Trader's monthly intelligencer''. Cave's innovation was to create a monthly digest of news and commentary on any topic the educated public might be interested in, from commodity prices to Latin poetry. It carried original content from a stable of regular contributors, as well as extensive quotations and extracts from other periodicals and books. Cave, who edited ''The Gentleman's Magazine'' under the pen name "Sylvanus Urban", was the first to use the term '' magazine'' (meaning "storehouse") for a periodical. Contributions to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numeral System
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number ''eleven'' in the decimal numeral system (used in common life), the number ''three'' in the binary numeral system (used in computers), and the number ''two'' in the unary numeral system (e.g. used in tallying scores). The number the numeral represents is called its value. Not all number systems can represent all numbers that are considered in the modern days; for example, Roman numerals have no zero. Ideally, a numeral system will: *Represent a useful set of numbers (e.g. all integers, or rational numbers) *Give every number represented a unique representation (or at least a standard representation) *Reflect the algebraic and arithme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Anderson Of Hermiston
James Anderson FRSE FSAScot (1739 – 15 October 1808) was a Scottish agriculturist, journalist and economist. A member of the Edinburgh Philosophical Society, Anderson was a prominent figure in the Scottish Enlightenment. He invented the Scotch plough. Life Anderson was born at Hermiston, Midlothian and while still young attended lectures on chemistry by William Cullen, at the University of Edinburgh. At the age of 15, after the death of his parents, he took over the working of the family farm. In 1768 he moved to Aberdeenshire to manage the farm of Monkshill on land owned by Mr. Udny of Udny under a long lease granted to him for the purpose of demonstrating the benefits of improved agriculture. Economic theorist In 1777 Anderson published ''An Enquiry into the Nature of the Corn Laws'', in which he anticipated David Ricardo's theory of rent. Some historians believe Anderson was the root source for Marx's critique of capitalist agriculture. Rent, Anderson argued, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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