Octal
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Octal
The octal numeral system, or oct for short, is the radix, base-8 number system, and uses the Numerical digit, 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, 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 numeral system, 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 repr ...
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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 specif ...
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Numerical Digit
A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits (Latin ''digiti'' meaning fingers) of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal (ancient Latin adjective ''decem'' meaning ten) digits. For a given numeral system with an integer base, the number of different digits required is given by the absolute value of the base. For example, the decimal system (base 10) requires ten digits (0 through to 9), whereas the binary system (base 2) requires two digits (0 and 1). Overview In a basic digital system, a numeral is a sequence of digits, which may be of arbitrary length. Each position in the sequence has a place value, and each digit has a value. The value of the numeral is computed by multiplying each digit in the sequence by i ...
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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, and ...
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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 __FORCETOC__ A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ... (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 uniqu ...
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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 ...
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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 ...
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Pame Language
The Pame languages are a group of languages in Mexico that is spoken by around 12,000 Pame people in the state of San Luis Potosí. It belongs to the Oto-Pamean branch of the Oto-Manguean language family. Distribution and languages Ethnologue notes two living varieties of Pame both spoken in the state of San Luis Potosí: Central Pame, in the town of Santa María Acapulco, and Northern Pame, in communities from the north of Río Verde to the border with Tamaulipas. The third variety, Southern Pame, was last described in the mid 20th century, is assumed to be extinct, and is very sparsely documented. It was spoken in Jiliapan, Hidalgo, and Pacula, Querétaro. *Northern Pame (Ñãʔũ) (~6,000) *Central Pame (Šiʔúi) (~6,000) *Southern Pame (Šiyúi) (†) Classification The Pame languages are part of the Oto-Pamean branch of the Oto-Manguean language family. They are most closely related to the Chichimeca Jonaz language, spoken in Guanajuato, and together, they form t ...
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ICT 1900 Series
ICT 1900 was a family of mainframe computers released by International Computers and Tabulators (ICT) and later International Computers Limited (ICL) during the 1960s and 1970s. The 1900 series was notable for being one of the few non-American competitors to the IBM System/360, enjoying significant success in the European and British Commonwealth markets. Origins In early 1963, ICT was engaged in negotiations to buy the computer business of Ferranti. In order to sweeten the deal, Ferranti demonstrated to ICT the Ferranti-Packard 6000 (FP6000) machine, which had been developed by its Canadian subsidiary Ferranti-Packard, to a design known as Harriac that had been initiated in Ferranti by Harry Johnson and fleshed out by Stanley Gill and John Iliffe. The FP6000 was an advanced design, notably including hardware support for multiprogramming. ICT considered using the FP6000 as their medium-sized processor in the 1965–1968 timeframe, replacing the ICT 1302. Another pla ...
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PDP-8
The PDP-8 is a 12-bit minicomputer that was produced by Digital Equipment Corporation (DEC). It was the first commercially successful minicomputer, with over 50,000 units being sold over the model's lifetime. Its basic design follows the pioneering LINC but has a smaller instruction set, which is an expanded version of the PDP-5 instruction set. Similar machines from DEC are the PDP-12 which is a modernized version of the PDP-8 and LINC concepts, and the PDP-14 industrial controller system. Overview The earliest PDP-8 model, informally known as a "Straight-8", was introduced on 22 March 1965 priced at $18,500 (). It used diode–transistor logic packaged on flip chip cards in a machine about the size of a small household refrigerator. It was the first computer to be sold for under $20,000, making it the best-selling computer in history at that time. The Straight-8 was supplanted in 1966 by the PDP-8/S, which was available in desktop and rack-mount models. Using a one-bit ...
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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 ...
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Yuki Language
Yuki, also known as Ukomno'm, is an extinct language of California, formerly spoken by the Yuki people. The Yuki are the original inhabitants of the Eel River area and the Round Valley Reservation of northern California. Yuki ceased to be used as an everyday language in the early 20th century and its last speaker, Arthur Anderson, died in 1983. Yuki is generally thought to be distantly related to the Wappo language. Classification Yuki consisted of three dialects, from east to west: Round Valley Yuki, Huchnom (Clear Lake Yuki) and Coast Yuki. These were at least partially mutually intelligible, but are sometimes counted as distinct languages. These languages are categorized as (Northern) Yukian within the Yuki–Wappo family, which also includes the distant Wappo language. It is thought that the ancestor of the Yukian languages diverged from Wappo around 1500 . The three Yukian languages diverged from each other over the last one thousand years, while dialectal variations in ...
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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 ...
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