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Binary number

Index Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one). [1]

129 relations: A Symbolic Analysis of Relay and Switching Circuits, Absolute value, Adder (electronics), Algebra, American Mathematical Society, Ancient Egyptian multiplication, Arabic numerals, Arithmetic, Arithmetic shift, Bacon's cipher, Bagua, Bell Labs, Bi-quinary coded decimal, Binary code, Binary-coded decimal, Bit, Bit numbering, Bitwise operation, Boolean algebra, Booth's multiplication algorithm, Chaitin's constant, Claude Shannon, Complex number, Computer, Concatenation, Cut-the-Knot, Dartmouth College, Decimal, Decimal separator, Digital electronics, Disk storage, Division (mathematics), Division by two, Divisor, Dyadic rational, Egyptian fraction, Endianness, Ex nihilo, Exclusive or, Eye of Horus, Fifth Dynasty of Egypt, Finger binary, Floating-point arithmetic, Francis Bacon, French Polynesia, Fuxi, Geomancy, Geometric series, George Boole, George Stibitz, ..., Gottfried Wilhelm Leibniz, Gray code, Hekat (unit), Hexadecimal, Hexagram (I Ching), Horner's method, Horus, I Ching, I Ching divination, Ifá, Irrational number, Joachim Bouvet, John Mauchly, John Napier, John von Neumann, Juan Caramuel y Lobkowitz, Konrad Zuse, Light-emitting diode, Linear-feedback shift register, Location arithmetic, Logic, Logic gate, Logical conjunction, Logical connective, Logical disjunction, Long division, Magnet, Magnetic field, Mangareva, Massachusetts Institute of Technology, Mathematics, Metre (poetry), Middle Ages, Modulo operation, Morse code, Multiplication, Negation, Negative number, Nineteenth Dynasty of Egypt, Norbert Wiener, Number, Octal, Offset binary, Pingala, Positional notation, Power of two, Prime number, Quaternary numeral system, Quotient, Radix, Radix point, Ramon Llull, Rational number, Reduction of summands, Redundant binary representation, Repeating decimal, Rhind Mathematical Papyrus, Rudolph Augustus, Duke of Braunschweig-Wolfenbüttel, Sexagesimal, Shao Yong, Signed number representations, Sinophile, Slit drum, Song dynasty, Square root of 2, Subtraction, SZTAKI Desktop Grid, Teletype Corporation, Thomas Harriot, Two's complement, Universality (philosophy), Voltage, Yes and no, Yin and yang, Z1 (computer), Zhou dynasty, 0, 1, 2. Expand index (79 more) »

A Symbolic Analysis of Relay and Switching Circuits

A Symbolic Analysis of Relay and Switching Circuits is the title of a master's thesis written by computer science pioneer Claude E. Shannon while attending the Massachusetts Institute of Technology (MIT) in 1937.

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Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

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Adder (electronics)

An adder is a digital circuit that performs addition of numbers.

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Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Ancient Egyptian multiplication

In mathematics, ancient Egyptian multiplication (also known as Egyptian multiplication, Ethiopian multiplication, Russian multiplication, or peasant multiplication), one of two multiplication methods used by scribes, was a systematic method for multiplying two numbers that does not require the multiplication table, only the ability to multiply and divide by 2, and to add.

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Arabic numerals

Arabic numerals, also called Hindu–Arabic numerals, are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, based on the Hindu–Arabic numeral system, the most common system for the symbolic representation of numbers in the world today.

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Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

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Arithmetic shift

In computer programming, an arithmetic shift is a shift operator, sometimes termed a signed shift (though it is not restricted to signed operands).

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Bacon's cipher

Bacon's cipher or the Baconian cipher is a method of steganography (a method of hiding a secret message as opposed to just a cipher) devised by Francis Bacon in 1605.

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The Bagua or Pa Kua are eight symbols used in Taoist cosmology to represent the fundamental principles of reality, seen as a range of eight interrelated concepts.

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Bell Labs

Nokia Bell Labs (formerly named AT&T Bell Laboratories, Bell Telephone Laboratories and Bell Labs) is an American research and scientific development company, owned by Finnish company Nokia.

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Bi-quinary coded decimal

Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, including the Colossus.

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Binary code

A binary code represents text, computer processor instructions, or any other data using a two-symbol system.

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Binary-coded decimal

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight.

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The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

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Bit numbering

In computing, bit numbering (or sometimes bit endianness) is the convention used to identify the bit positions in a binary number or a container for such a value.

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Bitwise operation

In digital computer programming, a bitwise operation operates on one or more bit patterns or binary numerals at the level of their individual bits.

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Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

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Booth's multiplication algorithm

Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation.

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Chaitin's constant

In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt.

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Claude Shannon

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory".

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

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In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end.

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Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.

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Dartmouth College

Dartmouth College is a private Ivy League research university in Hanover, New Hampshire, United States.

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The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

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Decimal separator

A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form.

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Digital electronics

Digital electronics or digital (electronic) circuits are electronics that operate on digital signals.

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Disk storage

Disk storage (also sometimes called drive storage) is a general category of storage mechanisms where data is recorded by various electronic, magnetic, optical, or mechanical changes to a surface layer of one or more rotating disks.

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Division (mathematics)

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

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Division by two

In mathematics, division by two or halving has also been called mediation or dimidiation.

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In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

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Dyadic rational

In mathematics, a dyadic fraction or dyadic rational is a rational number whose denominator, when the ratio is in minimal (coprime) terms, is a power of two, i.e., a number of the form \frac where a is an integer and b is a natural number; for example, 1/2 or 3/8, but not 1/3.

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Egyptian fraction

An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other.

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Endianness refers to the sequential order in which bytes are arranged into larger numerical values when stored in memory or when transmitted over digital links.

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Ex nihilo

Ex nihilo is a Latin phrase meaning "out of nothing".

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Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

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Eye of Horus

The Eye of Horus is an ancient Egyptian symbol of protection, royal power, and good health.

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Fifth Dynasty of Egypt

The Fifth Dynasty of ancient Egypt (notated Dynasty V) is often combined with Dynasties III, IV and VI under the group title the Old Kingdom.

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Finger binary

Finger binary is a system for counting and displaying binary numbers on the fingers of one or more hands.

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Floating-point arithmetic

In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision.

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Francis Bacon

Francis Bacon, 1st Viscount St Alban, (22 January 15619 April 1626) was an English philosopher, statesman, scientist, jurist, orator, and author.

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French Polynesia

French Polynesia (Polynésie française; Pōrīnetia Farāni) is an overseas collectivity of the French Republic; collectivité d'outre-mer de la République française (COM), sometimes unofficially referred to as an overseas country; pays d'outre-mer (POM).

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Fuxi (Chinese: 伏羲), also romanized as Fu-hsi, is a culture hero in Chinese legend and mythology, credited (along with his sister Nüwa 女娲) with creating humanity and the invention of hunting, fishing and cooking as well as the Cangjie system of writing Chinese characters c. 2,000 BCE.

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Geomancy (Greek: γεωμαντεία, "earth divination") is a method of divination that interprets markings on the ground or the patterns formed by tossed handfuls of soil, rocks, or sand.

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Geometric series

In mathematics, a geometric series is a series with a constant ratio between successive terms.

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George Boole

George Boole (2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland.

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George Stibitz

George Robert Stibitz (April 30, 1904 – January 31, 1995) was a Bell Labs researcher internationally recognized as one of the fathers of the modern first digital computer.

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Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

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Gray code

The reflected binary code (RBC), also known just as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit).

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Hekat (unit)

The hekat or heqat (transcribed HqA.t) was an ancient Egyptian volume unit used to measure grain, bread, and beer.

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In mathematics and computing, hexadecimal (also base, or hex) is a positional numeral system with a radix, or base, of 16.

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Hexagram (I Ching)

The I Ching book consists of 64 hexagrams.

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Horner's method

In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S..) is either of two things.

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Horus is one of the most significant ancient Egyptian deities.

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I Ching

The I Ching,.

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I Ching divination

Among the many forms of divination is a cleromancy method using the I Ching (易經, yì jīng) or Book of Changes.

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Ifá is a religion and system of divination and refers to the verses of the literary corpus known as the Odu Ifá.

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Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

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Joachim Bouvet

Joachim Bouvet (courtesy name: 明远) (b. Le Mans, July 18, 1656 – June 28, 1730, Peking) was a French Jesuit who worked in China, and the leading member of the Figurist movement.

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John Mauchly

John William Mauchly (August 30, 1907 – January 8, 1980) was an American physicist who, along with J. Presper Eckert, designed ENIAC, the first general purpose electronic digital computer, as well as EDVAC, BINAC and UNIVAC I, the first commercial computer made in the United States.

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John Napier

John Napier of Merchiston (1550 – 4 April 1617); also signed as Neper, Nepair; nicknamed Marvellous Merchiston) was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioannes Neper. John Napier is best known as the discoverer of logarithms. He also invented the so-called "Napier's bones" and made common the use of the decimal point in arithmetic and mathematics. Napier's birthplace, Merchiston Tower in Edinburgh, is now part of the facilities of Edinburgh Napier University. Napier died from the effects of gout at home at Merchiston Castle and his remains were buried in the kirkyard of St Giles. Following the loss of the kirkyard there to build Parliament House, he was memorialised at St Cuthbert's at the west side of Edinburgh.

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John von Neumann

John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.

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Juan Caramuel y Lobkowitz

Juan Caramuel y Lobkowitz (Juan Caramuel de Lobkowitz, May 23, 1606 in Madrid — September 7 or 8, 1682 in Vigevano) was a Spanish Catholic scholastic philosopher, ecclesiastic, mathematician and writer.

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Konrad Zuse

Konrad Zuse (22 June 1910 – 18 December 1995) was a German civil engineer, inventor and computer pioneer.

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Light-emitting diode

A light-emitting diode (LED) is a two-lead semiconductor light source.

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Linear-feedback shift register

In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state.

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Location arithmetic

Location arithmetic (Latin arithmeticæ localis) is the additive (non-positional) binary numeral systems, which John Napier explored as a computation technique in his treatise Rabdology (1617), both symbolically and on a chessboard-like grid.

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Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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Logic gate

In electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and produces a single binary output.

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Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

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Logical connective

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective.

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Logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.

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Long division

In arithmetic, long division is a standard division algorithm suitable for dividing multidigit numbers that is simple enough to perform by hand.

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A magnet is a material or object that produces a magnetic field.

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Magnetic field

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials.

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Mangareva is the central and largest island of the Gambier Islands in French Polynesia.

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Massachusetts Institute of Technology

The Massachusetts Institute of Technology (MIT) is a private research university located in Cambridge, Massachusetts, United States.

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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Metre (poetry)

In poetry, metre is the basic rhythmic structure of a verse or lines in verse.

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Middle Ages

In the history of Europe, the Middle Ages (or Medieval Period) lasted from the 5th to the 15th century.

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Modulo operation

In computing, the modulo operation finds the remainder after division of one number by another (sometimes called modulus).

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Morse code

Morse code is a method of transmitting text information as a series of on-off tones, lights, or clicks that can be directly understood by a skilled listener or observer without special equipment.

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Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

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In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P (¬P), which is interpreted intuitively as being true when P is false, and false when P is true.

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Negative number

In mathematics, a negative number is a real number that is less than zero.

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Nineteenth Dynasty of Egypt

The Nineteenth Dynasty of Egypt (notated Dynasty XIX, alternatively 19th Dynasty or Dynasty 19) is classified as the second Dynasty of the Ancient Egyptian New Kingdom period, lasting from 1292 BC to 1189 BC.

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Norbert Wiener

Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher.

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A number is a mathematical object used to count, measure and also label.

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The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7.

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Offset binary

Offset binary, also referred to as excess-K, excess-N, excess code or biased representation, is a digital coding scheme where all-zero corresponds to the minimal negative value and all-one to the maximal positive value.

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Pingala (Devanagari: पिङ्गल) (c. 3rd/2nd century BC) was an ancient Indian mathematician who authored the (also called Pingala-sutras), the earliest known treatise on Sanskrit prosody.

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Positional notation

Positional notation or place-value notation is a method of representing or encoding numbers.

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Power of two

In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Quaternary numeral system

Quaternary is the base- numeral system.

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In arithmetic, a quotient (from quotiens "how many times", pronounced) is the quantity produced by the division of two numbers.

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In mathematical numeral systems, the radix or base is the number of unique digits, including zero, used to represent numbers in a positional numeral system.

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Radix point

In mathematics and computing, a radix point (or radix character) is the symbol used in numerical representations to separate the integer part of a number (to the left of the radix point) from its fractional part (to the right of the radix point).

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Ramon Llull

Ramon Llull, T.O.S.F. (c. 1232 – c. 1315; Anglicised Raymond Lully, Raymond Lull; in Latin Raimundus or Raymundus Lullus or Lullius) was a philosopher, logician, Franciscan tertiary and Spanish writer.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Reduction of summands

Reduction of summands is an algorithm for fast binary multiplication of non-signed binary integers.

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Redundant binary representation

A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations.

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Repeating decimal

A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely-repeated portion is not zero.

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Rhind Mathematical Papyrus

The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of Egyptian mathematics.

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Rudolph Augustus, Duke of Braunschweig-Wolfenbüttel

Rudolph Augustus (May 16, 1627 – January 26, 1704), a member of the House of Welf, was Duke of Brunswick-Lüneburg and ruled as Prince of Brunswick-Wolfenbüttel from 1666 until his death.

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Sexagesimal (base 60) is a numeral system with sixty as its base.

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Shao Yong

Shao Yong (1011–1077), courtesy name Yaofu (堯夫), named Shào Kāngjié (邵康節) after death, was a Song dynasty Chinese philosopher, cosmologist, poet and historian who greatly influenced the development of Neo-Confucianism in China.

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Signed number representations

In computing, signed number representations are required to encode negative numbers in binary number systems.

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A Sinophile or a Chinophile is a person who demonstrates a strong interest and love for Chinese culture or its people.

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Slit drum

A slit drum is a hollow percussion instrument.

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Song dynasty

The Song dynasty (960–1279) was an era of Chinese history that began in 960 and continued until 1279.

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Square root of 2

The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2.

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Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

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SZTAKI Desktop Grid

SZTAKI Desktop Grid (SzDG) was a BOINC project located in Hungary run by the Computer and Automation Research Institute (SZTAKI) of the Hungarian Academy of Sciences.

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Teletype Corporation

The Teletype Corporation, a part of American Telephone and Telegraph Company's Western Electric manufacturing arm since 1930, came into being in 1928 when the Morkrum-Kleinschmidt Company changed its name to the name of its trademark equipment.

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Thomas Harriot

Thomas Harriot (Oxford, c. 1560 – London, 2 July 1621), also spelled Harriott, Hariot or Heriot, was an English astronomer, mathematician, ethnographer and translator who made advances within the scientific field.

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Two's complement

Two's complement is a mathematical operation on binary numbers, best known for its role in computing as a method of signed number representation.

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Universality (philosophy)

In philosophy, universality is the idea that universal facts exist and can be progressively discovered, as opposed to relativism.

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Voltage, electric potential difference, electric pressure or electric tension (formally denoted or, but more often simply as V or U, for instance in the context of Ohm's or Kirchhoff's circuit laws) is the difference in electric potential between two points.

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Yes and no

Yes and no, or word pairs with a similar usage, are expressions of the affirmative and the negative, respectively, in several languages including English.

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Yin and yang

In Chinese philosophy, yin and yang (and; 陽 yīnyáng, lit. "dark-bright", "negative-positive") describes how seemingly opposite or contrary forces may actually be complementary, interconnected, and interdependent in the natural world, and how they may give rise to each other as they interrelate to one another.

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Z1 (computer)

The Z1 was a mechanical computer designed by Konrad Zuse from 1935 to 1936 and built by him from 1936 to 1938.

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Zhou dynasty

The Zhou dynasty or the Zhou Kingdom was a Chinese dynasty that followed the Shang dynasty and preceded the Qin dynasty.

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0 (zero) is both a number and the numerical digit used to represent that number in numerals.

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1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.

New!!: Binary number and 1 · See more »


2 (two) is a number, numeral, and glyph.

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Redirects here:

011000100110100101101110011000010111001001111001, 0b (prefix), BIN (calculator mode), Base 2, Base two, Base-2, Base-2 number system, Base-2 numeral system, Base2, Binadd, Binario, Binary (numeral system), Binary Arithmetic, Binary Number System, Binary Sistem, Binary addition, Binary arithmetic, Binary calculus, Binary coding, Binary counting system, Binary division, Binary expansion, Binary fraction, Binary math, Binary mathematics, Binary multiplication, Binary notation, Binary number system, Binary numbers, Binary numbers and letters, Binary numeral, Binary numeral system, Binary representation, Binary subtraction, Binary system (numeral), Binary value, Binary-to-decimal conversion, Dyadic number system, Dyadic numeral system, Generalized binary number, Mathematical operations using zeros and ones, Natural binary code, Pure binary code, Quadrosexagesimal, Straight binary code, Zeros and ones.


[1] https://en.wikipedia.org/wiki/Binary_number

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