|
Number Base
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 398 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positional Numeral System
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred (however, the value may be negated if placed before another digit). In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string. The Babylonian numeral system, base 60, was the first positional system to be developed, and its influence is present today ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexadecimal
In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexadecimal uses 16 distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9, and "A"–"F" (or alternatively "a"–"f") to represent values from 10 to 15. Software developers and system designers widely use hexadecimal numbers because they provide a human-friendly representation of binary-coded values. Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble). For example, an 8-bit byte can have values ranging from 00000000 to 11111111 in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value would be expressed in hexadecimal as . In programming, a number o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed Radix
Mixed radix numeral systems are non-standard positional numeral systems in which the numerical base varies from position to position. Such numerical representation applies when a quantity is expressed using a sequence of units that are each a multiple of the next smaller one, but not by the same factor. Such units are common for instance in measuring time; a time of 32 weeks, 5 days, 7 hours, 45 minutes, 15 seconds, and 500 milliseconds might be expressed as a number of minutes in mixed-radix notation as: ... 32, 5, 7, 45; 15, 500 ... ∞, 7, 24, 60; 60, 1000 or as :32∞577244560.15605001000 In the tabular format, the digits are written above their base, and a semicolon indicates the radix point. In numeral format, each digit has its associated base attached as a subscript, and the radix point is marked by a full stop or period. The base for each digit is the number of corresponding units that make up the next larger unit. As a consequence there is no base (written as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base (exponentiation)
In exponentiation, the base is the number b in an expression of the form bn. Related terms The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power" or "b to the power n". For example, the fourth power of 10 is 10,000 because . The term ''power'' strictly refers to the entire expression, but is sometimes used to refer to the exponent. Radix is the traditional term for ''base'', but usually refers then to one of the common bases: decimal (10), binary (2), hexadecimal (16), or sexagesimal (60). When the concepts of variable and constant came to be distinguished, the process of exponentiation was seen to transcend the algebraic functions. In his 1748 ''Introductio in analysin infinitorum'', Leonhard Euler referred to "base a = 10" in an example. He referred to ''a'' as a "constant number" in an extensive consideration of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negative Base
A negative base (or negative radix) may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base is equal to for some natural number (). Negative-base systems can accommodate all the same numbers as standard place-value systems, but both positive and negative numbers are represented without the use of a minus sign (or, in computer representation, a sign bit); this advantage is countered by an increased complexity of arithmetic operations. The need to store the information normally contained by a negative sign often results in a negative-base number being one digit longer than its positive-base equivalent. The common names for negative-base positional numeral systems are formed by prefixing ''nega-'' to the name of the corresponding positive-base system; for example, negadecimal (base −10) corresponds to deci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Number
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, (1 + \sqrt)/2, is an algebraic number, because it is a root of the polynomial . That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number 1 + i is algebraic because it is a root of . All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as and , are called transcendental numbers. The set of algebraic numbers is countably infinite and has measure zero in the Lebesgue measure as a subset of the uncountable complex numbers. In that sense, almost all complex numbers are transcendental. Examples * All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer and a (non-zero) natural number , satisfies the above definition, bec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Ratio Base
Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number ≈ 1.61803399 symbolized by the Greek letter φ) as its base. It is sometimes referred to as base-φ, golden mean base, phi-base, or, colloquially, phinary. Any non-negative real number can be represented as a base-φ numeral using only the digits 0 and 1, and avoiding the digit sequence "11" – this is called a ''standard form''. A base-φ numeral that includes the digit sequence "11" can always be rewritten in standard form, using the algebraic properties of the base φ — most notably that φ (φ1) + 1 (φ0) = φ2. For instance, 11φ = 100φ. Despite using an irrational number base, when using standard form, all non-negative integers have a unique representation as a terminating (finite) base-φ expansion. The set of numbers which possess a finite base-φ representation is the ring Z .html" ;"title="/a>" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal numbers'', and numbers used for ordering are called ''ordinal numbers''. Natural numbers are sometimes used as labels, known as '' nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers). Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural numbers form a set. Many other number sets are built by succ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems. 108 pages. Time in physics is operationally defined as "what a clock reads". The physical nature of time is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minute Of Arc
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth circumference is very near . A minute of arc is of a radian. A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol , is of an arcminute, of a degree, of a turn, and (about ) of a radian. These units originated in Babylonian astronomy as sexagesimal subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying, and marksmanship. To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond (mas) and microarcsecond (μas), for instance, are commonly used in astro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Babylonia
Babylonia (; Akkadian: , ''māt Akkadī'') was an ancient Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Syria). It emerged as an Amorite-ruled state c. 1894 BCE. During the reign of Hammurabi and afterwards, Babylonia was called "the country of Akkad" (''Māt Akkadī'' in Akkadian), a deliberate archaism in reference to the previous glory of the Akkadian Empire. It was often involved in rivalry with the older state of Assyria to the north and Elam to the east in Ancient Iran. Babylonia briefly became the major power in the region after Hammurabi (fl. c. 1792–1752 BCE middle chronology, or c. 1696–1654 BCE, short chronology) created a short-lived empire, succeeding the earlier Akkadian Empire, Third Dynasty of Ur, and Old Assyrian Empire. The Babylonian Empire rapidly fell apart after the death of Hammurabi and reverted to a small kingdom. Like Assyria, the Babylonian state ret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sumer
Sumer () is the earliest known civilization in the historical region of southern Mesopotamia (south-central Iraq), emerging during the Chalcolithic and early Bronze Ages between the sixth and fifth millennium BC. It is one of the cradles of civilization in the world, along with ancient Egypt, Elam, the Caral-Supe civilization, Mesoamerica, the Indus Valley civilisation, and ancient China. Living along the valleys of the Tigris and Euphrates rivers, Sumerian farmers grew an abundance of grain and other crops, the surplus from which enabled them to form urban settlements. Proto-writing dates back before 3000 BC. The earliest texts come from the cities of Uruk and Jemdet Nasr, and date to between c. 3500 and c. 3000 BC. Name The term "Sumer" ( Sumerian: or , Akkadian: ) is the name given to the language spoken by the "Sumerians", the ancient non- Semitic-speaking inhabitants of southern Mesopotamia, by their successors the East Semitic-speaking Akkadians. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
