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Radix
In a positional numeral system, the radix (radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal system (the most common system in use today) the radix 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. For base ten, the subscript is usually assumed and omitted (together with the enclosing 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 Generally, in a system with radix ''b'' (), a string of digits denotes the number , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positional Numeral System
Positional notation, also known as place-value notation, positional numeral system, or simply place value, 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 values may be modified when combined). 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octal
Octal (base 8) is a numeral system with eight as the base. 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 can be added at the left: , corresponding to the octal digits , yielding the octal representation 112. Usage In China The eight bagua or trigrams of the I Ching correspond to octal digits: * 0 = ☷, 1 = ☳, 2 = ☵, 3 = ☱, * 4 = ☶, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary System (numeral)
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" ( zero) and "1" ( one). A ''binary number'' may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two. 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 Harrio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexadecimal
Hexadecimal (also known as base-16 or simply hex) is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen. Software developers and system designers widely use hexadecimal numbers because they provide a convenient representation of binary code, binary-coded values. Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble). For example, an 8-bit byte is two hexadecimal digits and its value can be written as to 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, several notations denote hexadecimal numbers, usually involving a prefi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base36
Base36 is a binary-to-text encoding scheme that represents binary data in an ASCII string format by translating it into a radix-36 representation. The choice of 36 is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters a-z (the lowercase ISO basic Latin alphabet). Each base36 digit needs less than 6 bits of information to be represented. Conversion Signed 32- and 64- bit integers will only hold at most 6 or 13 base-36 digits, respectively (that many base-36 digits can overflow the 32- and 64-bit integers). For example, the 64-bit signed integer maximum value of " 9223372036854775807" is "" in base-36. Similarly, the 32-bit signed integer maximum value of " 2147483647" is "" in base-36. Standard implementations The C standard library since C89 supports base36 numbers via the strtol and strtoul functions In the Common Lisp standard (ANSI INCITS 226-1994), functions like parse-integer support a radix of 2 to 36. Ja ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Digit
A numerical digit (often shortened to just digit) or numeral is a single symbol used alone (such as "1"), or in combinations (such as "15"), to represent numbers in positional notation, such as the common base 10. The name "digit" originates from the Latin ''digiti'' meaning fingers. For any numeral system with an integer base, the number of different digits required is the absolute value of the base. For example, decimal (base 10) requires ten digits (0 to 9), and binary (base 2) requires only two digits (0 and 1). Bases greater than 10 require more than 10 digits, for instance hexadecimal (base 16) requires 16 digits (usually 0 to 9 and A to F). 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 its place value, and summing the results. Di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duodecimal
The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "100" means twelve squared (144), "1,000" means twelve cubed (1,728), and "0.1" means a twelfth (0.08333...). Various symbols have been used to stand for ten and eleven in duodecimal notation; this page uses and , as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , , and finally 10. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published material: (a turned 2) for ten (dek, pronounced dɛk) and (a turned 3) for eleven (el, pronounced ɛl). The number twelve, a superior highly composite number, is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sumer
Sumer () is the earliest known civilization, located in the historical region of southern Mesopotamia (now south-central Iraq), emerging during the Chalcolithic and Early Bronze Age, early Bronze Ages between the sixth and fifth millennium BC. Like nearby Elam, it is one of the Cradle of civilization, cradles of civilization, along with ancient Egypt, Egypt, the Indus Valley Civilisation, Indus Valley, the Erligang culture of the Yellow River valley, Caral-Supe civilization, Caral-Supe, and Mesoamerica. Living along the valleys of the Tigris and Euphrates rivers, Sumerian farmers grew an abundance of grain and other crops, a surplus of which enabled them to form urban settlements. The world's earliest known texts come from the Sumerian cities of Uruk and Jemdet Nasr, and date to between , following a period of proto-writing . Name The term "Sumer" () comes from the Akkadian Empire, Akkadian name for the "Sumerians", the ancient non-Semitic languages, Semitic-speaking inhabitan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sexagesimal
Sexagesimal, also known as base 60, is a numeral system with 60 (number), sixty as its radix, base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinate system, geographic coordinates. The number 60, a superior highly composite number, has twelve divisors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6. ''In this article, all sexagesimal digits are represented as decimal numbers, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vigesimal
A vigesimal ( ) or base-20 (base-score) numeral system is based on 20 (number), twenty (in the same way in which the decimal, decimal numeral system is based on 10 (number), ten). ''wikt:vigesimal#English, Vigesimal'' is derived from the Latin adjective , meaning 'twentieth'. Places In a vigesimal Numerical digit, place system, twenty individual numerals (or digit symbols) are used, ten more than in the decimal system. One modern method of finding the extra needed symbols is to write 10 (number), ten as the letter A, or , where the 20 means radix, base , to write 19 (number), nineteen as , and the numbers between with the corresponding letters of the alphabet. This is similar to the common Computer science, computer-science practice of writing hexadecimal numerals over 9 with the letters "A–F". Another less common method skips over the letter "I", in order to avoid confusion between I20 as 18 (number), eighteen and 1 (number), one, so that the number eighteen is written as J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minute Of Arc
A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of a degree. Since one degree is of a turn, or complete rotation, one arcminute 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's circumference is very near . A minute of arc is of a radian. A second of arc, arcsecond (abbreviated as arcsec), or arc second, denoted by the symbol , is a unit of angular measurement equal to of a minute of arc, of a degree, of a turn, and (about ) of a radian. These units originated in Babylonian astronomy as sexagesimal (base 60) 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 milliar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
