## Numeral system |

This article includes a its sources remain unclear because it has insufficient . (January 2011) ( |

Numeral systems |
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East Asian |

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A **numeral system** (or **system of numeration**) is a

The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number *eleven* in the *three* in the

The number the numeral represents is called its value.

Ideally, a numeral system will:

- Represent a useful set of numbers (e.g. all
integers , orrational numbers ) - Give every number represented a unique representation (or at least a standard representation)
- Reflect the algebraic and arithmetic structure of the numbers.

For example, the usual

Numeral systems are sometimes called * number systems*, but that name is ambiguous, as it could refer to different systems of numbers, such as the system of

- main numeral systems
- positional systems in detail
- generalized variable-length integers
- see also
- references
- sources
- external links

The most commonly used system of numerals is the ^{[1]} Two

The simplest numeral system is the `/` is chosen, for example, then the number seven would be represented by `///////`.

The unary notation can be abbreviated by introducing different symbols for certain new values. Very commonly, these values are powers of 10; so for instance, if / stands for one, − for ten and + for 100, then the number 304 can be compactly represented as `+++ ////` and the number 123 as `+ − − ///` without any need for zero. This is called

More useful still are systems which employ special abbreviations for repetitions of symbols; for example, using the first nine letters of the alphabet for these abbreviations, with A standing for "one occurrence", B "two occurrences", and so on, one could then write C+ D/ for the number 304. This system is used when writing *soixante dix-neuf* (60 + 10 + 9) and in Welsh is *pedwar ar bymtheg a thrigain* (4 + (5 + 10) + (3 × 20)) or (somewhat archaic) *pedwar ugain namyn un* (4 × 20 − 1). In English, one could say "four score less one", as in the famous

More elegant is a * positional system*, also known as place-value notation. Again working in base 10, ten different digits 0, ..., 9 are used and the position of a digit is used to signify the power of ten that the digit is to be multiplied with, as in 304 = 3×100 + 0×10 + 4×1 or more precisely 3×10

Arithmetic is much easier in positional systems than in the earlier additive ones; furthermore, additive systems need a large number of different symbols for the different powers of 10; a positional system needs only ten different symbols (assuming that it uses base 10).

The positional decimal system is presently universally used in human writing. The base 1000 is also used (albeit not universally), by grouping the digits and considering a sequence of three decimal digits as a single digit. This is the meaning of the common notation 1,000,234,567 used for very large numbers.

In ^{32} or 2^{64} (grouping binary digits by 32 or 64, the length of the

In certain biological systems the ^{[2]} The nucleus in the brain of the songbirds that plays a part in both the learning and the production of bird song is the HVC (

The numerals used when writing numbers with digits or symbols can be divided into two types that might be called the *both* arithmetic and geometric numerals.

In certain areas of computer science, a modified base *k* positional system is used, called *k* (*k* ≥ 1), and zero being represented by an empty string. This establishes a *k* numeration is also called *k*-adic notation, not to be confused with *p*-adic numbers

Other Languages

Alemannisch: Zahlensystem

العربية: نظام عد

azərbaycanca: Say sistemləri

বাংলা: সংখ্যা পদ্ধতি

Bân-lâm-gú: Sò͘-jī

беларуская: Сістэма злічэння

беларуская (тарашкевіца): Сыстэма зьлічэньня

български: Бройна система

bosanski: Brojevni sistem

català: Sistema de numeració

Чӑвашла: Шутлав йĕрки

čeština: Číselná soustava

chiShona: Tsika yekurava nhamba

dansk: Talsystem

Deutsch: Zahlensystem

eesti: Arvusüsteem

español: Sistema de numeración

Esperanto: Nombrosistemo

euskara: Zenbaki-sistema

فارسی: دستگاه شمارش

français: Système de numération

galego: Sistema de numeración

한국어: 기수법

հայերեն: Հաշվարկման համակարգ (մաթեմատիկա)

हिन्दी: संख्या पद्धतियाँ

hrvatski: Brojevni sustav

Bahasa Indonesia: Sistem bilangan

íslenska: Talnakerfi

italiano: Sistema di numerazione

עברית: שיטת ספירה

Basa Jawa: Sistem wilangan

ქართული: თვლის სისტემა

қазақша: Санау жүйесі

Kreyòl ayisyen: Sistèm nimewotasyon

Latina: Systema numerale

latviešu: Skaitīšanas sistēma

magyar: Számrendszer

македонски: Броен систем

മലയാളം: സംഖ്യാസമ്പ്രദായങ്ങൾ

Bahasa Melayu: Sistem angka

Mirandés: Sistema de numeraçon

Nederlands: Talstelsel

日本語: 命数法

norsk: Tallsystem

occitan: Sistèma de numeracion

олык марий: Чотрадам системе

oʻzbekcha/ўзбекча: Sanoq tizimi

polski: System liczbowy

português: Sistema de numeração

română: Sistem de numerație

русский: Система счисления

Scots: Numeral seestem

Sesotho sa Leboa: Lebadi

සිංහල: සංඛ්යාත පද්ධති

Simple English: Numeral system

slovenčina: Číselná sústava

slovenščina: Številski sistem

српски / srpski: Бројевни систем

srpskohrvatski / српскохрватски: Brojevni sistem

suomi: Lukujärjestelmä

svenska: Talsystem

Tagalog: Numerasyon

தமிழ்: எண்குறி முறைமை

తెలుగు: తెలుగు

ไทย: ระบบเลข

Türkçe: Sayısal sistem

українська: Система числення

اردو: عددی نظام

Tiếng Việt: Hệ đếm

文言: 表數法

Winaray: Sistema pag-ihap

ייִדיש: נומערן סיסטעם

粵語: 記數法

中文: 记数系统