संख्या पद्धतियों की सूची

मुक्त ज्ञानकोश विकिपीडिया से
यहाँ जाएँ: भ्रमण, खोज

यहाँ संख्या पद्धतियों की सूची दी गयी है।

स्थानीय प्रतीक[संपादित करें]

ये सभी स्थानीय-मान पर आधारित हैं। इनमें से कुछ निम्नलिखित हैं-

मानक (Standard)[संपादित करें]

A binary clock might use LEDs to express binary values. In this clock, each column of LEDs shows a binary-coded decimal numeral of the traditional sexagesimal time.

For the definition of standard positional numeral systems, see Non-standard positional numeral systems.

The common names are derived somewhat arbitrarily from Latin and Greek. For more information, see Hexadecimal#Etymology.

Base Name Usage
2 Binary All modern digital computations.
3 Ternary Cantor set (all points in [0,1] that can be represented in ternary with no 1s.)
4 Quaternary Data transmission and Hilbert curves.
5 Quinary
6 Senary Diceware
7 Septenary
8 Octal Charles XII of Sweden, Unix-like permissions
9 Nonary
10 Decimal Most widely used by modern civilizations.[1][2]
11 Undecimal
12 Duodecimal
13 Tridecimal The Maya calendar.
14 Tetradecimal Programming for the HP 9100A/B calculator[3] and image processing applications[4].
15 Pentadecimal Telephony routing over IP and the Huli language.
16 Hexadecimal Human-friendly representation (hex dump) of binary data and Base16 encoding.
20 Vigesimal Celtic numerals, Maya numerals
24 Tetravigesimal
26 Hexavigesimal
27 Septemvigesimal Telefol and Oksapmin languages.
30 Trigesimal
32 Duotrigesimal Base32 encoding and the Ngiti language.
36 Hexatridecimal Base36 encoding.
60 Sexagesimal The Babylonian numerals positional numeral system.
64 Tetrasexagesimal Base64 encoding.
85 Ascii85 encoding.

Non-standard[संपादित करें]

Bijective numeration[संपादित करें]

Base Name Usage
1 Unary Tally marks.
10 Decimal without a zero

Signed-digit representation[संपादित करें]

Base Name Usage
2 Non-adjacent form
3 Balanced ternary Ternary computers.

Negative bases[संपादित करें]

The common names of the negative base numeral systems are formed using the prefix nega-, giving names such as:

Base Name Usage
−2 Negabinary
−3 Negaternary
−10 Negadecimal

Complex bases[संपादित करें]

Base Name Usage
2i Quater-imaginary base
−1 ± i Twindragon base Twindragon fractal shape.

Non-integer bases[संपादित करें]

Base Name Usage
φ Golden ratio base Early Beta encoder.[5]
e Base e
π Base π
√2 Base √2

अन्य[संपादित करें]

गैर-स्थानीय अंकन (non-positional notation)[संपादित करें]

बेबिलोन अंकों (Babylonian numerals) के पहले विकसित सभी संख्या पद्धतियाँ स्थानीय मान पर आधारित नहीं हैं।

अंक[संपादित करें]

नाम आधार नमूना सर्वप्रथम कब प्रयुक्त हुआ (लगभग)
बेबीलोनी अंक 60 Babylonian 1.svgBabylonian 2.svgBabylonian 3.svgBabylonian 4.svgBabylonian 5.svgBabylonian 6.svgBabylonian 7.svgBabylonian 8.svgBabylonian 9.svgBabylonian 10.svg 3100 B.C.
ग्रीक अंक 10 α β γ δ ε ϝ ζ η θ ι
रोमन अंक 10 I II III IV V VI VII VIII IX X 1000 B.C.
चीनी छड़ अंक]] 10 Counting rod v1.png Counting rod v2.png Counting rod v3.png Counting rod v4.png Counting rod v5.png Counting rod v6.png Counting rod v7.png Counting rod v8.png Counting rod v9.png Counting rod h1.png 1st century
हिन्दू अंक 10 0 1 2 3 4 5 6 7 8 9 10 9वीं शताब्दी

सन्दर्भ[संपादित करें]

  1. The History of Arithmetic, Louis Charles Karpinski, 200pp, Rand McNally & Company, 1925.
  2. Histoire universelle des chiffres, Georges Ifrah, Robert Laffont, 1994 (Also: The Universal History of Numbers: From prehistory to the invention of the computer, Georges Ifrah, ISBN 0-471-39340-1, John Wiley and Sons Inc., New York, 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk)
  3. http://www.hpmuseum.org/prog/hp9100pr.htm
  4. See a patent at Free Patents Online
  5. Ward, Rachel (2008), "On Robustness Properties of Beta Encoders and Golden Ratio Encoders", IEEE Transactions on Information Theory 54 (9): 4324–4334, doi:10.1109/TIT.2008.928235