Nonary
From Wikipedia, the free encyclopedia
|
|
This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2009) |
|
|
This article may not meet the general notability guideline. Please help to establish notability by adding reliable, secondary sources about the topic. If notability cannot be established, the article is likely to be merged, redirected, or deleted. (October 2009) |
| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Eastern Arabic Indian family Khmer |
Mongolian Thai Western Arabic |
| East Asian numerals | |
| Chinese Counting rods Japanese |
Korean Suzhou |
| Alphabetic numerals | |
| Abjad Armenian Āryabhaṭa Cyrillic |
Ge'ez Greek (Ionian) Hebrew |
| Other systems | |
| Attic Babylonian Brahmi Egyptian Etruscan Inuit |
Mayan Quipu Roman Urnfield |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 1, 2, 3, 4, 5, 8, 12, 16, 20, 60, more… | |
Nonary is a base-9 numeral system, typically using the digits 0-8, but not the digit 9.
The first few numbers in nonary and decimal are:
| Nonary | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 10 | 11 | 12 | 13 | 14 |
| Decimal | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
The multiplication table in nonary is:
| * | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 2 | 2 | 4 | 6 | 8 | 11 | 13 | 15 | 17 |
| 3 | 3 | 6 | 10 | 13 | 16 | 20 | 23 | 26 |
| 4 | 4 | 8 | 13 | 17 | 22 | 26 | 31 | 35 |
| 5 | 5 | 11 | 16 | 22 | 27 | 33 | 38 | 44 |
| 6 | 6 | 13 | 20 | 26 | 33 | 40 | 46 | 53 |
| 7 | 7 | 15 | 23 | 31 | 38 | 46 | 54 | 62 |
| 8 | 8 | 17 | 26 | 35 | 44 | 53 | 62 | 71 |
Nonary notation can be used as a concise representation of ternary data. This is similar to using quaternary notation for binary data, though the digit set is closer in size to octal.
Except for three, no primes in nonary end in 0, 3 or 6, since any nonary number ending in 0, 3 or 6 is divisible by three.
A nonary number is divisible by two, four or eight, if the sum of its digits is also divisible by two, four or eight respectively.
If x is a triangular number, so is 9x+1. This means that one finds 3, 31, 311, 3111, 31111... in the triangular numbers. Likewise, 6, 61, 611, 6111, ....
The Nonary system of notation is used by the fictional civilization, The Culture, found in Iain M. Banks' books.[citation needed]