Base 27
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A septemvigesimal numeral system has a base of twenty-seven. It is used in two natural languages, the Telefol language[1] and the Oksapmin language of Papua New Guinea.[2]
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Use in natural language [edit]
The Oksapmin use a system of counting in which numbers are associated with body parts, starting at one thumb, continuing across the body and face, and ending at the little finger of the other hand. The numbers that may be expressed in this system range from 1 to 27. Similar counting systems are widespread in Papua New Guinea, where the Oksapmin live.[2]
Relation to ternary [edit]
Septemvigesimal notation can be used as a concise representation of ternary data, where each septemvigesimal digit represents three ternary digits. This is similar to using octal notation to represent binary data, though the digit set is closer in size to hexadecimal.
Examples: (Digits 10–26 are represented by letters A through Q.)
| Decimal | Ternary | Septemvigesimal |
|---|---|---|
| 0 | 000 | 0 |
| 1 | 001 | 1 |
| 2 | 002 | 2 |
| 3 | 010 | 3 |
| 5 | 012 | 5 |
| 10 | 101 | A |
| 15 | 120 | F |
| 20 | 202 | K |
| 25 | 221 | P |
| 26 | 222 | Q |
| 27 | 1000 | 10 |
| 81 | 10000 | 30 |
Alphabetic encoding [edit]
An alternate encoding, mapping 0 to space and 1–26 to A–Z, is occasionally used in puzzles to transform ternary triplets into words or messages,[citation needed] to provide checksums for alphabetic data such as personal names,[3] or as the basis for a form of gematria.[4]
References [edit]
- ^ Fedden, Sebastian (2012), "Change in Traditional Numerals Systems in Mian and other Trans New Guinea Languages", Journal of the Linguistic Society of Papua New Guinea (Special Issue 2012 Part I): 1–20, ISSN 0023-1959.
- ^ a b Saxe, Geoffrey B.; Moylan, Thomas (1982), "The development of measurement operations among the Oksapmin of Papua New Guinea", Child Development 53 (5): 1242–1248, JSTOR 1129012.
- ^ Grannis, Shaun J.; Overhage, J. Marc; McDonald, Clement J. (2002), "Analysis of identifier performance using a deterministic linkage algorithm", Proc AMIA Symp., pp. 305–309, PMC 2244404.
- ^ Sallows, Lee (1993), "Base 27: the key to a new gematria", Word Ways 26 (2): 67–77.
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