# Base 27

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]

## Use in natural language

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

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,[3] though the digit set is closer in size to hexadecimal.

Examples:

Decimal Ternary Septemvigesimal     Decimal Ternary Septemvigesimal
0–9 A–Q 0 A–Z 0–9 A–Q 0 A–Z
0 000 0 0 27 1 000 10 A0
1 001 1 A 28 1 001 11 AA
2 002 2 B 29 1 002 12 AB
3 010 3 C 30 1 010 13 AC
4 011 4 D 53 1 222 1Q AZ
5 012 5 E 54 2 000 20 B0
6 020 6 F 55 2 001 21 BA
7 021 7 G 80 2 222 2Q BZ
8 022 8 H 81 10 000 30 C0
9 100 9 I 82 10 001 31 CA
10 101 A J 100 10 201 3J CS
11 102 B K 200 21 102 7B GK
12 110 C L 243 100 000 90 I0
13 111 D M 258 100 120 9F IO
14 112 E N 300 102 010 B3 KC
15 120 F O 400 112 211 EM NV
16 121 G P 500 200 112 IE RN
17 122 H Q 600 211 020 M6 VF
18 200 I R 700 221 221 PP YY
19 201 J S 729 1 000 000 100 A00
20 202 K T 800 1 002 122 12H ABQ
21 210 L U 900 1 020 100 169 AFI
22 211 M V 1000 1 101 001 1A1 AJA
23 212 N W 2187 10 000 000 300 C000
24 220 O X 6561 100 000 000 900 I000
25 221 P Y 10000 111 201 101 DJA MSJ
26 222 Q Z 19683 1 000 000 000 1000 A000

## Alphabetic encoding

An alternate encoding, mapping 0 to space and 1–26 to A–Z, is occasionally used to provide checksums for alphabetic data such as personal names,[4] to provide a concise encoding of alphabetic strings,[5] or as the basis for a form of gematria.[6]

## References

1. ^ 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.
2. ^ 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.
3. ^ Connelly, Jeff (August 29, 2008), Ternary Computing Testbed: 3-Trit Computer Architecture, California Polytechnic State University of San Luis Obispo, Computer Engineering Dept., p. 9.
4. ^ 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.
5. ^ Stephens, Kenneth Rod (1996), Visual Basic Algorithms: A Developer's Sourcebook of Ready-to-run Code, Wiley, p. 215, ISBN 9780471134183.
6. ^ Sallows, Lee (1993), "Base 27: the key to a new gematria", Word Ways 26 (2): 67–77.