ceafinney > miscellania > bases

Names of bases for number systems

A base-2 number system is called binary and a base-10 system decimal, but what how does one term number systems based on 3, 4, 5, 8 or 12 ? This is a question that I had to answer in 1999 March, so I did some research, and below are (almost all of) my findings. Please inform me of errors that I have made or of additions that you would like to make via email.

Base Name
2 binary
3 ternary [A]
4 quaternary
5 quinary
6 senary
7 septenary
8 octonary [B]
9 nonary
10 decimal
11 undenary
12 duodecimal
13 tridecimal
14 quattuordecimal
15 quindecimal
16 sexadecimal [C]
17 septendecimal
18 octodecimal
19 nonadecimal
20 vigesimal
30 trigesimal
40 quadragesimal
50 quinquagesimal
60 sexagesimal
70 septagesimal
80 octagesimal
90 nonagesimal
100 centimal
200 bicentimal
300 tercentimal
400 quattrocentimal
500 quincentimal

[A] Also “trinary”.
[B] Most commonly “octal” but also “octonal” or “octimal”.
[C] “hexadecimal” is the common computer-science terminology, but it is unsatisfactory because it is a combination of the Greek “hexa” and the Latin “decim”. The proper Latin should be “sedecim” or “sexdecim”, yielding either “sedecimal” or “sexadecimal”. Schwartzman writes: “Since hexadecimal is a rather long word, it is sometimes abbreviated hex. The word hexadecimal is unusual because Greek and Latin elements are combined; the expected purely Latin form would be sexadecimal, but then computer hackers would be tempted to shorten the word to sex.” [emphasis added]


Schwartzman S (1994). The Words of Mathematics: an etymological dictionary of mathematical terms used in English (ISBN 0-88385-511-9).