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### Names of Bases (Octal, Hexadecimal, etc.)

```Date: 04/15/2002 at 07:40:28
From: Eric McDaniel
Subject: Base names, i.e.: octal, decimal, hexadecimal...

I don't know the names of the bases after nonadecimal.
```

```
Date: 04/16/2002 at 13:59:32
From: Doctor Peterson
Subject: Re: Base names, i.e.: octal, decimal, hexadecimal...

Hi, Eric.

Here is a short list that covers 2-12, 16, 20, and 60, which are the
main bases in actual use.

MathWorld - Eric Weisstein
http://mathworld.wolfram.com/BaseNumber.html

Base Name
2  binary
3  ternary
4  quaternary
5  quinary
6  senary
7  septenary
8  octal
9  nonary
10  decimal
11  undenary
12  duodecimal
16  hexadecimal
20  vigesimal
60  sexagesimal

The following page has a longer list that differs from the accepted
names above, apparently trying to be more consistent than people have
been in reality; take it with a grain of salt, but it does seem to
reflect considerable research:

Numbers, Numerical Adjectives, Prefixes for Numbers
http://phrontistery.50megs.com/numbers.html

Table 1: Latin-Prefixed Numerical Words

Numeral   Prefix        Base          Relation
1 unus      uni           N/A           unary
2 duo       bi/duo        binal         binary
3 tres,tria tri           trial,tertial trinary, ternary
4 quattuor  quadri/quart  quartal       quaternary
5 quinque   quinque/quint quintal       quinary, quinquenary
6 sex       sex(t),se     sextal        senary, sexenary
7 septem    sep(t)        septimal      septenary
8 octo      oct           octal,octaval octonary
9 novem     nonus/novem   nonal         nonary
10 decem     dec(a),de     decimal       denary
11 undecim   undec,unde    undecimal     undenary
12 duodecim  duodec,duode  duodecimal    duodenary

Table 3: Latin Numerical Words: 13 to 1000

Numeral       Prefix        Base            Relation
13 tredecim      tredec,tridec *tridecimal     *tridenary
14 quattuordecim quatuordec    *quatuordecimal *quatuordenary
15 quindecim     quinde(c)     *quindecimal    quindenary
16 sedecim       sede(c)       hexadecimal     *sedenary
17 septendecim   septende(c)   septendecimal   *septendenary
18 duodeviginti  decennoct     *decennoctal    *decenoctonary
19 undeviginti   decennov      decennoval      *decennonary
20 viginti       vige,vice     vigesimal       vigenary
30 triginta      trige,trice   trigesimal      tricenary
40 quadraginta   quadrage      quadragesimal   quadragenary
50 quinquaginta  quinquage     quinquagesimal  quinquagenary
60 sexaginta     sexage        sexagesimal     sexagenary
70 septuaginta   septuage      septuagesimal   septuagenary
80 octoginta     octage        octagesimal     octogenary
90 nonaginta     nonage        nonagesimal     nonagenary
100 centum        cente         centesimal      centenary
1000 mille         mille         millesimal      millenary

He puts an asterisk on the names he admits to inventing (following
natural rules). Note that the "base" and "relation" columns are often
mixed up in reality.

Another site that lists names on a reasonably sound basis is

Names of bases for number systems - C. E. A. Finney
http://www.ceafinney.com/miscellania/bases.html

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."

My own list, putting all these ideas together, would be something
like this:

Base Name
2 binary
3 ternary
4 quaternary
5 quinary
6 senary
7 septenary
8 octal
9 nonary
10 decimal
11 undenary
12 duodecimal
13 *tridecimal
14 *quattuordecimal
15 *quindecimal
16 hexadecimal
17 septendecimal
18 *octodecimal
19 *nonadecimal
20 vigesimal
30 trigesimal
40 quadragesimal
50 quinquagesimal
60 sexagesimal
70 septuagesimal
80 octagesimal
90 nonagesimal
100 centesimal

I've found no references to names like "unvigesimal," so you are free
to invent your own combinations for 21, 22, and so on.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory
Middle School Number Sense/About Numbers

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