# Base-three number system **URL:** \ **Category:** Factual Questions\ **Created:** [September 1, 2001, 4:55pm UTC](https://boards.straightdope.com/t/base-three-number-system/79298 "2001-09-01T16:55:20Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![struct](https://avatars.discourse-cdn.com/v4/letter/s/f0a364/32.png) [@struct](https://boards.straightdope.com/u/struct)\ **Post date:** [September 1, 2001, 4:55pm UTC](https://boards.straightdope.com/t/base-three-number-system/79298/1 "2001-09-01T16:55:20Z")
Is the proper term for a base-three number system “trinary” or “ternary”? Would a base-four system be “quaternary”? I know that base-two is “binary”, base-eight is “octal”, base-ten is “decimal” and base-sixteen is “hexadecimal” but what would the others between base-two and base-sixteen be? I have some educated guesses on a few: Base-nine - “nonal”? Base-eleven - “unadecimal”? Base-twelve - “duodecimal”? Oh and there is actually such a thing as “unary” (e.g. the “-” in “-16” is a unary mathematical operator) but I don’t think you could actually have a unary or base-one number system, for obvious reasons. ---
**Author:** ![Sultan\_Kinkari](https://avatars.discourse-cdn.com/v4/letter/s/7bcc69/32.png) [@Sultan\_Kinkari](https://boards.straightdope.com/u/Sultan_Kinkari)\ **Post date:** [September 1, 2001, 5:08pm UTC](https://boards.straightdope.com/t/base-three-number-system/79298/2 "2001-09-01T17:08:56Z")
**tertiary** Main Entry: 2tertiary Function: adjective Etymology: Latin tertiarius of or containing a third, from tertius third Date: circa 1656 1 a : of third rank, importance, or value b chiefly British : of, relating to, or being higher education c : of, relating to, or constituting the third strongest of the three or four degrees of stress recognized by most linguists (as the stress of the third syllable of basketball team) 3 a : involving or resulting from the substitution of three atoms or groups \ \ b : being or containing a carbon atom having bonds to three other carbon atoms \ \ 4 : occurring in or being a third stage: as a : being or relating to the recovery of oil and gas from old wells by means of the underground application of heat and chemicals b : being or relating to the purification of wastewater by removal of fine particles, nitrates, and phosphates ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [September 1, 2001, 5:21pm UTC](https://boards.straightdope.com/t/base-three-number-system/79298/3 "2001-09-01T17:21:30Z")
The accepted term for a base three number system is “ternary”. Bases other than 2, 4, 8, 10, and 16 don’t show up often enough to warrant special names (at least in my experience); base k is usually just referred to as “base k”. There is a unary number system, suitable only for representing integers. 1 is represented as 1, 2 is represented as 11, and so on and so forth. It does require a different symbol for zero, though. Clearly this is not the same as a base 1 number system. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [September 1, 2001, 8:39pm UTC](https://boards.straightdope.com/t/base-three-number-system/79298/4 "2001-09-01T20:39:31Z")
I found a table in a Google cache, but I can’t manage to link to it. > [@](#): > > 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