History Main / AlternativeNumberSystem

This may be used to indicate the collective intelligence of the society that produced it, if it is portrayed as more sophisticated or more primitive than our system. There may also be an inferred correlation between the ten digits in our numeral system and the ten digits on the average pair of human hands. Therefore, a race of aliens with FourFingeredHands may use a base eight numeral system. Finally, it is very common for robots or other computer-based intelligences to count in base two.

* The ''TabletopGame/{{Warhammer 40000}}'', the Tau use base 8 owing to their FourFingeredHands, leading to a delicious little StealthPun: their [[MiniMecha battlesuits]]' designations are based on their size, such as [=XV25=] for the smaller Stealth suits, [=XV8=] for the main Crisis suit, or [=XV88=] for the heavy Broadside variant. Which means that the new [=XV9=] Hazard Close Support Armour units are taking things UpToEleven.

** In ''VideoGame/MystIIIExile'', Saavedro's journal pages are numbered in a base 5 system similar to tallies, but with a leaf motif in keeping with the rest of his culture..

* ''WebVideo/Numberphile'': Discussed in videos:

* Related to the above examples, [[https://www.youtube.com/watch?v=qID2B4MK7Y0 "a better way to count"]] by Creator/JanMisali discusses base ''six,'' otherwise known as seximal.

* Related to the above examples, [[https://www.youtube.com/watch?v=qID2B4MK7Y0 "A better way to count"]] by [[WebVideo/ConlangCritic jan Misali]] discusses base ''six,'' otherwise known as Seximal.

** According to the appendices, elves habitually count in base 12.

* The Kilrathi from ''Videogame/WingCommander'' use Base 8 for their numbering system, given that they have a total of eight fingers. For the most part this isn't really mentioned much, but it's prominent in the dates for history of the Kilrathi war from their viewpoint as done in the manual for ''Armada'', "Voices of War".

* One of the puzzles in the Kitchen in ''VisualNovel/NineHoursNinePersonsNineDoors'' requires you to use base 16 in order to figure out the code to open a locked safe.

* In ''WebComic/GirlGenius''' world of [[MadScientist mad science]] there's bound to be examples showing up: "[[http://www.girlgeniusonline.com/comic.php?date=20051014#.VwBgmaQrLIU Tell the landlord that he is to stop trying to make change in base eight, or he'll pay his taxes in base twelve.]]"

* Vestiges of base 20 remain in English ("four score years and ten ago") and in French ("quatre-vingts"[[note]]4*20=80[[/note]], also in the name of the Parisian hospital ''Quinze-Vingts''[[note]]15*20[[/note]] which was originally founded to house 300 patients). In addition, numbers after sixty and eighty go up to sixty-nineteen (''soixante-dix-neuf'', instead of seventy-nine) and eighty-nineteen (''quatre-vingts-dix-neuf'', instead of ninety-nine). It's thought to be either a Celtic or a Basque influence, or an influence of the "Vasconic language-group" (of which Basque is the only surviving member) ''on'' Celtic.

* Related to the above examples, [[https://www.youtube.com/watch?v=qID2B4MK7Y0 "A better way to count"]] by jan Misali discusses base ''six,'' otherwise known as Seximal.

[[folder:Comicbooks]]

[[folder:Web Originals]]
* In some of the Literature/ChakonaSpace stories, Caitians are mentioned to be using base 8 math and the less mathematically minded ones struggle with everyone else's usage of base 10 math.

* In the ''Literature/{{Discworld}}'' books, trolls apparently have a "base Many" system (actually base four). As in, "one, two, three, many, many-one, many-two..." This is revealed in ''Discworld/MenAtArms'', when it turns out that Detritus is not incompetent with numbers, he is in fact very good at counting ''in powers of two''.

* According to the ''Magazine/{Dragon}}'' article "The Ecology of the Spellweaver", these ''TabletopGame/DungeonsAndDragons'' monsters count in base six, although they also have a decimal notation. The number six is ''really'' significant to spellweavers, who not only have six arms, but can regenerate on death six times, following which they produce six offspring.

* In the ''Franchise/StarWarsExpandedUniverse'', the Hutts use a base 8 system due to only having four fingers on each hand. Being Hutts, they don't always tell this to their business partners, most of whom use base 10.

---> '''Carter''': Trust me; its a math thing.

* Ancient Babylonians counted in base 60. This is reflected in the modern measurement of time (hours, minutes and seconds), as well as angular measure (degrees, minutes, seconds). It came about because of two tribes. One used base 10, counting each finger, and a neighboring tribe used base 12, on one hand they would use the thumb to count the remaining twelve segments of the remaining four fingers. Since they had different systems, they would convert to a larger base. Sixty is the smallest common multiple of 10 and 12.

The number system used by most of the modern world today is called the decimal system, involving ten digits ("Base 10"). Sometimes, if a writer wants to portray a society as being significantly alien to our own, they will include a mention of an alternative number system for this society, with the "base" being a number other than ten.

This may be used to indicate the collective intelligence of the society that produced it, if it is portrayed as more sophisticated or more primitive than our system. There may also be an inferred correlation between the ten digits in our number system and the ten digits on the average pair of human hands. Therefore, a race of aliens with FourFingeredHands may use a base eight number system. Finally, it is very common for robots or other computer-based intelligences to count in base two.

* In ''Literature/AFireUponTheDeep'' by Creator/VernorVinge, the doglike Tines have two different number systems: one where they count "by legs" (in base 4) and one where they count "by fore-claws" (in base 10). Confusion between these two systems leads to the accidental meeting of two of the major characters. Amdiranifani is housed in room 33, Jefri is supposed to be imprisoned in room 15 (33 in base 4), and the guard who's taking him there uses the wrong numbering system.

* Creator/GregEgan's ''Literature/{{Orthogonal}}'' trilogy is presumably fed to the reader through a ''thick'' soup of TranslationConvention, and thus all numbers are in decimal. Despite this, it's easy to infer that the alien race uses a duodecimal (base-12) number system. For one thing, ''all'' of their units (length, mass, etc.) increment in powers of 12.

** There's a fan theory that the constellations on the gate actually correspond to digits in a base-38 number system. Which means that a gate address is not six arbitrary points in space with the destination at the intersection,[[note]]which contradicts the in-series assertion that all addresses are unique[[/note]] but three two-digit base-38 coordinates.

* The aliens in ''VideoGame/{{Iji}}'' use a ternary number system.

* A significant portion of the game ''{{VideoGame/Rama}}'', based on Arthur C. Clarke's novel series of the [[TheGameOfTheBook same name]], involves solving mathematical puzzles based on the native number systems of the Avians (base 16) and Octospiders (base 8). (Which is at odds with the Ramans, who use base 3. Neither the Avians nor the Octospiders are Ramans. They're just samples of other space-faring species that the Ramans had gathered.)

* ''Literature/EmpireFromTheAshes'': During the scenes set on the Achuultani ships, The characters "twelves, Higher Twelves and Greater Twelves".