History Main / AlternativeNumberSystem

* The ''TabletopGame/Warhammer40000'', 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 even further.

* Vestiges of base 20 remain in English ("four score and seven years 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.

* At one point in ''[[Literature/TheFangsOfKaath The Fangs of K'aath]]'', the FunnyAnimal civilization's use of base 8 is explained (due, again, to their fingers) by one character to another; they write 8 as "10". They are apparently fond of mathematics, too, which is fitting, as this particular FantasyCounterpartCulture is based on the medieval Islamic lands.

* In ''Literature/AFireUponTheDeep'' by Creator/VernorVinge, the doglike Tines have two different numeral 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.

* The rabbits of ''Literature/WatershipDown'' can count up to four, presumably because that's how many paws they have. The number "hrair" in their language of Lapine means "any quantity greater than four" and/or "too many to count"; depending on context, it may also be translated into English as "five" or "a thousand."

* In Creator/LeoFrankowski's ''Literature/TheCrossTimeEngineer'' series, the new civilization Conrad Stargard starts up in Medieval Europe uses base 12 mathematics, because Stargard believes it's more useful than decimal.

* In ''ComicBook/ElfQuest'', the elves use base 8 because of their FourFingeredHands -- that page has more details.
* The same goes for ''ComicBook/AlbedoErmaFelnaEDF'', albeit by TranslationConvention all the numbers are translated to base-10 for the readers' sake. This became later into a plot point when [[spoiler:the characters find an human ship who uses base-10 for obvious reasons]].

* In ''Webcomic/{{Hoofstuck}}'', Twilight Sparkle mentions that Equestria uses base eight rather than ten, since there's nothing on a pony you can use to count to ten (whereas four hooves times two make more sense). They used to run with base four originally, symbolising the four races (earth ponies, pegasi, unicorns, alicorns) but the earth ponies took offense at being considered the "zeroes".
* Averted in the Fanfic/TriptychContinuum. Equestria uses Base Ten. Neither Celestia nor Luna have any idea ''why''.
* In ''Fanfic/TheElementsOfFriendship'', the Equestrians use base-12, complete with neologisms for the new names for numbers of years. The author even [[https://www.fimfiction.net/blog/432662/a-summation-of-the-numerical-system-in-the-elements-of-friendship wrote a blog post]] explaining the system.
** Discord notably doesn't do this, and at one point offhandedly derides the ponies for not using the decimal system.
* In ''[[http://www.fimfiction.net/story/327837/friendship-is-sufficiently-advanced Friendship is Sufficiently Advanced]]'', an MLP: FIM/Eldraeverse crossover, ponies use base eight, counting the joints in equine limbs, while eldrae use base 12 as mentioned below. In chapter VII Twilight and the eldrae main character compare numerals when the former notes that the latter's ship designation (1129) is written in only three digits (seven-ten-one, or two-one-five-one in equine numbers).

* In ''Franchise/StarWarsLegends'', 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.
* 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 ''Literature/MenAtArms'', when it turns out that Detritus is not incompetent with numbers, he is in fact very good at counting ''in powers of two''.
* Even Discworld's trolls are better with numbers than the tree frogs of the ''Literature/NomesTrilogy'', who can only grasp "one" as a number. Faced with the quandary of two different bromeliads, a frog genius makes a breakthrough when it comprehends them as "one, and one ''more'' one".
* A subversion in ''Literature/TheRestaurantAtTheEndOfTheUniverse'': When Creator/DouglasAdams revealed that the question which produced the Ultimate Answer (42) was [[spoiler:What do you get if you multiply six by nine?]], somebody pointed out that the math actually did add up, using base 13. Adams responded, "[[SelfDeprecation I may be a sad individual]], but [[EvenNerdsHaveStandards I don't make jokes in base 13.]]"
* In ''Literature/TheLordOfTheRings'':
** According to the appendices, elves habitually count in base 12. This is not because they have a different number of fingers. Most likely though, it's because patterns based on 3, 6 and 12 are very common in nature: particularly plants, constellations and crystals. Though Tolkien never completely committed to this: in other instances he seems to imply a base ten system. He waffled back and forth about this for his entire life.
** The Wild Men seem to use a base-20 system. When Ghan-buri-Ghan counts the number of soldiers in the Rohan army, he expresses it as "A score of scores counted ten times and five" (6,000).
* The ''gukuy'' in Creator/EricFlint's ''Literature/MotherOfDemons'' count using an eight-base system.
* It's never mentioned in the books themselves, or the series, but the "Gallifreyan numerals" used on the spines and chapter headings of the ''Series/DoctorWho'' Literature/NewSeriesAdventures (9th and 10th Doctors) are in base 7.

* In ''Literature/LearningTheWorld'' by Creator/{{Ken MacLeod}}, the aliens are four-fingered, and count in base 8. When they learn that humans use base 10, their reaction is that having a base that isn't a power of two must be awfully inconvenient.
* In ''Literature/AFireUponTheDeep'' by Creator/VernorVinge, the doglike Tines have two different numeral 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.
* On Literature/{{Gor}}, the alien species the Kurii use base-12, presumably because they have 12 digits on their "hands."
* ''Literature/LittleFuzzy'', a series begun by Creator/HBeamPiper, uses a modified form of base 5. 1, 2, 3, 4, one hand. At 125, they've reached a hand of hands. It then goes to many, and many many. The fuzzies soon adopt the humans' base 10 system.
* Creator/LarryNiven and Jerry Pournelle's ''Literature/TheMoteInGodsEye''. The Moties have a total of 12 digits on their right hands and use base 12.
* ''Literature/KnownSpace'': The Kzinti count in base eight due to having four-fingered hands.

* ''Literature/StrangerInAStrangeLand'': The Martians apparently have a numerical system based on three and powers of three. "Three fulfilled," they call it.
* ''Franchise/StarTrek'': [[AllThereInTheManual According to]] ''The Klingon Dictionary'', the Klingons used to count in a ternary (base-three) system, but have since switched over to decimal.
* ''Literature/{{Footfall}}'': The Fithp use base 8.
* ''Literature/{{Contact}}'': A message is encoded in base 11, by someone or something capable of messing with the values of mathematical constants.
* ''Literature/RendezvousWithRama'': The aliens appear to use base 3.
* In ''Literature/TheIronStandard'' by Creator/HenryKuttner, the six-fingered Venusians use base-12.
* ''Literature/OutOfTheDark'' gives us the Shongairi, who count in base-twelve. Possibly.
* Zamonien in Creator/WalterMoers' novels uses base 8. The author even created new symbols for the numbers.

* The Megarites of the ''Franchise/StarTrek'' universe use base 8, according to ''Literature/StarTrekExMachina''.
* In ''Literature/BattlefieldEarth'' the Psychlos use a base-11 system (they have an extra finger on one hand). While this causes the human characters endless frustration when trying to work with Psychlo mathematics, it gets nonsensical when other alien races share these complaints, lauding the values of a sensible base-10 system and concluding that the Psychlos were just being perverse when designing their math.
* Gully dwarves from ''Literature/{{Dragonlance}}'', being astonishingly stupid, can only count up to two. Any higher quantity is described as "One and one and no more than two."
* In ''Literature/ChildhoodsEnd'' by Creator/ArthurCClarke, the Overlords are mentioned to count in base 14 (their hands have five fingers and two thumbs).
* 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) numeral system. For one thing, ''all'' of their units (length, mass, etc.) increment in powers of 12.

* At one point in ''[[Literature/TheFangsOfKaath The Fangs of K'aath]]'', the FunnyAnimal civilization's use of base 8 is explained (due, again, to their fingers) by one character to another; they write 8 as "10". They are apparently fond of mathematics, too, which is fitting, as this particular FantasyCounterpartCulture is based on the medieval Islamic lands.
* In the ''Literature/{{Eldraeverse}}'', the Eldrae use base 12, and had a brief flirtation with base 16. Not because of their number of digits (baseline Eldrae have as many as humans), but because their language was standardized by [[https://eldraeverse.com/2016/03/31/trope-a-day-alternative-number-system/ mathematical philosophers]].
* In a throwaway joke in ''Literature/AgathaHAndTheClockworkPrincess'', Prince Aaronev Sturmvoraus sends a message to one of his subjects stating that if he's caught making change in base 8 one more time, he'll be paying his taxes in base 12.
* Currency in the ''Literature/HarryPotter'' universe is a mixture of base 17 (17 sickles to the galleon) and base 29 (29 knuts to the sickle). This is possibly a joke based on the currency units of RL Britain until the 70s (though at least they didn't use prime numbers).
* ''Literature/EmpireFromTheAshes'': During the scenes set on the Achuultani ships, The characters mention "Twelves, Higher Twelves and Greater Twelves".
* One of Ian Stewart's popular maths books features an alien race who count in base seven. They're keen on cricket, but they go mad with excitement just ''before'' a player scores a half-century, because to them, he's just scored a century.
* 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 ''Literature/{{Incandescence}}'', the insectoid aliens of the Splinter have six legs, and their number system is based on that. Their word for "very many" translates to "thirty-six times thirty-six."

* In Radio/TheFrantics' sketch [[https://www.youtube.com/watch?v=fjFaKD9BuOc "Roman Numerals"]] a Roman citizen is baffled by the new decimal system.
-->Customer: How much is "forty-four" in real numbers?\\
Shopkeeper: XLIV [[note]]pronounced "ex-ell-eye-vee"[[/note]].\\
Customer: Well why don't you just '''say''' XLIV? Who can remember "forty-four?"
** When Arabic positional decimal notation (i.e. today's numbers) were first introduced in Europe, some regions passed laws against the use of "deceptive ciphers" and mandated continuing the use of "real quantities" (i.e. Roman numerals).

* ''Series/BabylonFive'':
** The Minbari use base eleven (a byproduct of using fingers, toes, and the head as "digits" for counting).
** According to tie-in RPG materials, the Dilgar used base 25.
* ''Series/{{Foundation}}'': While discussing the new society they'll create, a member of the Foundation argues that even using base 10 numbers shouldn't be assumed, noting that 12 divides better than 10.

* 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.

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

* There is a popular theory among ''VideoGame/HalfLife'' fans that the Combine use a base-17 system, based on how [[ArcNumber prominent]] 17 seems to be. If nothing, it reinforces the [[SufficientlyAdvancedAlien utterly alien]] nature of the Combine.
* 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".
* ''Franchise/{{Halo}}'' fans speculate that the Forerunners might have counted using a Base-7 counting system.

* ''VisualNovel/NineHoursNinePersonsNineDoors'':
** One of the puzzles in the Kitchen requires you to use base 16 in order to figure out the code to open a locked safe.
** The Nonary Game itself, per its name, indirectly involves base 9 via [[https://en.wikipedia.org/wiki/Digital_root digital roots]]. [[spoiler:The last door, represented by the letter ''q'', is locked behind at least base 27.]]
* ''Franchise/MassEffect'' mentions math systems not based on ten, such as a superweapon that relies on specialized base-12 mathematics and a krogan NPC muttering about the stupidity of base-10 math and the consequences of having extra fingers.
* One puzzle in the freeware interactive fiction game ''The Muldoon Legacy'' can only be solved when you realize that you're dealing with an example of this, rather than Base-10.

* ''Cowbirds in Love'' [[http://cowbirdsinlove.com/43 points out]] that every base is base 10 (from the perspective of anyone using it). For bonus points, the alien in the comic uses base 4 and appears to be four-fingered.

* Done subtly in ''WesternAnimation/{{Animaniacs}}''. Snow White imprisons Dot for being too cute, and Dot counts the time in hashmarks that only have four strokes each... presumably because [[FourFingeredHands she's a cartoon character]].

* In Creator/LeoFrankowski's ''The Cross Time Engineer'' series, the new civilization Conrad Stargard starts up in Medieval Europe uses base 12 mathematics, because Stargard believes it's more useful than decimal.
* In ''Learning the World'' by Creator/{{Ken MacLeod}}, the aliens are four-fingered, and count in base 8. When they learn that humans use base 10, their reaction is that having a base that isn't a power of two must be awfully inconvenient.

* In ''The Iron Standard'' by Creator/HenryKuttner, the six-fingered Venusians use base-12.

->"Base eight is just like base ten, really. If you're missing two fingers."

* The Kzinti of Creator/LarryNiven's ''Literature/KnownSpace'' count in base eight.
* Literature/TheCulture uses a nonary (base nine, that is) system for their writing, although it's actually binary in a 3x3 square. Binary is mentioned as being used by some civilisations, and powers of two are the closest thing to a universally-regarded 'round number'.
* In ''Literature/StrangerInAStrangeLand'', the Martians apparently have a numerical system based on three and powers of three. "Three fulfilled," they call it.
* [[AllThereInTheManual According to]] ''[[Franchise/StarTrek The Klingon Dictionary]]'', the Klingons used to count in a ternary (base-three) system, but have since switched over to decimal.
* In ''Literature/{{Footfall}}'', the Fithp use base 8.
* In ''Literature/{{Contact}}'', a message is encoded in base 11, by someone or something capable of messing with the values of mathematical constants.
* The aliens in the ''[[Literature/RendezvousWithRama Rama]]'' books appear to use base 3.

* [[AllThereInTheManual Behind-the-scenes material]] on ''Film/{{Avatar}}'' claims that the Na'vi also use base 8 for the same reason as the ''ComicBook/ElfQuest'' elves.

* In ''Literature/StrangerInAStrangeLand'', the Martians apparently have a numerical system based on three and powers of three. "Three fulfilled," they call it...

* In ''Literature/BattlefieldEarth'' the Psychlos use a base-11 system (they have an extra finger on one hand). While this causes the human characters endless frustration when trying to work with Psychlo mathematics, it gets nonsensical when other alien races share these complaints, lauding the values of a sensible base-10 system and concluding that the Psychlos were just being perverse when designing their math. \\
\\
It doesn't help that Psychlo mathematics requires that the user have a basic knowledge of the Psychlo homeworld's geography. Yet another bit of evidence that they're just trolling the universe.

* Vogons in ''Film/TheHitchhikersGuideToTheGalaxy'' have a unary system, meaning that writing the number ''1,000'' means writing ''1'' a thousand times.

* One particularly [[GuideDangIt convoluted]] (but thankfully option) puzzle in ''VideoGame/KingdomOfLoathing'' involves deciphering the [[OxymoronicBeing 11-foot dwarves]]' written language to find out how many ores of each kind you need to put into a machine to create a piece of (mediocre) gear. One of the step requires not only deciphering what number corresponds to each glyph, you have to convert that from base 7 to get the results.

** ''VideoGame/{{Obduction}}'', ''Myst'''s SpiritualSuccessor, features a base-four system associated with one of the setting's alien races. They also use a particular notation based on drawing lines among a diagonal grid of dots: lines attached to the central dot are ones; the dot above represents fours, the one on the right represents sixteens, and so on in an expanding spiral.

** And then there's [=Base64=], which is mainly used as an encoding scheme to increase the information density when storing or transmitting data, especially in a text-based format.[[note]]Representing 3 bytes of data requires 6 hex digits, but only 4 [=Base64=] digits.[[/note]]

* ''Wiki/SCPFoundation'':