# History Main / AlternativeNumberSystem

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[[folder:Anime and Manga]]
* Getting the Shinigami Eyes in ''Franchise/DeathNote'' gives you the ability to see a person's name and remaining lifespan when you look at their face. Sadly the lifespan only appears in a number system recognisable to {{Shinigami}} that just looks like random numbers to a human.
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** 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]]

* 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.

* ''Webcomic/SchlockMercenary'': Implied. An alien with an odd number of fingers ([[HiveMind and an odd number of bodies]]) says a long, complicated number will be easy to remember since it's a round number. It's certainly not round in Base 10. Most of the galaxy uses Base 10, likely because of human cultural supremacy.

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

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---> '''Carter''': Trust me; its it's 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.

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* 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).seconds), and indirectly, the basis for scoring in tennis (Love, 15, 30, 40, and Game, which used to be 0, 15, 30, 45, and 60). 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.

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The number numeral 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 numeral 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 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 number numeral 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.

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

* 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.

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* 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 numeral 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.

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** There's a fan theory that the constellations on the gate actually correspond to digits in a base-38 number numeral 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.

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

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* 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 numeral 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.)

** Due to the influence of German, both "thirty-six" and "six and thirty" are gramatically correct in Czech, although the big-endian version is more common.

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

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

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

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

** Spanish is another language that zig-zags. Your little endians go all the way to fifteen, switch to big-endian to twenty (''veinte''), switch ''again'' to little-endian, and then end again at thirty (''treinta''), so you have your singulars (''uno, seis'' 1, 6) your teens (''doce, catorce'', 12, 14), your big-endian teens (''diecisiete'', "ten and seven"), and then your twenties (''veintiuno, veintiocho'', 21, 28) before it goes entirely to big endian from there (''treinta y nueve'', "thirty-and-nine"). The cycle repeats once you make it to triple-digits, as they are referred to a lot closer to English but with the aforementioned endian cycle (''dos cientos cuarenta y tres'', "Two hundred forty-and-three").

-->-- Music/TomLehrer, ''New Math''.

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-->-- Music/TomLehrer, ''New Math''.
'''Music/TomLehrer''', "New Math", ''Music/ThatWasTheYearThatWas''

* Roman numerals could be considered a combination of base 5 and base 10. With unique symbols for 1 (I), 5 (V), 10 (X), 50 (L), 100 (C), 500 (D), and 1,000 (M). All other numbers being an additive or subtractive combination of the unique signs.

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* Roman numerals could be considered a combination of base 5 and base 10. With 10, with unique symbols for 1 (I), 5 (V), 10 (X), 50 (L), 100 (C), 500 (D), and 1,000 (M). All (M), all other numbers being an additive or subtractive combination of the unique signs.

** Some languages are weirder: Arabic stays little-endian until ''100''. So "16" is ''sitta-`ashar'' (six-ten) and "36" is ''sitta-wa-thalaathuun'' (six-and-thirty), but "136" is ''mi'ah wa sitta wa thalaathuun'' (a-hundred-and-six-and-thirty). This, however, is a relatively modern construction. Like the language itself, the numbers were read from right to left; "sitta wa thalaathuun wa mi'ah" (six-and-thirty-and-hundred)

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** Some languages are weirder: Arabic stays little-endian until ''100''. So "16" is ''sitta-`ashar'' (six-ten) and "36" is ''sitta-wa-thalaathuun'' (six-and-thirty), but "136" is ''mi'ah wa sitta wa thalaathuun'' (a-hundred-and-six-and-thirty). This, however, is a relatively modern construction. Like the language itself, the numbers were read from right to left; left, e.g. "sitta wa thalaathuun wa mi'ah" (six-and-thirty-and-hundred)(six-and-thirty-and-hundred).

* Up until the 1970s, British currency was a mix of base 12 (12 pence to the shilling), and base 20 (20 shillings to the pound). They were the last first world nation to switch to a decimal based currency.

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* Up until the 1970s, British currency was a mix of base 12 (12 pence to the shilling), shilling) and base 20 (20 shillings to the pound). They were the last first world First World nation to switch to a decimal based currency.

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