Bibi-binary: Difference between revisions
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The central observation driving this system is that sixteen can be written as 2 to the power of 2, to the power of 2. As we use the term [[binary]] for numbers written in base two, Lapointe reasoned that one could also say "bi-binary" for base four, and thus "bibi-binary" for base 16. Its name may also be a pun,{{ref?}} as the word ''bibi'' in French is slang for "me" or "myself"; various forms of word play were at the centre of Lapointe's artistic œuvre. |
The central observation driving this system is that sixteen can be written as 2 to the power of 2, to the power of 2. As we use the term [[binary]] for numbers written in base two, Lapointe reasoned that one could also say "bi-binary" for base four, and thus "bibi-binary" for base 16. Its name may also be a pun,{{ref?}} as the word ''bibi'' in French is slang for "me" or "myself"; various forms of word play were at the centre of Lapointe's artistic œuvre. |
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== Pronunciation == |
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In addition to unique graphical representations, Lapointe also devised a pronunciation for each of the sixteen digits. Using four consonants and four vowels, one obtains sixteen combinations: |
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== Pourquoi ''Bibi'' == |
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À partir de ce postulat, [[Boby Lapointe]] inventa la notation et la prononciation de seize chiffres. À l'aide de quatre consonnes et de quatre voyelles, on obtient les seize combinaisons nécessaires : |
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HO, HA, HE, HI, BO, BA, BE, BI, KO, KA, KE, KI, DO, DA, DE, DI. |
HO, HA, HE, HI, BO, BA, BE, BI, KO, KA, KE, KI, DO, DA, DE, DI. |
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To identify any number, it suffices to enumerate the (hexadecimal) digits that make it up. For example: the number written as "2000" in base ten, which translates to "7D0" in conventionally-written hexadecimal, would in Bibi-binary be spoken aloud as "BIDAHO". |
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Pour définir un nombre, il suffit d'énumérer les chiffres (hexadécimaux) qui le composent. |
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== Negative numbers == |
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Exemple : en Bibi, le nombre ''2000'' (en base décimale), qui se traduit, en hexadécimal, par ''7D0'', est appelé ''BIDAHO''. |
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Contrary to the numeric conventions used in modern computers, the bibi-binary system represents negative numbers using [[one's complement]],{{ref?}} rather than [[two's complement]]. Thus: |
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== Nombres négatifs == |
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and their sum is written as "1 1111" (one of two representations of zero in this system; zero can also be written as "0 0000"). |
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On modern machines, in classic binary notation, −7 would be written 1 1001, and the sum of −7 and 7 would give "0 0000"; this "two's complement" system thus needs only a single representation for the number zero. |
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Contrairement à la numération retenue dans les ordinateurs actuels, le Bibi représente les nombres négatifs en [[complément à un]]{{refsou}}, et non [[Complément à deux|à deux]]. |
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Ainsi : |
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et leur addition donne : |
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1 1111 (une des 2 représentations de « zéro » dans ce système ; « zéro » y est aussi représenté par 0 0000). |
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Sur les ordinateurs contemporains, en notation binaire classique, -7 s'écrit 1 1001 (on propage le « 1 » dans les bits supérieurs) ; et l'addition de -7 et 7 donnera 0 0000. Il n'y a ainsi qu'une seule notation pour le chiffre zéro. |
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{{Palette|Base de numération positionnelle}} |
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{{Portail|mathématiques|informatique théorique}} |
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{{DEFAULTSORT:Bibi, numeration, système bibi-binaire}} |
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== External links == |
== External links == |
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* [http://www.graner.net/nicolas/nombres/bibibinaire.php Conversion en ligne décimal ↔ bibi-binaire] (in French) |
* [http://www.graner.net/nicolas/nombres/bibibinaire.php Conversion en ligne décimal ↔ bibi-binaire] (in French) |
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== References == |
== References == |
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Revision as of 01:12, 17 October 2016
The Bibi-binary system for numeric notation (in French système Bibi-binaire, or abbreviated "système Bibi") was first described in 1968[1] by Robert "Boby" Lapointe (1922-1972), based on the concept of hexadecimal notation. At the time, it attracted the attention of André Lichnerowicz, then engaged in studies at the University of Lyon. It found some use in a variety of unforeseen applications: stochastic poetry, stochastic art, colour classification, aleatory music, architectural symbolism, etc.[citation needed]
The notational system directly and logically encodes the binary representations of the digits in a hexadecimal (base sixteen) number. However, in place of the arabic numerals and letters currently used, it presents sixteen newly-devised symbols (thus evading any risk of confusion with the decimal system). The graphical and phonetic conception of these symbols renders the use of the Bibi-binary "language" simple and fast.
The description of the language first appeared in Les Cerveaux non-humains ("Non-human brains"),[2] and the system can also be found in Boby Lapointe by Huguette Long Lapointe.[3]
Why Bibi
The central observation driving this system is that sixteen can be written as 2 to the power of 2, to the power of 2. As we use the term binary for numbers written in base two, Lapointe reasoned that one could also say "bi-binary" for base four, and thus "bibi-binary" for base 16. Its name may also be a pun,[citation needed] as the word bibi in French is slang for "me" or "myself"; various forms of word play were at the centre of Lapointe's artistic œuvre.
Pronunciation
In addition to unique graphical representations, Lapointe also devised a pronunciation for each of the sixteen digits. Using four consonants and four vowels, one obtains sixteen combinations:
HO, HA, HE, HI, BO, BA, BE, BI, KO, KA, KE, KI, DO, DA, DE, DI.
To identify any number, it suffices to enumerate the (hexadecimal) digits that make it up. For example: the number written as "2000" in base ten, which translates to "7D0" in conventionally-written hexadecimal, would in Bibi-binary be spoken aloud as "BIDAHO".
Negative numbers
Contrary to the numeric conventions used in modern computers, the bibi-binary system represents negative numbers using one's complement,[citation needed] rather than two's complement. Thus:
- +7 is written 0 0111
- −7 is written 1 1000
and their sum is written as "1 1111" (one of two representations of zero in this system; zero can also be written as "0 0000").
On modern machines, in classic binary notation, −7 would be written 1 1001, and the sum of −7 and 7 would give "0 0000"; this "two's complement" system thus needs only a single representation for the number zero.
External links
- Conversion en ligne décimal ↔ bibi-binaire (in French)
References
- ^ Brevet d'invention n° 1.569.028, Procédé de codification de l'information, Robert Jean Lapointe, demandé le 28 mars 1968, délivré le 21 avril 1969. Downloaded from INPI.
- ^ Jean-Marc Font, Jean-Claude Quiniou, Gérard Verroust, Les Cerveaux non-humains : introduction à l'Informatique, Denoël, Paris, 1970.
- ^ Huguette Long Lapointe, Boby Lapointe, Encre, Paris, 1980 ISBN 2-86418-148-7