Bibi-binary: Difference between revisions

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{{Short description|Hexadecimal number system}}

[[Image:Table de correspondance entre le Bibinaire et les autres notations.svg|520px|thumb|right|Note: eachEach Bibi digit is formed from a square arranging the 1-bits in its binary representation. If only a single bit is 1 a vertical line runs through the centre and ends in that bit's corner; otherwise it relies on the order of the positions of the 1-bits. When there are exactly two 1-bits, the line passes round the centre. The forms are rounded when there are less than three 1-bits, and use sharp corners when three or four of the bits are 1.]]

The '''Bibi-binary''' system for numeric notation (in French '''{{langx|fr|système Bibi-binaire'''}}, or abbreviated "'''{{lang|fr|système Bibi}}'''") is a [[hexadecimal]] numeral system first described in 1968<ref>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. [http://bases-brevets.inpi.fr/fr/document/FR1569028/publications.html Downloaded] from [[Institut national de la propriété industrielle|INPI]].</ref> by singer/mathematician [[Boby Lapointe|Robert "Boby" Lapointe]] (1922–1972). 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|date=October 2016}}

The notational system directly and logically encodes the binary representations of the digits in a hexadecimal (base sixteen) numeral. In place of the Arabic numerals 0–9 and letters A–F currently used in writing hexadecimal numerals, it presents sixteen newly devised symbols (thus evading any risk of confusion with the decimal system). The graphical and phonetic conception of these symbols is meant to render the use of the Bibi-binary "language" simple and fast.

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The description of the language first appeared in ''Les Cerveaux non-humains'' ("Non-human brains"),<ref>Jean-Marc Font, Jean-Claude Quiniou, Gérard Verroust, ''Les Cerveaux non-humains : introduction à l'Informatique'', Denoël, Paris, 1970.</ref> and the system can also be found in ''Boby Lapointe'' by Huguette Long Lapointe.<ref>Huguette Long Lapointe, ''Boby Lapointe'', Encre, Paris, 1980 {{ISBN|2-86418-148-7}}</ref>

== Why ''Bibi''Name ==

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 number|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|date=October 2016}} as the word ''bibi'' in French is slang for "me" or "myself";<ref>{{citation|url=https://madd-bordeaux.fr/sites/BOR-MADD-DRUPAL/files/2020-12/documents/Livret%20anglais_IMPRESSION.pdf|title=Bibi-binaire code|work=Phenomena: Design lifts the veil on the invisible technologies of everyday life|type=Guide booklet|pages=8–9|publisher=Musée des arts décoratifs et du design, Bordeaux|date=November 2018 – March 2019}}</ref> various forms of word play were at the centre of Lapointe's artistic œuvre.

== Pronunciation ==

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HO, HA, HE, HI, BO, BA, BE, BI, KO, KA, KE, KI, DO, DA, DE, DI.

To express any number, it suffices to enumerate the (hexadecimal) digits that make it up. For example: the number written as "2000" in base tendecimal, 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|date=October 2016}} rather than [[two's complement]]. Thus:

* +7 is written 0 0111

* −7 is written 1 1000

and their sum is written as "1&nbsp;1111" (one of two representations of zero in this system; zero can also be written as "0&nbsp;0000").

On modern machines, in classic binary notation, −7 would be written 1&nbsp;1001, and the sum of −7 and 7 would give "0&nbsp;0000"; this "two's complement" system thus needs only a single representation for the number zero.

== References ==