The Bibi-binary system for numeric notation (in French système Bibi-binaire, or abbreviated "système Bibi") is a
hexadecimal numeral system first described in 1968 by singer/mathematician
Robert "Boby" Lapointe (1922–1972). At the time, it attracted the attention of
André Lichnerowicz
André Lichnerowicz (January 21, 1915, Bourbon-l'Archambault – December 11, 1998, Paris) was a noted French differential geometer and mathematical physicist of Polish descent. He is considered the founder of modern Poisson geometry.
Biograp ...
, then engaged in studies at the
University of Lyon
The University of Lyon (french: Université de Lyon), located in Lyon and Saint-Étienne, France, is a center for higher education and research comprising 11 members and 24 associated institutions. The three main universities in this center are: C ...
. It found some use in a variety of unforeseen applications: stochastic poetry, stochastic art, colour classification, aleatory music, architectural symbolism, etc.
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.
The description of the language first appeared in ''Les Cerveaux non-humains'' ("Non-human brains"), and the system can also be found in ''Boby Lapointe'' by Huguette Long Lapointe.
[Huguette Long Lapointe, ''Boby Lapointe'', Encre, Paris, 1980 ]
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
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two digits (0 and 1)
* Binary function, a function that takes two arguments
* Binary operation, a mathematical operation that ta ...
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, 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 (HBKD) and four vowels (OAEI), one obtains sixteen combinations:
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 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, rather than
two's complement
Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value (the leftmost bit in big- endian ...
. 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.
References
{{reflist, 30em
External links
Conversion en ligne décimal ↔ bibi-binaire(in French)
Hexadecimal numeral system
Positional numeral systems