Bibi-binary

Bibi-binary, also known as the Bibi-binaire system, is a hexadecimal numeral system invented in 1968 by the French singer, actor, and mathematician Robert "Boby" Lapointe (1922–1972) to provide a phonetic and mnemonic representation of base-16 numbers.^[1][2] The system assigns each of the 16 digits (0 through 15) a unique syllable formed by combining four consonants—H, B, K, and D—with four vowels—O, A, E, and I—resulting in pronounceable syllables like "ho" for 0, "ha" for 1, "he" for 2, up to "di" for 15.^[3][4] This structure makes it logical and easy to memorize, as the syllables follow a systematic pattern where the consonants represent multiples of 4 (H for 0, B for 4, K for 8, D for 12) and the vowels represent the offset within the group (O for 0, A for 1, E for 2, I for 3).^[5] Lapointe, known for his humorous songs and wordplay, developed Bibi-binary as a playful yet practical tool for encoding binary data in a more human-readable and speakable form, contrasting with the abstract digits of traditional hexadecimal notation like 0-9 and A-F.^[2][6] He patented the system in 1968, describing it as a "shorter binary code" that could represent hexadecimal values through graphic symbols and phonetic pronunciation, facilitating its use in mathematics, computing, and even artistic performances.^[1][3] For example, the decimal number 2000, which is 7D0 in standard hexadecimal, becomes "bi-da-ho" in Bibi-binary, allowing seamless verbal communication of complex numbers.^[4] The system's legacy endures through educational tools, programming libraries, and cultural tributes to Lapointe, such as the annual Printival Boby Lapointe festival in Pézenas, France, where it highlights his blend of mathematics and entertainment.^[5][7] Though not widely adopted in mainstream computing, Bibi-binary remains a notable example of creative numeral systems, influencing discussions on alternative notations for binary and hexadecimal data in recreational mathematics.^[6]

History

Invention by Boby Lapointe

Robert "Boby" Lapointe (1922–1972), born Robert Lapointe in Pézenas, France, was a multifaceted figure renowned for his careers as a singer-songwriter, actor, and mathematician.^[2] From an early age, he demonstrated exceptional aptitude in mathematics and linguistics, earning a baccalauréat in elementary mathematics in 1940 and pursuing advanced studies in Toulouse before World War II interrupted his education.^[8] After being conscripted into forced labor in Austria during World War II, from which he escaped twice, and working in various trades—including as a diver and antenna installer—Lapointe transitioned to the arts in the late 1950s, gaining fame for his witty, wordplay-filled chansons while maintaining a lifelong passion for mathematical pursuits.^[2] Lapointe conceived Bibi-binary in 1968 as a hexadecimal numeral system designed to logically notate numbers in a manner compatible with binary encoding, particularly useful in early computing contexts.^[8] He finalized the system in March of that year during his explorations of mathematical entertainments, blending his technical expertise with his humorous sensibility.^[8] The invention stemmed from his desire to create an alternative to standard hexadecimal notation (0-9, A-F).^[2] Central to Lapointe's motivation was enabling easy pronunciation and visualization of complex numbers through a syllabic, letter-based representation that produced amusing phonetic results, reflecting his playful approach to mathematics.^[9] This innovation allowed for intuitive handling of base-16 values—each grouping four binary digits—while avoiding the ambiguities of conventional symbols, making it a poetic enhancement suited to both technical and artistic expression.^[2]

Patent and early publications

The Bibi-binary system was formally patented by Robert Lapointe, known professionally as Boby Lapointe, under the title "Procédé de codification de l'information." The patent application was filed on 28 March 1968 with the Institut National de la Propriété Industrielle (INPI) and published on 21 April 1969 as Brevet n° 1.569.028. This legal protection covered the method for encoding information using a hexadecimal notation system derived from binary principles, emphasizing its utility for simplified numeric representation and computation. The invention garnered early academic interest from prominent mathematician André Lichnerowicz, who praised the system.^[10] Lichnerowicz, a leading figure in differential geometry and mathematical physics, included Lapointe's work in a key anthology he edited, providing one of the system's first scholarly endorsements. The inaugural major publication of Bibi-binary appeared in 1970 within Les Cerveaux non-humains: Introduction à l'informatique, a collection edited by Lichnerowicz and published by Éditions Denoël. Lapointe contributed a chapter titled "Recherches pour un langage," detailing the system's phonetic and graphic elements as a bridge between human-readable notation and machine-oriented binary processes. This exposure in a volume focused on early informatics helped position Bibi-binary as an innovative tool amid growing interest in computer science. Lapointe's death from cancer on 29 June 1972 curtailed the system's immediate dissemination and practical adoption during his lifetime.^[11] Nonetheless, the patent and publication ensured its preservation within mathematical and computational literature, where it has since been referenced for its creative approach to numeral systems.^[12]

Etymology

Origin of the name

The full name of the system is système Bibi-binaire, as documented in the patent filed by Robert Lapointe (known as Boby Lapointe) on March 28, 1968, and granted the following year.^[13] The component "Bibi" draws from French slang, in which bibi serves as a familiar, affectionate term for "me" or "myself," embodying Lapointe's characteristic wordplay and self-referential humor in titling his creation.^[14] This linguistic choice aligns with Lapointe's artistic style, where puns and personal quirks frequently infused his mathematical and musical endeavors.^[2] The "binaire" element underscores the system's reliance on binary bit patterns to encode hexadecimal values, with each of the 16 digits derived from unique 4-bit binary sequences that inform their symbols and pronunciations.^[3] Within Lapointe's own publications and performances, the system was routinely shortened to système Bibi, a convention that persisted in later scholarly and educational references to the notation.^[2]

Connection to binary concepts

The name "Bibi-binary" reflects a deliberate mathematical connection to binary systems, rooted in the structure of powers of 2. Robert Lapointe conceptualized base-16 as an extension of binary (base-2) notation: just as "binary" describes base-2, "bi-binary" denotes base-4 ($2^2$22), and "bibi-binary" signifies base-16 ($(2^2)^2$(22)2 or equivalently $2^{2^2} = 2^4 = 16$222=24=16). This layered interpretation underscores the system's foundation in binary arithmetic, where each digit encapsulates multiple binary units for compactness.^[15] Central to this connection is the role of Bibi-binary in efficiently representing binary data through nibble grouping. A nibble consists of four binary digits, yielding $2^4 = 16$24=16 possible combinations, which align directly with one Bibi-binary digit. This grouping allows binary strings to be condensed without loss of information, facilitating easier manipulation and visualization in computational tasks. For instance, the binary sequence 1011 (decimal 11) is represented as a single Bibi-binary symbol corresponding to its hexadecimal equivalent B.^[9] In distinction from pure binary notation, which relies solely on 0s and 1s and often results in verbose strings for larger values, Bibi-binary functions as a specialized hexadecimal overlay optimized for human readability. It preserves the exactitude of binary while mitigating issues like the interpretive ambiguities that arise in decimal systems, particularly in early computing contexts where binary-hexadecimal mappings were emerging. This design emphasizes conceptual efficiency over exhaustive bit-level detail, aligning with broader trends in numeral systems for machine-readable data.^[9]

System Overview

Base and purpose

Bibi-binary is a hexadecimal numeral system, operating in base-16, which encodes numerical values using 16 distinct digits to represent quantities from 0 to 15 in a single symbol. This base allows for a more compact notation compared to binary or decimal systems, particularly suited for handling computer-related data where powers of 2 are fundamental.^[9] The primary purpose of Bibi-binary is to represent binary data in a compact and unambiguous manner, enabling efficient grouping and interpretation of binary sequences without the ambiguities introduced by standard alphanumeric notations. Each digit in the system corresponds precisely to four binary bits, or a nibble, which simplifies conversions between binary and hexadecimal formats by aligning directly with binary structure— for instance, an 8-bit byte becomes two hexadecimal digits. This nibble-based encoding reduces the length of representations while preserving exact binary fidelity, making it advantageous for computational tasks involving low-level data manipulation.^[9][16] A key design feature of Bibi-binary is its avoidance of reuse of standard Latin letters or numerals, instead utilizing unique symbols and associated phonetic elements constructed from a limited set of consonants (H, B, K, D) and vowels (O, A, E, I) to form syllable-like pairs. This approach ensures no overlap with decimal digits 0-9, promoting clarity in written computation, verbal communication, and visual distinction from everyday text or numbers.^[9]

Structure of digits

Bibi-binary utilizes 16 distinct digits, each uniquely representing the integer values from 0 to 15, which align with the hexadecimal range 0 through F. These digits are derived from binary quartets, wherein each group of 4 bits (a nibble) is systematically mapped to a corresponding symbol and phonetic syllable, enabling a compact representation of binary data in a human-readable form.^[9] The core organizational framework of these digits employs a 4×4 grid structure, leveraging four consonants—H, B, K, and D—to denote the rows (corresponding to base-4 increments of 0 to 3) and four vowels—O, A, E, and I—to denote the columns (likewise spanning 0 to 3). This combinatorial approach generates all 16 unique syllable pairs, such as HO (row H with column O), BA (row B with column A), KE (row K with column E), and DI (row D with column I), ensuring each position in the grid captures a precise value within the hexadecimal spectrum.^[9] This grid-based composition not only facilitates intuitive syllable formation for pronunciation but also mirrors the quaternary (base-4) subdivision inherent in grouping binary digits, promoting ease of conversion between binary, hexadecimal, and Bibi-binary notations.^[9]

Representations

Visual symbols

The visual symbols of Bibi-binary consist of 16 unique graphical designs, each corresponding to one of the hexadecimal digits from 0 to 15, constructed from the 4-bit binary representation arranged within a 2x2 square grid.^[9] These symbols emphasize the binary structure by visually encoding the positions of set bits (1s), providing a compact and intuitive alternative to standard numerals while facilitating recognition of binary patterns. The design prioritizes simplicity and distinctiveness, ensuring each symbol is easily differentiable at a glance. Symbol construction begins with the 2x2 grid, where the four bits are arranged to form the basis of the glyph. Lines or marks are placed only in cells with set bits, forming the core shape; empty cells (0s) may incorporate connecting curves to maintain the square's integrity and enhance fluidity. Set bits (1s) are typically represented by straight lines or angles, while 0 bits use curves.^[4] This mapping process translates the binary pattern directly into a visual form without requiring arithmetic computation, simply by plotting the active bit locations to create a cohesive glyph. These examples illustrate how the system balances minimalism for low values with structured complexity for higher ones, aiding quick visual parsing in applications like notation or puzzles.^[9]

Syllabic pronunciation

The syllabic pronunciation system of Bibi-binary assigns a unique syllable to each of the 16 hexadecimal digits (0 through F), constructed from four consonants (H, B, K, D) and four vowels (O, A, E, I). This creates a phonetic representation that corresponds directly to numerical values, where the consonant provides the base value (H=0, B=4, K=8, D=12) and the vowel adds the offset (O=0, A=1, E=2, I=3), resulting in additive combinations for each digit.^[9][17][7] The full mapping of syllables to values is as follows: Pronunciation rules emphasize clarity and rhythm: the 'H' is typically silent (e.g., "HO" as "o"), the 'E' is pronounced as a closed "e" (avoiding open "è" or accented "é" where possible), and each syllable is delivered in a single beat to allow fluid, rhythmic reading of multi-digit numbers.^[17][7] This structure ensures no ambiguous sounds, making the system ideal for oral transmission.^[9] The purpose of this syllabic system is to enable easy verbal articulation of complex numbers, particularly in performative contexts like songs, where the rhythmic flow enhances memorability and entertainment without sacrificing precision.^[9][17] For instance, the decimal number 123, which equals 7B in hexadecimal, is pronounced as "BI KI," forming a two-beat phrase.^[9]

Applications

Use in Lapointe's creative works

Boby Lapointe (1922–1972), a French singer, songwriter, and mathematician, integrated Bibi-binary into his musical compositions following its invention in 1968, employing it to give musicality to numbers.^[4] This approach aligned with his style of constrained art, similar to Oulipo techniques, where numerical systems served as playful constraints for artistic expression.^[2][3] Lapointe used Bibi-binary in his works, as in lyrical phrases like "bibi plus koka égale hahoho" to illustrate simple arithmetic (119 + 137 = 256).^[4][9] The cultural impact of Bibi-binary in Lapointe's oeuvre lay in its promotion of mathematics as a source of joy and surprise, reinforcing his reputation as a cabaret artist who democratized complex ideas through humor. By embedding the system in his post-1968 repertoire, Lapointe encouraged listeners to appreciate numerical poetry, influencing perceptions of math in French popular culture as an entertaining rather than esoteric pursuit. His works not only entertained but also subtly educated, fostering a legacy of interdisciplinary creativity that merged computation with chanson.^[1][2]

Modern digital implementations

In the digital era, Bibi-binary has seen adaptations through online tools that facilitate conversions between its hexadecimal representation and conventional numeral systems. A prominent example is the Bibi-binary code converter on dCode.fr, which translates sequences of Bibi syllables into decimal or hexadecimal equivalents, supporting both encoding and decoding operations. For instance, the sequence "DE KO DE" converts to the hexadecimal value 0xE8E, equivalent to 3726 in decimal, demonstrating the system's utility for quick base-16 manipulations with a playful phonetic interface.^[9] Programming libraries have further integrated Bibi-binary for systematic numeral conversions. The Rust crate bibicode, published in 2021, provides functionality to shift numbers between various bases, including Bibi-binary, by using binary as an intermediate pivot radix to ensure accurate and efficient transformations without direct base-to-base computation. This approach leverages binary's simplicity for handling arbitrary numeral systems, with Bibi-binary predefined as one of its supported formats, enabling developers to incorporate it into applications for data encoding or educational purposes.^[18] Digital fonts and visualization projects on GitHub have enabled the rendering of Bibi-binary symbols in modern software. For example, projects such as Etash212010/bibi-binaire-cerveaux-non-humains explore the system's presentation in the 1970 book Les Cerveaux non-humains, providing digital interfaces for understanding its historical context.^[19] Additionally, as of GNU Unifont version 15.0.01 (September 2023), Unicode code points in the range U+EBE0–U+EBEF have been assigned to Bibi-binary notations, facilitating their display in text editors and web browsers across platforms.^[20] Recent interest in Bibi-binary has manifested in online developer communities, with discussions on Hacker News in 2023 highlighting its potential for encoding binary data in creative coding projects, such as procedural art generation or alternative data visualization. A Reddit post in May 2025 introduced the system in the context of neography, reviving interest in its phonetic and symbolic aspects.^[21][22]