Binary System
The historical journey of the binary system reveals how this mathematical idea evolved into the foundation of modern computing. Thomas Harriot, an English mathematician, sketched around 1600 the first outlines of a numerical representation based solely on 0 and 1. His research on combinations led him to observe that any number could be expressed as a sum of powers of 2. These works, never published, remained in obscurity until the 1920s.
A century later, Gottfried Wilhelm Leibniz rediscovered this system by chance. In the 1670s, while working intensively on number division and prime numbers, binary notation appeared to him as an elegant solution for certain mathematical calculations. Initially, he used it simply to illustrate his theorems without imagining its practical use. In his 1697 letter to the Duke of Brunswick, Leibniz proposed creating a commemorative medal and developed a theological reading of binary where 1 symbolizes being and 0 represents nothingness. This medal never came to fruition, but the letter launched a series of publications on this system.
In 1703, in the Mémoires de l'Académie Royale des Sciences, Leibniz published his "Explanation of Binary Arithmetic". This text outlined the principles of the system and demonstrated how to perform basic operations while acknowledging the cumbersomeness of these long sequences of 0s and 1s for everyday use.
The 18th century saw mathematicians like Jean Bernoulli and Leonard Euler take up the binary system. Euler notably used it to study the properties of numbers of the form 2n + 1. Other researchers established connections between this system and other number bases such as octal and hexadecimal.
The practical application of binary emerged in the 19th century with the advent of telecommunications. Morse's telegraph, patented in 1837, relied on two electrical states, presence or absence of current, to transmit information. Its code combined dots and dashes, foreshadowing the future use of binary in digital communications. Émile Baudot took this a step further in 1870 with his explicitly binary telegraphic code. In 1901, Charles Bouton demonstrated the usefulness of binary for analyzing the game of Nim, paving the way for its application in game theory.
The revolution came with 20th-century electronics. The Eccles-Jordan flip-flop circuit, created in 1919, gave physical existence to the 0 and 1 states. This crucial invention made the first binary memory circuits possible. In 1937, Claude Shannon demonstrated in his thesis the connection between Boolean algebra and the binary system for designing electronic switching circuits.
Early computers like ENIAC (1946) still operated in decimal, with ten vacuum tubes per digit. The 1947 Burks-Goldstine-von Neumann report changed the game by demonstrating binary's advantages: simpler circuits, increased reliability, and natural harmony with logical operations. This recommendation influenced all subsequent computers.
The 1950s and 1960s saw the rise of electronic memories, strengthening binary's dominance. Magnetic core memories and later semiconductor memories naturally relied on two distinct states. Some manufacturers attempted to explore four- or sixteen-level memories in the 1970s and 1980s; Intel experimented with four-level ROMs in certain processors, but these attempts remained marginal compared to the robustness of binary storage.
Binary extended beyond computer hardware. Digital telecommunications adopted it for its noise resistance and signal regeneration capability. Optical media such as CD-ROMs and DVD-ROMs also used it. Its success stems from its conceptual simplicity, which makes circuits more reliable, its compatibility with Boolean algebra, which makes it the natural language of logical operations, and its robustness against disturbances, explained by the distinction of only two states.
Research on other numerical systems has not disappeared, however. The ternary system (with three states) was the subject of extensive studies in the Soviet Union in the 1950s. More recently, quantum computing has opened new horizons with its qubits capable of existing in a superposition of states. Despite these alternatives, the binary system remains the soul of classical computing. Its ability to encode any information using only two symbols gives it remarkable universality.