How a 17th-century philosopher's notebook became the foundation of every digital device on Earth
The I Ching (Book of Changes) is one of the oldest Chinese classic texts, built on a system of 64 hexagrams — figures composed of six stacked horizontal lines, each line being either broken (yin: ⚋) or unbroken (yang: ⚊). With 2⁶ = 64 possible combinations, this is essentially a 6-bit binary system, predating modern binary by nearly 3,000 years. The philosopher Gottfried Wilhelm Leibniz was fascinated by the I Ching and saw in it a confirmation of his binary number system.
Gottfried Wilhelm Leibniz, the German polymath who co-invented calculus, described the modern binary number system in his 1697 essay "Explication de l'Arithmétique Binaire." He demonstrated how any number could be represented using only 0 and 1, and how arithmetic operations (addition, subtraction, multiplication, division) worked in binary. Leibniz saw philosophical and theological significance in binary — to him, 1 represented God and 0 represented nothingness, and the fact that all numbers could be created from these two symbols suggested divine creation from nothing. His system was mathematically complete but had no practical application in his lifetime.
George Boole, a self-taught English mathematician, published "The Mathematical Analysis of Logic" in 1847, introducing a system where variables could only be TRUE or FALSE, and operations like AND, OR, and NOT could produce logical conclusions. Boole's algebra was a purely mathematical curiosity for 90 years. No one connected it to electronic circuits because electronic circuits did not exist yet. But his work provided the exact mathematical framework that binary computers would later require.
In what might be the most important master's thesis in history, 22-year-old Claude Shannon showed that Boolean algebra could be implemented with electrical switching circuits. His 1938 paper "A Symbolic Analysis of Relay and Switching Circuits" proved that any Boolean expression could be built with relays — and therefore, any logical or mathematical operation could be performed by a machine. This single insight bridged pure mathematics and electrical engineering, making binary computers theoretically possible. Shannon went on to found information theory in 1948, where he coined the term "bit" and proved that all information could be measured and transmitted in binary.
From the first transistor at Bell Labs (1947) to the Intel 4004 microprocessor (1971) to the billions of binary devices manufactured in 2026, Leibniz's 300-year-old idea has become the universal language of technology. Binary was the right abstraction, discovered centuries before the hardware existed to implement it. Use our free binary translator to see your own words in the language Leibniz first described in 1697.