Binary code The modern binary number system, the basis for binary code, was invented by Gottfried Leibniz in 1689 and appears in his article "Explication de l'Arithmétique Binaire". The full title is translated into English as the "Explanation of the binary arithmetic", which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi." (1703). Leibniz's system uses 0 and 1, like the modern binary numeral system. Leibniz encountered the "I Ching" through French Jesuit Joachim Bouvet and noted with fascination how its hexagrams correspond to
Binary GCD algorithm Binary GCD algorithm The binary GCD algorithm, also known as Stein's algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction. Although the algorithm was first published by the Israeli physicist and programmer Josef Stein in 1967, it may have been known in 1st-century China. The algorithm reduces the problem of finding the GCD by repeatedly applying these identities: The algorithm requires O(n) worst-case time, where n is the number of bits in the larger of