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
Signed number representations as the largest positive number that can be represented, and vice versa if the word has an odd number of bits. The following table shows the positive and negative integers that can be represented using four bits. Same table, as viewed from "given these binary bits, what is the number as interpreted by the representation system": Google's Protocol Buffers "zig-zag encoding" is a system similar to sign-and-magnitude, but uses the least significant bit to represent the sign and has a single representation of zero. This allows a variable-length quantity encoding intended for nonnegative (unsigned) integers to be used efficiently for