Binary number in 1703) The full title of Leibniz's article is translated into English as the ""Explanation of 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. An example of Leibniz's binary numeral system is as follows: Leibniz interpreted the hexagrams of the I Ching as evidence of binary calculus. As a Sinophile, Leibniz was aware of the I Ching, 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