Binary number to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong (1011–1077) rearranged the hexagrams in a format that resembles modern binary numbers, although he did not intend his arrangement to be used mathematically. Viewing the least significant bit on top of single hexagrams in Shao Yong's square and reading along rows either from bottom right to top left with solid lines as 0 and broken lines as 1 or from top left to bottom right with solid lines as 1 and broken lines
Binary number as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature". (See Bacon's cipher.) John Napier in 1617 described a system he called location arithmetic for doing binary calculations using a non-positional representation by letters. Thomas Harriot investigated several positional numbering systems, including binary, but did not publish his results; they were found later among his papers. Possibly the first publication of the system in Europe was by Juan Caramuel y Lobkowitz, in 1700. Leibniz studied binary numbering in 1679; his work appears in his article "Explication de l'Arithmétique Binaire" (published