Binary number and overflow is repeated for each digit of significance. Counting progresses as follows: Binary counting follows the same procedure, except that only the two symbols "0" and "1" are available. Thus, after a digit reaches 1 in binary, an increment resets it to 0 but also causes an increment of the next digit to the left: In the binary system, each digit represents an increasing power of 2, with the rightmost digit representing 2, the next representing 2, then 2, and so on. The equivalent decimal representation of a binary number is sum of the powers of 2 which each
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