Skew binary number system Skew binary number system The skew binary number system is a non-standard positional numeral system in which the "n"th digit contributes a value of formula_1 times the digit (digits are indexed from 0) instead of formula_2 times as they do in binary. Each digit has a value of 0, 1, or 2. Notice that a number can have many skew binary representations. For example, a decimal number 15 can be written as 1000, 201 and 122. Each number can be written uniquely in skew binary canonical form where there is only at most one instance of the digit 2, which
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