Binary star size, luminosity, and approximate shape) of both members of the system. While a number of binary star systems have been found to harbor extrasolar planets, such systems are comparatively rare compared to single star systems. Observations by the Kepler space telescope have shown that most single stars of the same type as the Sun have plenty of planets, but only one-third of binary stars do. According to theoretical simulations, even widely separated binary stars often disrupt the discs of rocky grains from which protoplanets form. On the other hand, other simulations suggest that the presence of a binary companion can
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