Reflected Number Systems

Many papers have been written about the reflected binary system and it is well known in the computer field for analog-to-digital conversion. The method used in creating this system may be extended to systems of bases other than two. It is the purpose of this paper to carry this extension to its logical conclusion. The author describes how reflected systems of different bases may be composed. The equations for translating between the conventional and reflected systems are then derived. It is also demonstrated how the reflected binary system is a special case of reflected number systems and how the general case simplifies for the reflected binary case.