Absolute Position Encoders Using Double-Track Gray Codes

A slight increase in the physical dimensions of the single-track gray code (STGC) encoders in exchange for using fewer reading heads (fewer bits) is the subject that is addressed in this article. A construction algorithm is proposed to combine two STGCs in order to obtain a double-track gray code (DTGC). The proposed algorithm can be repeatedly used to obtain triple-track gray codes (TTGCs) and so on. The proposed algorithm can be used to quickly obtain very high period codes with a sufficiently small number of tracks. Furthermore, it can be used to obtain desirable codes by trading off the number of tracks and the length of the code. For a given desired period, this tradeoff may provide the opportunity of using fewer bits compared to STGCs. In particular, length n period <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{n}$ </tex-math></inline-formula> encoders can be constructed with almost half the number of tracks of the corresponding conventional gray code encoders.