Abstract: A pseudorandom sequence is bidirectionally synthesized for any arbitrary encoding resolution. The synthesis of such a pseudorandom sequence includes providing within the sequence a conventionally disallowed code (e.g., an all zeroes or an all ones code) and/or pinching out one or more codes of the pseudorandom sequence to provide a sequence that is other than a maximal length sequence. The synthesizing capability can be included in a decoder that accepts, as input, tags of an encoded pseudorandom sequence, and outputs therefrom the absolute positions of those tags.

Abstract: A system for measuring the accuracy of a machines and mechanisms having a driving member and a driven member is disclosed. The absolute position of the driving member is determined using a first absolute encoder operatively engaged to the driving member. The actual absolute position of the driven member is also determined using a second absolute encoder operatively engaged to the driven member. The theoretical absolute position of the driven member is then calculated based upon the absolute position of the driving member. The actual absolute position of the driven member is compared to the theoretical absolute position of the driven member, preferably by subtraction, to determine the accuracy of the machines and mechanisms. Optical absolute encoders may be used and the process may be performed using a microprocessor which may utilize a ratio function to calculate the theoretical absolute position of the driven member based upon the absolute position of a driving member.