This might be acceptable in a linear encoder which wouldn't need to wrap. It would be possible to generate a Gray-ish code that didn't have this property if, for example, the number of steps was not even or a power of 2. That is it can wrap while still maintaining only one-bit change. There's a generic definition about the cyclic nature of the Gray code further down the Wikipedia Gray code article mentioned in altai's answer: "The last entry in Gn differs by only one bit from the first entry. This group is called the factor group or quotient group and is denoted. Is well-defined, and the cosets of H form a group under this operation. Step-by-Step Solution: Step 1 of 3 The objective is to prove a factor group of a cyclic group is cyclic. This prevents errors on transitions from one code to the adjacent one due to misalignment of sensors, etc. Prove that a factor group of a cyclic group is cyclic. The bits are arranged so that only one bit changes at a time. The cyclic pattern of each bit is clearly visible on this optical absolute encoder disc.Įach bit has a repeating on-off pattern with a 50% mark-space ratio. This is most obvious in an encoder disc.įigure 1. You haven't given a reference for the 'cyclic code' terminology but there is certainly a cyclic patter.
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