12 Facts About Unit-distance code

Binary-reflected Gray Unit-distance code represents the underlying scheme of the classical Chinese rings puzzle, a sequential mechanical puzzle mechanism described by the French Louis Gros in 1872.

Balanced Gray Unit-distance code can be constructed, that flips every bit equally often.

Typical use of Gray Unit-distance code counters is building a FIFO data buffer that has read and write ports that exist in different clock domains.

The input and output counters inside such a dual-port FIFO are often stored using Gray Unit-distance code to prevent invalid transient states from being captured when the count crosses clock domains.

One possibility is to start with a balanced Gray Unit-distance code and remove pairs of values at either the beginning and the end, or in the middle.

Related searches

The -Gray Unit-distance code produced by the above algorithm is always cyclical; some algorithms, such as that by Guan, lack this property when k is odd.

Gray code is uniform or uniformly balanced if its transition counts are all equal, in which case we have for all k Clearly, when, such codes exist only if n is a power of 2.

Example, a balanced 4-bit Gray Unit-distance code has 16 transitions, which can be evenly distributed among all four positions, making it uniformly balanced:.

Whereas a balanced 5-bit Gray Unit-distance code has a total of 32 transitions, which cannot be evenly distributed among the positions.

An example of an 8-bit Beckett–Gray Unit-distance code can be found in Donald Knuth's Art of Computer Programming.

Yet another kind of Gray code is the single-track Gray code developed by Norman B Spedding and refined by Hiltgen, Paterson and Brandestini in "Single-track Gray codes".

The Gray Unit-distance code nature is useful, as only one sensor will change at any one time, so the uncertainty during a transition between two discrete states will only be plus or minus one unit of angular measurement the device is capable of resolving.