16 Facts About Gray code

In principle, there can be more than one such code for a given word length, but the term Gray code was first applied to a particular binary code for non-negative integers, the binary-reflected Gray code, or BRGC.

Frank Gray introduced the term reflected binary code in his 1947 patent application, remarking that the code had "as yet no recognized name".

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

The "PCM tube" apparatus that Gray patented was made by Raymond W Sears of Bell Labs, working with Gray and William M Goodall, who credited Gray for the idea of the reflected binary code.

In contrast, the Gray code used by position encoders ensures that the codes for any two consecutive positions will differ by only one bit and, consequently, only one bit can change at a time.

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

Typical use of Gray 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 code to prevent invalid transient states from being captured when the count crosses clock domains.

One way to increment a Gray code number is to convert it into ordinary binary code, add one to it with a standard binary adder, and then convert the result back to Gray code.

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

The -Gray 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 code has 16 transitions, which can be evenly distributed among all four positions, making it uniformly balanced:.

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

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

The Gray 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.