Binary notation

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Gray code A binary (n, n) block code having the following properties:

(a) there are 2n codewords, each of length n bits;

(b) successive codewords differ by the complementation of a single bit, i.e. the Hamming distance between them is unity.

A Gray code can be conveniently represented by its transition sequence, i.e. the ordered list of bit positions that change when moving from one codeword to the next. The Good-de Bruijn graph of a Gray code forms a Hamiltonian cycle. Gray codes are used in encoding the positions of shafts, wheels, etc., in order to avoid the problems that would arise when several digits were supposed to change at the same time.

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binary notation See binary system.