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State diagram of 4-bit system, Gray code traverses just over its edges: Changes value always just of one bit step by step. The picture and this template share the same colors. See also: Template: Hexadecimal table; Template:Logical connectives table and Hasse diagram; commons:Category:Colored nibbles (blue, green, white)
One such type of Gray code is the n-ary Gray code, also known as a non-Boolean Gray code. As the name implies, this type of Gray code uses non-Boolean values in its encodings. For example, a 3-ary Gray code would use the values 0,1,2. [31] The (n, k)-Gray code is the n-ary Gray code with k digits. [63]
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Powers of the 4-bit Gray code permutation (compare A195467) The permutation matrices are arranged in a cycle graph of the cyclic group Z 4 like , but the identity is in the top left position, so that the symmetric matrices are mirrored at the diagonal. Cayley table of the cyclic group (The orange vectors are the same as in the cycle graph.)
A Hamiltonian cycle on a tesseract with vertices labelled with a 4-bit cyclic Gray code. Every hypercube Q n with n > 1 has a Hamiltonian cycle, a cycle that visits each vertex exactly once. Additionally, a Hamiltonian path exists between two vertices u and v if and only if they have different colors in a 2-coloring of the graph.
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This is a list of some binary codes that are (or have been) used to represent text as a sequence of binary digits "0" and "1". Fixed-width binary codes use a set number of bits to represent each character in the text, while in variable-width binary codes, the number of bits may vary from character to character.
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