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The one-bit Gray code is G 1 = (0,1). This can be thought of as built recursively as above from a zero-bit Gray code G 0 = ( Λ ) consisting of a single entry of zero length. This iterative process of generating G n+1 from G n makes the following properties of the standard reflecting code clear:
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)
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.)
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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.
The 5-bit Baudot code used in early synchronous multiplexing telegraphs can be seen as an offset-1 (excess-1) reflected binary (Gray) code. One historically prominent example of offset-64 (excess-64) notation was in the floating point (exponential) notation in the IBM System/360 and System/370 generations of computers.