Gray codes are named after Frank Gray, a physicist at Bell Telephone Laboratories who in the 1930's invented the method we now use for broadcasting color TV in a way that's compatible with the black-and-white transmission and reception methods then in existence; that is, when the color signal is received by a black-and-white set, the picture appears in shades of gray.
Martin Gardner [Gard] discusses applications of Gray codes involving the Chinese ring puzzle, the Tower of Hanoi puzzle, and Hamiltonian paths through graphs that represent hypercubes. He also shows how to convert from the decimal representation of an integer to a decimal Gray code representation.
Gray codes are used in position sensors. A strip of material is made with conducting and nonconducting areas, corresponding to the 1's and 0's of a Gray-coded integer. Each column has a conducting wire brush positioned to read it out. If a brush is positioned on the dividing line between two of the quantized positions, so that its reading is ambiguous, then it doesn't matter which way the ambiguity is resolved. There can be only one ambiguous brush, and interpreting it as a 0 or 1 gives a position adjacent to the dividing line.
The strip can instead be a series of concentric circular tracks, giving a rotational position sensor. For this application, the Gray code must be cyclic. Such a sensor is shown in Figure 13-3, where the four dots represent the brushes.