单词 | Gray Code | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
释义 | Gray CodeAn encoding of numbers so that adjacent numbers have a single Digit differing by 1. A Binary Gray code with To convert a Binary number To convert a binary reflected Gray code ![]() If ![]() ![]() ![]() ![]() and so on. The resulting number ![]() The code is called reflected because it can be generated in the following manner. Take the Gray code 0, 1. Write it forwards,then backwards: 0, 1, 1, 0. Then append 0s to the first half and 1s to the second half: 00, 01, 11, 10. Continuing, write 00,01, 11, 10, 10, 11, 01, 00 to obtain: 000, 001, 011, 010, 110, 111, 101, 100, ... (Sloane's A014550). Each iteration thereforedoubles the number of codes. The Gray codes corresponding to the first few nonnegative integers are given in the followingtable.
The binary reflected Gray code is closely related to the solution of the Towers of Hanoias well as the Baguenaudier. See also Baguenaudier, Binary, Hilbert Curve, Ryser Formula, Thue-Morse Sequence,Towers of Hanoi
Gardner, M. ``The Binary Gray Code.'' Ch. 2 in Knotted Doughnuts and Other Mathematical Entertainments. New York: W. H. Freeman, 1986. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Gray Codes.'' §20.2 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 886-888, 1992. Sloane, N. J. A. Sequence A014550in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html. Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, pp. 111-112 and 246, 1991. |
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