Martin Gardner wrote a popular account of the Gray code in his August 1972 Mathematical Games column in Scientific American. Similarly, the so called Towers of Bucharest and Towers of Klagenfurt game configurations yield ternary and pentary Gray codes.
It can serve as a solution guide for the Towers of Hanoi problem, based on a game by the French Édouard Lucas in 1883.
The binary-reflected Gray code represents the underlying scheme of the classical Chinese rings puzzle, a sequential mechanical puzzle mechanism described by the French Louis Gros in 1872. Reflected binary codes were applied to mathematical puzzles before they became known to engineers. History and practical application Mathematical puzzles The Gray code was sometimes attributed, incorrectly, to Elisha Gray. Other names include "cyclic binary code", "cyclic progression code", "cyclic permuting binary" or "cyclic permuted binary" (CPB). A 1954 patent application refers to "the Bell Telephone Gray code". Two different 1953 patent applications use "Gray code" as an alternative name for the "reflected binary code" one of those also lists "minimum error code" and "cyclic permutation code" among the names. This makes the transmission system less susceptible to noise.ĭespite the fact that Stibitz described this code before Gray, the reflected binary code was later named after Gray by others who used it. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point. For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. In modern digital communications, Gray codes play an important role in error correction. This is called the cyclic or adjacency property of the code. Visualized as a traversal of vertices of a tesseract Decimalįor decimal 15 the code rolls over to decimal 0 with only one switch change. These codes are also known as unit-distance, single-distance, single-step, monostrophic or syncopic codes, in reference to the Hamming distance of 1 between adjacent codes. This problem can be solved by changing only one switch at a time, so there is never any ambiguity of position, resulting in codes assigning to each of a contiguous set of integers, or to each member of a circular list, a word of symbols such that no two code words are identical and each two adjacent code words differ by exactly one symbol. If the output feeds into a sequential system, possibly via combinational logic, then the sequential system may store a false value. When the switches appear to be in position 001, the observer cannot tell if that is the "real" position 1, or a transitional state between two other positions. Even without keybounce, the transition might look like 011 - 001 - 101 - 100. In the brief period while all are changing, the switches will read some spurious position. In the transition between the two states shown above, all three switches change state. The problem with natural binary codes is that physical switches are not ideal: it is very unlikely that physical switches will change states exactly in synchrony. If that device uses natural binary codes, positions 3 and 4 are next to each other but all three bits of the binary representation differ: Many devices indicate position by closing and opening switches.
Razorsql registration code 5.6.4 tv#
Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems. That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two. In Gray code, these values are represented as " 001" and " 011". The reflected binary code ( RBC), also known just as reflected binary ( RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit).įor example, the representation of the decimal value "1" in binary would normally be " 001" and "2" would be " 010". Ordering of binary values, used for positioning and error correction
0 kommentar(er)
