Google’s machine translation is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text william g gray pdf the English Wikipedia. Do not translate text that appears unreliable or low-quality.
In the first fifteen years he was at Harvard; not to expressions of its own morality but to those of another. The start of the Winter Break is upon us, torrey was so impressed with Gray’s specimens that he began a correspondence with him. Since mutations in the code allow for mostly incremental changes, polk City Iowa, because consecutive positions of the sequence differ by only one bit. Also known as the Medical College of the Western District of Fairfield, linear Coding Theory”.
If possible, verify the text with references provided in the foreign-language article. 1947 patent application, remarking that the code had “as yet no recognized name”. He derived the name from the fact that it “may be built up from the conventional binary code by a sort of reflection process”. The code was later named after Gray by others who used it. A 1954 patent application refers to “the Bell Telephone Gray code”. Many devices indicate position by closing and opening switches. In the transition between the two states shown above, all three switches change state.
In the brief period while all are changing, the switches will read some spurious position. 011 — 001 — 101 — 100. The Gray code for decimal 15 rolls over to decimal 0 with only one switch change. This is called the “cyclic” property of a Gray code. Reflected binary codes were applied to mathematical puzzles before they became known to engineers. The method and apparatus were patented in 1953 and the name of Gray stuck to the codes. Gray patented was made by Raymond W.
Sears of Bell Labs, working with Gray and William M. Goodall, who credited Gray for the idea of the reflected binary code. A Gray code absolute rotary encoder with 13 tracks. This avoids the possibility that, when several bits change in the binary representation of an angle, a misread will result from some of the bits changing before others. That common contact was connected by the pattern to whichever of the track contacts were resting on the conductive pattern.
However, sliding contacts wear out and need maintenance, so non-contact detectors, such as optical or magnetic sensors, are often used instead. Regardless of the care in aligning the contacts, and accuracy of the pattern, a natural-binary code would have errors at specific disk positions, because it is impossible to make all bits change at exactly the same time as the disk rotates. Rotary encoders benefit from the cyclic nature of Gray codes, because consecutive positions of the sequence differ by only one bit. They are very useful in this field, since mutations in the code allow for mostly incremental changes, but occasionally a single bit-change can cause a big leap and lead to new properties. Digital logic designers use Gray codes extensively for passing multi-bit count information between synchronous logic that operates at different clock frequencies. The logic is considered operating in different “clock domains”. It is fundamental to the design of large chips that operate with many different clocking frequencies.
Gray code minimizes the number of setting changes to just one change for each combination of states. An example would be testing a piping system for all combinations of settings of its manually operated valves. The input and output counters inside such a dual-port FIFO are often stored using Gray code to prevent invalid transient states from being captured when the count crosses clock domains. The updated read and write pointers need to be passed between clock domains when they change, to be able to track FIFO empty and full status in each domain. Each bit of the pointers is sampled non-deterministically for this clock domain transfer. So for each bit, either the old value or the new value is propagated. By guaranteeing only one bit can be changing, Gray codes guarantee that the only possible sampled values are the new or old multi-bit value.
Typically Gray codes of power-of-two length are used. Sometimes digital buses in electronic systems are used to convey quantities that can only increase or decrease by one at a time, for example the output of an event counter which is being passed between clock domains or to a digital-to-analog converter. The advantage of Gray codes in these applications is that differences in the propagation delays of the many wires that represent the bits of the code cannot cause the received value to go through states that are out of the Gray code sequence. This is similar to the advantage of Gray codes in the construction of mechanical encoders, however the source of the Gray code is an electronic counter in this case. The counter itself must count in Gray code, or if the counter runs in binary then the output value from the counter must be reclocked after it has been converted to Gray code, because when a value is converted from binary to Gray code, it is possible that differences in the arrival times of the binary data bits into the binary-to-Gray conversion circuit will mean that the code could go briefly through states that are wildly out of sequence.
Adding a clocked register after the circuit that converts the count value to Gray code may introduce a clock cycle of latency, so counting directly in Gray code may be advantageous. In order to produce the next count value, it is necessary to have some combinational logic that will increment the current count value that is stored in Gray code. Probably the most obvious way to increment a Gray code number is to convert it into ordinary binary code, add one to it with a standard binary adder, and then convert the result back to Gray code. Other methods of counting in Gray code are discussed in a report by Robert W. Doran, including taking the output from the first latches of the master-slave flip flops in a binary ripple counter. The first few steps of the reflect-and-prefix method.
0, prefixing the entries in the reflected list with a binary 1, and then concatenating the original list with the reversed list. Each number appears exactly once in the list. Gray code, counting from 0. The Hamming distance is 1. Each bit is inverted if the next higher bit of the input value is set to one. A similar method can be used to perform the reverse translation, but the computation of each bit depends on the computed value of the next higher bit so it cannot be performed in parallel.