A binary reflected Gray code, also known as a "Gray code," is a type of binary code that is used to represent numbers in a way that minimizes the number of changes required to move between consecutive numbers. This is particularly useful in applications where it is important to avoid errors or ambiguities when representing and manipulating numerical data.
The Gray code was first proposed by Frank Gray, an American researcher, in 1947. It is based on the idea of "reflected" binary code, which means that each number is represented by a sequence of binary digits (0s and 1s) that is reflected about the midpoint of the sequence. For example, the Gray code for the number 4 (100 in binary) would be 011, with the leftmost digit being "reflected" to the right side of the sequence.
One of the key advantages of the Gray code is that it allows for a minimal number of changes to be made when transitioning from one number to the next. For example, when moving from the number 4 to the number 5 (101 in binary), only a single digit needs to be changed (from 0 to 1). This is in contrast to standard binary code, which would require two digits to be changed (from 100 to 101). This makes the Gray code less prone to errors and more suitable for use in applications where errors must be avoided, such as in telecommunications or control systems.
In addition to its error-reducing properties, the Gray code is also useful because it can be easily implemented in hardware. This is because the code can be generated using a simple lookup table, which allows for fast and efficient encoding and decoding of numerical data.
Despite its many advantages, the Gray code is not without its limitations. One of the main drawbacks is that it is not as efficient as other codes when it comes to representing large numbers. This is because the Gray code requires more digits to represent larger numbers, which can lead to a decrease in efficiency.
Overall, the binary reflected Gray code is a useful and important tool for representing and manipulating numerical data in a variety of applications. Its error-reducing properties and hardware implementation make it a valuable tool in fields such as telecommunications and control systems, and it continues to be widely used and studied in the field of computer science and engineering.
Consider the following invocations that look completely harmless but generate totally unintended results: generateGray Collections. In this case, the maximum position error will be small, indicating a position adjacent to the actual position. What does it mean when Gray code is not weighted? For many years, Torsten Sillke Norman B. As in the 2-bit case, in the case of 3-bit Gray code, we shift the mirror to the new position below 10 and write the reflected code words below the mirror as shown in Fig. In Gray Code, every sequence of successive bits differs by 1 bit only. Advanced Computer Architecture Laboratory.
. . London, UK: Morgan-Grampain Publishers Limited. PDF from the original on 2020-08-05. Reflective codes: A code is reflective when the code is self complementing. Gray Code is employed in many electronic devices that use rotary switches for position encoders.
Later others started calling it as Gray code. In: Proceedings of the Forty-seventh Annual ACM Symposium on Theory of Computing, STOC 2015, pp. That reflection is conspiciously absent in the code you present here. Gray code is not weighted that means it does not depends on positional value of digit. The four-bit version of this is shown below: Decimal Binary Gray Decimal of Gray 0 0000 0000 0 1 0001 0001 1 2 0010 0011 3 3 0011 0010 2 4 0100 0110 6 5 0101 0111 7 6 0110 0101 5 7 0111 0100 4 8 1000 1100 12 9 1001 1101 13 10 1010 1111 15 11 1011 1110 14 12 1100 1010 10 13 1101 1011 11 14 1110 1001 9 15 1111 1000 8 For decimal 15 the code rolls over to decimal 0 with only one switch change. It needs, however, a lot of space. Centre for Discrete Mathematics and Theoretical Computer Science, PDF from the original on 2020-05-22.
Mineral Point, Wisconsin, USA. Written at Cambridge, Massachusetts, USA. Could you explain it a bit more? In the transition between the two states shown above, all three switches change state. Similarly, you can convert n-bit b nb n-1. Berne, Switzerland: PDF from the original on 2020-12-21.
Berne, Switzerland: Le Bureau International des Administrations Télégraphiques. London, Bath, Melbourne, New York:. In the case of absolute encoders, the indicated position may be far away from the actual position and, in the case of incremental encoders, this can corrupt position tracking. Written at Ames, Iowa, USA. In: Proceedings of the Fourteenth Symposium on Computing: The Australasian Theory, CATS 2008, vol. . The reflected binary code or Gray code is an ordering of the binary numeral system such that two successive values differ in only one bit binary digit.
. So, the Gray code can eliminate this problem easily since only one bit changes its value during any transition between two numbers. When working with sensors that output multiple, gray-encoded values in a serial fashion, one should therefore pay attention whether the sensor produces those multiple values encoded in 1 single gray-code or as separate ones, as otherwise the values might appear to be counting backwards when an "overflow" is expected. What is reflective code? PDF from the original on 2016-10-30. Proceedings of the National Scientific Council, Republic of China, Part A. This paper examines this Gray code function and its inverse and gives simple algorithms to generate both.
Design Methods for Digital Systems. That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two. An example would be testing a piping system for all combinations of settings of its manually operated valves. PDF from the original on 2020-08-05. Sie erfordert allerdings sehr viel Platz. If the most significant bit the inner ring in Figure 1 is rotated enough, it exactly matches the next ring out. 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.
Now, this is exactly the same operation as the reflect-and-prefix method to generate the Gray code. Nutley, New Jersey, USA: PDF from the original on 2020-08-06. This important property of Gray code has many practical applications. Electrical and Computer Engineering Department, College of Engineering,. Error Detecting Logic for Digital Computers 1sted.
Wikipedia tells me that a binary reflected gray code works by concatenating the original list with each element having 0 prepended and the reflected original list with each element having 1 prepended. Gray codes are very useful in the normal sequence of binary numbers generated by the hardware that may cause an error or ambiguity during the transition from one number to the next. If current gray code bit is 0, then copy previous binary code bit, else copy invert of previous binary code bit. With recursion it's especially important to think of the "termination condition" in your code. PDF from the original on 2020-07-25. A Cyclic Progressive Binary-coded-decimal System of Representing Numbers Technical Note MS15.