Gray codes are binary codes with a 1-bit difference between successive codes which makes it reduces the error occurrence and provides accuracy. The gray codes have its applications in different fields like digital circuits, Karnaugh maps, signal processing, error detection, angle measuring devices, genetic algorithms etc. In this article, we will explore all the applications of gray codes in detail.
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The codes in which the consecutive codes have only 1-bit changes are called as gray codes . In other words, the codes in which neighboring numbers differ from each other by 1-bit are referred to as gray codes. The gray codes are also called as the reflected binary codes.
If Bn …. B2, B1 represents the binary code and Gn, …, G2, G1 represents the gray code then the expression for converting binary code to gray code is given by:
Gn = Bn
Gn-1 = Bn XOR Bn-1
…
G2 = B3 XOR B2
G1 = B2 XOR B1
Below table gives conversion of 4-bit binary code to gray code.
Gray codes have multiple applications in different fields like electronics, computers, signal processing and many more. Some of the applications of gray code are given below.
Karnaugh map uses gray code because the difference between consecutive cells of K-map should be of 1-bit only so that the adjacent cells can be grouped to minimize and simplify the Boolean function. Karnaugh maps also called K-maps are the graphical method to minimize and simplify the Boolean functions. The Karnaugh maps axes use gray code because it has only 1- bit change which decreases the occurrence of errors while simplifying the Boolean functions .
Below is the K-map representation in which gray code is used in its axes. The gray code helps in identifying the adjacent cells that can be grouped which makes the simplification of the Boolean function easier. Gray codes play an important role in Karnaugh maps due to its 1-bit change property among its consecutive codes.
Gray codes are used in different signal processing because it has only 1- bit difference between its consecutive values which reduces the error occurrences. Gray codes are mainly used when there is rapid change in the values and the single bit property of gray code decreases the error frequency.
The gray codes are used to represent the input signal and output voltage because it minimizes the changes in the voltage and signal. In analog to digital converters (ADC) and digital-to-analog converters (DAC) the gray codes reduce the probability of errors that arises due to small variations in the voltages or signal level. These gray codes are used in digital hardware like rotatory encoders.
Digital rotatory encoders use gray codes because the changes in the values are very quick in these types of rotatory shafts and due to hardware and interfaces errors may occur. So, the gray code is used as it minimizes the error occurrences and provides the accurate location. Below diagram shows the application of gray code in rotatory mechanical and optical encoders . Below diagram represents application of gray code in .
Use of Gray Codes in Digital Rotatory Encoders
Angle measuring device uses gray codes as it decreases the probability of error. Gray code avoids the angle measuring misread and gives the accurate angle measurements. The accuracy of the gray code helps in positioning the angular position sensors and providing the cheaper alternative of optical shaft resolution. Gray codes provide the precise and reliable tracking of the incremental changes that reduces the probability of the misread and errors.
The gray codes minimize the errors at the time of the state change in the angle measuring devices. The gray code plays an important in handling the angle measuring devices due to its 1-bit change property which provides the less occurrences of angle misread and helps in the reading more precisely. Below diagram represents the application of gray codes in angle measuring devices.
Encoder gray code and signal output
Genetic algorithms use gray codes because the genetic algorithms allow only incremental changes in the code. Since the gray code has single bit change property it is used in these types of algorithms. The gray code minimizes the hamming distances and hamming walls in the genetic algorithms. Gray codes are used in genetic algorithms for preventing the premature crossing, encoding solutions, enabling crossover operations and simplifying the genetic operators.
The gray codes are used in encoding solution as they are optimized as binary strings and helps in detecting small changes. The premature crossing uses gray code by verifying the mutations of genotype and providing only 1-bit change in phenotype. The gray codes are also used in simplifying the genetic operators and helps to generate new solutions.
Gray codes have several advantages and disadvantages.
Some advantages of gray codes are listed below.
Some disadvantages of gray codes are listed below.
From the above discussion we can conclude that the gray codes are useful for various applications in different fields. It is used in Karnaugh maps, error detection in signals, in angle measuring devices etc. Also, gray codes are used in multiple genetic algorithm and rotatory shafts where the values are rapidly changing because it has only 1-bit difference in its consecutive values.
The codes that represent numbers in form of 0 and 1 and has its base 2 are called binary codes.
Karnaugh map is a method of minimizing Boolean functions.
A logic gate which gives output 1 when all th inputs are different is called XOR gate.
