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	Gray code - Wikipedia, the free encyclopedia
		The use of his eponymous codes that Gray was most interested in was to minimize the effect of error in the transmission of digital signals; his codes are still used today for this purpose, and others.
		Gray codes are used in angle-measuring devices in preference to straightforward binary encoding.
		The sequence of elements in the (3,2)-Gray code is: {00, 01, 02, 12, 11, 10, 20, 21, 22}.
	en.wikipedia.org /wiki/Gray_code (2447 words)

	Talk:Gray code - Wikipedia, the free encyclopedia
		I suppose you can define a Gray code sequence for non-binary numbers such that only one digit changes.
		Gray codes are codes where neighbouring elements only differ in one symbol.
		There are times when it is convenient to think of the bits from a sensor (whether it uses natural binary codes or gray codes) as bits of a binary fraction (i.e., a value from 0 to 1), rather than the bits of a binary integer.
	en.wikipedia.org /wiki/Talk:Gray_code (647 words)

	Gray Code Explained
		The gray code is sometimes referred to as reflected binary, because the first eight values compare with those of the last 8 values, but in reverse order.
		The gray code is often used in mechanical applications such as shaft encoders.
		The excess 3 gray code is such a code, the values for zero and nine differ in only 1 bit, and so do all values for successive numbers.
	www.pc-control.co.uk /gray_code.htm (394 words)

	Problem C - Gray Code
		To construct n-bit gray code keep any of the n bits fixed (either 0 or 1) for the first 2^(n-1) rows and use (n-1)-bit gray code (generated using this logic) for remaining (n-1) bits.
		Then invert the fixed bit for the next 2^(n-1) rows and also use (n-1)-bit gray code for remaining (n-1) bits whose bit pattern of the first row is the same as the bit pattern of the last row of previous 2^(n-1) rows.
		G(n-1)'th n-bit gray code has its leftmost bit fixed and it uses 1st (n-1)-bit gray code for upper half and G(n-1)'th (n-1)-bit gray code for lower half.
	acm.uva.es /p/v104/10455.html (578 words)

	Encoders
		The gray code is designed so that only one track (one bit) will change state for each count transition, unlike the binary code where multiple tracks (bits) change at certain count transitions.
		For the gray code, the uncertainty during a transition is only one count, unlike with the binary code, where the uncertainty could be multiple counts.
		Since the gray code provides data with the least uncertainty but the natural binary code is the preferred choice for direct interface to computers and other digital devices, a circuit to convert from gray to binary code is desirable.
	mechatronics.mech.northwestern.edu /design_ref/sensors/encoders.html (772 words)

	C CODE
		Gray codes actually have a longer history, and the inquisitive reader may want to look up the August, 1972, issue of Scientific American, which contains two articles of interest: one on the origin of binary codes [2], and another by Martin Gardner on some entertaining aspects of Gray codes [3].
		A Gray code represents each number in the sequence of integers {0...2^N-1} as a binary string of length N in an order such that adjacent integers have Gray code representations that differ in only one bit position.
		The basic argument for using Gray coded bits is that single bit mutations in a Gray coded number will only change the value by a little bit also, as opposed to the usual power of 2 code, where changing one bit might change the value by as much as 2^(n-1) for n its.
	cafaq.com /extra/gray.html (1628 words)

	gray code from FOLDOC (Site not responding. Last check: 2007-10-06)
		The gray code originated when digital logic circuits were built from vacuum tubes and electromechanical relays.
		Gray code can also be used to convert the angular position of a disk to digital form.
		One possible algorithm for generating a gray code sequence is to toggle the lowest numbered bit that results in a new code each time.
	foldoc.org /?gray+code (173 words)

	Halfbakery: count in gray code (Site not responding. Last check: 2007-10-06)
		Gray code was developed to address a specific class of problem involving parallel interfaces with systems exhibiting asynchronous state changes.
		Incidentally, gray codes are also used in electronic design, for counters and particularly for state machine variables.
		Since it uses a certain amount of energy to change the value of a register, gray codes allow for a very power-efficient arrangement where only one bit need be changed per increment of a counter.
	www.halfbakery.com /idea/count_20in_20gray_20code (1485 words)

	6-2 THE GRAY CODE
		The Gray code is an example of a unit-distance code or a code having the property that the bit patterns for two consecutive strings differ in only one bit position.
		Such codes are used in instrumentation and data-acquisition systems where linear or angular displacement is measured and whenever it may be advantageous to avoid the possibility of intermediate glitch-producing states.
		As will be seen from the table, the Gray code only changes by one bit as we move around the disk from one segment to the next.
	www.thiel.edu /digitalelectronics/chapters/ch6_html/ch6-2.htm (786 words)

	Standardizing Non-Standard Optical Rotary Encoders (Site not responding. Last check: 2007-10-06)
		Consider the problem as to which code should be used to define the angular position information for the absolute encoder.
		Codes that satisfy the requirement that there is only a single bit change between successive numbers are called unit-distance codes, reflective codes, or cyclic codes.
		The Gray code is generated by the exclusive OR of adjacent binary bits.
	www.motion.org /9801vina.htm (968 words)

	PlanetMath: binary Gray code
		-bit binary Gray code is a non-repeating sequence of the integers from 0 to
		In addition, we also define a cyclic Gray code to be a Gray code where an extra condition is imposed: The last number in the sequence must differ by exactly one bit from the first number in the sequence.
		This is version 6 of binary Gray code, born on 2002-02-27, modified 2004-11-30.
	planetmath.org /encyclopedia/CyclicGrayCode.html (185 words)

	Gray code - Psychology Central (Site not responding. Last check: 2007-10-06)
		Image:Encoder disc.png Gray codes (not so named) were applied to mathematical puzzles before they became known to engineers.
		The actors could then be represented by a first in, first out queue data structure, so that the first actor to exit when a dequeue is called for is always the first actor which was enqueued into the structure [4].
		The Gray code nature is useful (compared to chain codes), as only one track will change at any one time, so the uncertainty during a transition between two discrete states will only be plus or minus one unit of angular measurement the device is capable of resolving [1].
	psychcentral.com /psypsych/Gray_code (2464 words)

	Gray codes (Site not responding. Last check: 2007-10-06)
		This worksheet and the text file gray.mpl contains four algorithms for generating a binary Gray code (essentially the "reflected" binary Gray code) of length n.
		One is the binary-to-reflected Gray code conversion [G].
		The third uses a relationship between the i-th codeword and the 2i-th codeword, which as far as we know is new.
	web.usna.navy.mil /~wdj/gray.htm (331 words)

	EE141 - Fall 1994- Project 1
		Gray codes are often used in designs where the multi-bit switches may cause circuit hazards, such as in A/D converters, as well as in designs where low power is desired.
		Gray encoding is also interesting from a power perspective, as only a single bit changes at a time in a counter application.
		This is expressed in Gray code as 000, 001, 011, 010, 110, 111, 101, 100.
	bwrc.eecs.berkeley.edu /Classes/icBook/PROJECTS/gray2binary.html (848 words)

	Your Personal PLC Tutor Site - Interactive Q & A - "Gray code"
		Grey (Gray) code is a specific Binary Coded Decimal (BCD), in which only one bit changes at a time.
		Since, with gray code, only one bit changes when going from one number to the next, the biggest error would be that the number hadn't changed yet.
		Because of the nature of gray code, it is most often used to transmit a number which is a power of two.
	www.plcs.net /dcforum/DCForumID5/1277.html (422 words)

	Bit Twiddler: Gray Code (Site not responding. Last check: 2007-10-06)
		Since this is not the case in the left Gray code above, it is not circular.
		Each input line describes a portion of a circular gray code to be generated.
		The line: 5 24 19 means to output the bit patterns used to encode the integers from 19 to 24 using a similarly generated 5-bit circular gray code.
	www.cs.pdx.edu /~acmc/prog/gray.html (519 words)

	Gray code (Site not responding. Last check: 2007-10-06)
		Gray codes for 4 or more bits are not unique, even allowing for permutation or inversion of bits.
		An n-bit Gray code corresponds to a Hamiltonian cycle on an n-dimensional hypercube.
		One way to construct a Gray code for n bits is to take a Gray code for n-1 bits with each code prefixed by 0 (for the first half of the code) and append the n-1 Gray code reversed with each code prefixed by 1 (for the second half).
	www.nist.gov /dads/HTML/graycode.html (304 words)

	Miller's Mathematical Ideas, 9th Edition Web site Chapter 4 -- Internet Project (Site not responding. Last check: 2007-10-06)
		Gray Codes and the Standard Gray Code can be used as a tool in finding solutions to many classic problems.
		The next entry in the Standard Gray Code is 001, formed by changing the digit corresponding to disk #1.
		The use of the Standard Gray Code here is valid no matter how many disks you start out with provided you are using three pegs.
	occawlonline.pearsoned.com /bookbind/pubbooks/miller2_awl/chapter4/essay1/deluxe-content.html (1614 words)

	A Segmented Gray Code for Low-Power Microcontroller Address Buses
		A novel segmented gray code is introduced that overcomes the exploding complexity disadvantage of higher bit width gray code incrementers compared to binary counters by breaking down the global scope of the common gray code.
		Resulting from this evaluation a gray code is presented for which the area and power consumption of its incrementer is smaller than for a binary counter.
		This code combined with the concept of the segmented gray code used for a microprocessor program counter leads to a decrease of the switching activity on the address bus by 25-30% as well as to a decrease in the area and power consumption of the program counter by about 10%.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/euromicro/1999/0321/01/0321toc.xml&DOI=10.1109/EURMIC.1999.794474 (263 words)

	Gray Codes
		A Gray Code is a system where numbers near one another are represented similarly.
		Out of this multitude, one particular realization of the Gray Code criterion has come to be the most important and useful by far.
		The word, "binary" suggests the fact that The Binary Reflected Gray Code is a system of representing numbers using ones and zeroes, and also that it is a cousin of the system of representing numbers using ones and zeroes that computers regularly utilize.
	www.washingtonart.net /whealton/gray.html (1006 words)

	House of Cards: Rooming house fire code violations result in 12 summonses (Site not responding. Last check: 2007-10-06)
		Unlike the 214 housing code violations Gray cited at the rooming house on Tuesday, the fire code violations resulted in summonses that were issued Wednesday.
		The code violations are the latest problems Kane faces in Asbury Park, where he stands accused by a mortgage company of conspiring to bilk the lender out of millions of dollars through fraudulent property sales.
		Gray pointed out that he has seen properties in worse condition than those owned by Cristo.
	www.injersey.com /news/cards/story/0,1449,32593,00.html (1056 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-06)
		The Gray code for the 2-cube is cyclic.
		This list of vertices is also a Gray code for the 3-cube.
		There are algorithms that allow you to generate the Gray codes (n-tuples of 0's and 1's) for any given n.
	mathforum.org /library/drmath/view/56220.html (330 words)

	8-bit Gray code (Site not responding. Last check: 2007-10-06)
		The reason why a Gray code was used instead of a simple binary code is that the Gray code of adjacent integers differ by only 1 bit.
		The most remarkable difference between the unary code and the Gray code is that the former has no weights for the output neurons/bits that comprise the word, increasing the level of redundancy in the set of representations (i.e.
		The advantage of the Gray code is that it is more efficient in terms of usage of output neurons.
	www.cs.usu.edu /~degaris/papers/gp98/node7.html (210 words)

	Gray code algorithms in Ruby (Site not responding. Last check: 2007-10-06)
		A Gray code is a way of encoding binary numbers so that only digit changes from one number to the next.
		Gray code is used instead of binary numbers because the fingers can't be lined up exactly.
		Gray Code from the NIST Dictionary of Algorithms, Data Structures, and Problems.
	yagni.com /graycode (632 words)

	Gray Code (Site not responding. Last check: 2007-10-06)
		Gray Code is a variation on binary code in which only 1 bit is changed from the preceding number.
		In each subsequent number in Gray code only the lowest bit possible has been changed.
		Gray code is used in the simplification of logic circuits.
	www.vuw.ac.nz /scps-students/tech102/lectures/week2/gray.htm (75 words)

	Joel Adams' Gray Code Converter Applet (Site not responding. Last check: 2007-10-06)
		The gray code number system has the property that each number i's successor and predecessor numbers differ from i in just one bit.
		These gray code numbers can be used to map an alternative topology like a ring onto a hypercube.
		For a hypercube, node whose decimal number is i, the bit that is different between gray-code(i) and gray-code(i+1) tells us which link we should follow from i to visit the next node in the ring.
	ohm.calvin.edu /applets/grayCodes (319 words)

	Gray Code
		An application of Gray Code is from the altitude encoder that feeds mode C Aircraft transponders so the the altitude is displayed with the radar image.
		Martin, your perception of the Gray code is analogous to stating that Einstein's Theory of Relativity led to the equation E=MC^1.999+.
		Gray code is unique because only 1 bit at a time changes in the progression (forward or backwards).
	www.control.com /950735019/index_html (1472 words)

	Gray Code and Binary Conversion (ResearchIndex)
		The correct spelling is \Gray" not \gray" or \grey".
		Gray rst patented the idea for use in shaft encoders.
		The idea here is that when a machine counts in Gray code, the consecutive numbers change only by one bit.
	citeseer.ist.psu.edu /465301.html (233 words)

	CS 242 Lab Exercise (Site not responding. Last check: 2007-10-06)
		A Gray code is a sequence of binary numbers (you know, all 0's and 1's) used in a number of information coding applications and mechanical sensor applications (including identifying hard disk sectors).
		The code was patented for Bell Labs by Frank Gray in 1953.
		The significant property of the Gray code is that each binary number in the sequence differs from the previous number in the sequence by exactly one bit.
	www.cs.wright.edu /~scarl/cs242/Proj1/proj1.html (1099 words)

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