Or you could just create a 9-bit 512 entry code, then short-circuit it to 360 entries. Any even length gray code can be trivially created, as long as you create the next-larger full 2^n entry code first.
Main Topics
Browse All Topics
Loading Advertisement...
Question
'single track gray code' sought for encoding 360 degrees with 9 sensors
A quote from Wikipedia (http://en.wikipedia.org/w
"a single-track gray code has been constructed that has exactly 360 angular positions, using only 9 sensors"
I've searched, but have not found this particular code. The ones I found required 12 sensors. Can anyone provide a source for the encoding that Wikipedia refers to?
This Question has been solved and asker verified All Experts Exchange premium technology solutions are available to subscription members.
Subscribe now for full access to Experts Exchange and get
Instant Access to this Solution
- Plus...
- 30 Day FREE access, no risk, no obligation
- Collaborate with the world's top tech experts
- Unlimited access to our exclusive solution database
- Never be left without tech help again
Trusted by hundreds of thousands everyday for fast, accurate and reliable tech support.
- "The time we save is the biggest benefit of Experts Exchange to Warner Bros. What could take multiple guys 2 hours or more each to find is accessed in around 15 minutes on Experts Exchange." Mike Kapnisakis, Warner Bros.
- "Our team likes having a resource that is more secure than just using Google and most experts using this service really know their stuff. It's nice to look here first versus using Google." Dayna Sellner, Lockheed Martin
- "Anytime that I've been stumped with a problem, 9 out of 10 times Experts Exchange has either the accepted solution or an open discussion of the potential solution to the problem." Kenny Red, eBay Inc.
See what Experts Exchange can do for you.
Got a question?
We've got the answer.
Experts Exchange has been collecting answers to technology questions since 1996…3 million and counting! If you have a question, chances are we already have your answer.
Need individual assistance?
Our experts are ready to help.
If you can't find the exact answer you're looking for, ask our exclusive community of 50,000 experts. You’ll get a personalized answer from a trusted professional.
Want to learn from the best?
Read articles from industry experts.
Thousands of free tech tips, tricks, how-to’s and tutorials are available in our peer reviewed articles section. See for yourself how smart our experts are, no login required.
Working on a long term project?
Store your work and research.
Save solutions to your questions, answers you’ve discovered through searching plus helpful articles in your personal knowledgebase for easy future access.
Access the answers to your technology questions today.
30-day free trial. Register in 60 seconds.
What Makes Experts Exchange Unique?
Members of the expert community talk about why the experience at Experts Exchange is different than what you will find anywhere else.
Trusted by the world's most respected brands.
Faithfully serving IT professionals since 1996.
Try it out and discover for yourself.
30-day free trial. Register in 60 seconds.
Free Tech Articles
-
WARNING: 5 Reasons why you should NEVER fix a computer for free.
It is in our nature to love the puzzle. We are obsessed. The lot of us. We love puzzles. We love the challenge. We thrive on finding the answer. We hate disarray. It bothers us deep in our soul. W...
-
SCCM OSD Basic troubleshooting
SCCM 2007 OSD is a fantastic way to deploy operating systems, however, like most things SCCM issues can sometimes be difficult to resolve due to the sheer volume of logs to sift through and the dispe...
-
Migrate Small Business Server 2003 to Exchange 2010 and Windows 2008 R2
This guide is intended to provide step by step instructions on how to migrate from Small Business Server 2003 to Windows 2008 R2 with Exchange 2010. For this migration to work you will need the fo...
-
Create a Win7 Gadget
This article shows you how to create a simple "Gadget" -- a sort of mini-application supported by Windows 7 and Vista. Gadgets can be dropped anywhere on the desktop to provide instant information, ...
-
Outlook continually prompting for username and password
There have been a lot of questions recently regarding Outlook prompting for a username and password whilst using Exchange 2007. There are a few reasons why this would happen and I will try to cover t...
-
Backup Exchange 2010 Information Store using Windows Backup
There seems to be quite a lot of confusion around the ability to backup Exchange 2010 using the built in Windows Backup feature. This stems from the omission of this feature prior to Exchange 2007 s...
Cloud Class Webinars
- Avoiding Bugs in Microsoft Access
Alison Balter takes and in-depth look at avoiding bugs in Access. In this webinar you will learn about using the immediate window to debug your applications, invoking the debugger, using breakpoints to troubleshoot, stepping through code, setting the next statement to execute, ...
- Top 10 Best New Features in Visio 2010
Scott Helmers gives live demonstrations of the top 10 new features in Visio 2010. This webinar will teach you how to create compelling diagrams by adding shapes to the page with a single click, linking the shapes in a diagram to data in Excel (or SQL Server, or SharePoint), ...
- IT Consultant Business Secrets Revealed
Michael Munger, Experts Exchange tech pro and IT consultant, pulls back the curtain on his very successful businesses and answers question on every IT consultant and business owner should know about. He shares secrets on what he did to solve the 5 most common problems in IT, ...
- Disaster Recovery and Business Continuity
Quest CTO, Mike Billon, gives an overview of the steps involved in building a dunamic disaster recovery plan. Through case studies and an examination of software/hardware tooles for monitoring and testing, you'll gain a better understandin of where you are, where you want ...
- Organize Your Visio Diagrams with Containers and Lists
Scott Helmers uses cross functional flowcharts, wireframe diagrams, data graphic legends and seating charts to teach you: how to ustilize all three new structured diagram components in Visio 2010, the best practices for organizeing shapes in previous version of Visio, how to organize ...
- How to Us Objects, Properties, Events and Methods in Microsoft Access
Alison Dalter gives an in-depbth look at objects, properties, events and methods in Microsoft Access. In this webinar you will learn about using the object browser, referring to objects, working with properties and methods, working with object variables, understanding the ...
Join the Community
Give a Little. Get a Lot.
Join the community of experts here and help other tech pros by answering question in your area of expertise. You can earn FREE access to all Experts Exchange's premium features and resources.
Answers
The paper's here: http://www.hpl.hp.com/tech
Beyond my understanding. What I did read of single track gray codes seems to be satisfied by your suggestion NovaDenizen - only a single bit changes between each position and the block is cyclic.
I was looking at an algorithm to produce such a cycle, but your's is much simpler to explain and to reproduce.
Why is this not a single track code?
NovaDenizen, the PDF you linked to is one that I had found--its appendix gives info for 12-bit and 15-bit encodings, but not for a 9-bit.
RobinD, a single-track gray code requires each 'column' of bits to be the same, just shifted, so that a rotary encoder only needs one 'track' of zeroes and ones, and the sensors can be spaced evenly around its circumference. A regular gray code requires one track per bit, because the columns are not shifted copies of each other.
Check out this paper: http://www.cs.technion.ac.
It is one of the Key references in the Hiltgen and Patterson paper.
Look at the Appendix on page 788 and the Length 9 Table.
If you string these 56 9-bit Necklaces together, you will get 504 position single-track gray code.
A 360 position code will require 40 of the 9-Bit Necklaces.
You have to maintain the 1-bit change between Necklaces.
For example, you can go from Code_01 [0 0000 0001] to Code_10 [0 0010 0001]
to generate a 48 x 9 = 432 position code.
I'm pretty sure you can make further reductions.
Try this....
- 9x360-Single-Track-Gray-Code.PNG
- 30 KB
String these together to get a 360 position Single Track Gray Code
Based on d-glitch's input, I constructed the following single-track gray code for encoding angle in degrees, with nine sensors spaced 40 degrees apart.
00110000000000000000001111
3 Ways to Join
Business Accounts
- Perfect for organizations
- Multiple users
- Save over 36%
- Create a Business Account
Answer for Membership
- Earn free access
- Showcase your knowledge
- No credit card required
- Sign Up to Answer
Loading Advertisement...
by: NovaDenizenPosted on 2008-07-25 at 07:58:28ID: 22089155
It's not hard to create a 60-position gray code using 6 bits, and a 6-position gray code using 3 bits. So just use the two together and you will have a 360-position code using 9 bits.
Here's how you can recursively construct a 2^n size n-bit gray code.
start with a trivial 2^1 entry 1-bit gray code, and transform it to a 2^2 entry 2-bit gray code.
0
1
Now take all the entries in the code and put them on a line, adding a 0 before each entry
00 01
Copy the line, except transforming each leading 0 to a 1.
00 01
10 11
Now, if you follow these codes clockwise, you have a 2-bit gray code.
00
01
11
10
Turn this into a 3-bit 8-entry gray code.
000 001 011 010
100 101 111 110
If you make a clockwise path around these codes, you get a sequence of 8 gray codes. But you can 'short-circuit' this and make a sequence of 6 gray codes.
000 001 011
100 101 111
If you keep extending the full 3-bit 8-entry gray code to a 6-bit 64-entry code, you can shorten it in the same way to make a 6-bit 60-entry code.
Then, just repeat the 60-entry code 6 times around the 'platter' or whatever you're using. Use the 6-entry code to distinguish each of these 60-entry segments. Now you have 360 positions using 9 bits.