Linear Feedback Shift Registers for the Uninitiated, Part XVII: Reverse-Engineering the CRC
Last time, we continued a discussion about error detection and correction by covering Reed-Solomon encoding. I was going to move on to another topic, but then there was this post on Reddit asking how to determine unknown CRC parameters:
I am seeking to reverse engineer an 8-bit CRC. I don’t know the generator code that’s used, but can lay my hands on any number of output sequences given an input sequence.
This is something I call the “unknown oracle”...
Making a connection 1
In order for your system to control devices, you must be able to connect it to those devices.
Besides different sizes based on wire size, there are a few different styles of connectors that can be used. There are also weather-resistant terminals that can be used if needed.
Ring
(Parks, 16)
- used for circuits that you don’t want to become easily disconnected
- ground wire attached to a stud
Push-On
- can be used on relay terminals
(Parks, 18)
- could be...
Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed-Solomon Error Correction
Last time, we talked about error correction and detection, covering some basics like Hamming distance, CRCs, and Hamming codes. If you are new to this topic, I would strongly suggest going back to read that article before this one.
This time we are going to cover Reed-Solomon codes. (I had meant to cover this topic in Part XV, but the article was getting to be too long, so I’ve split it roughly in half.) These are one of the workhorses of error-correction, and they are used in...
Troubleshooting notes from days past, TTL, Linear
General Troubleshooting
- Follow safety precautions.
- Always think “what if”.
- Analytical procedures
- Precautions when probing equipment
- Insulate all but last 1/8” of probe tip
- Learn from mistakes
- Don’t start with electronic test equipment, start with analytical thinking.
- If you get stuck, sleep on it.
- Many problems have simple solutions.
- Whenever possible, try to substitute a working unit.
- Don’t blindly trust test instruments.
- Coincidences do happen, but are relatively...
Linear Feedback Shift Registers for the Uninitiated, Part XV: Error Detection and Correction
Last time, we talked about Gold codes, a specially-constructed set of pseudorandom bit sequences (PRBS) with low mutual cross-correlation, which are used in many spread-spectrum communications systems, including the Global Positioning System.
This time we are wading into the field of error detection and correction, in particular CRCs and Hamming codes.
Ernie, You Have a Banana in Your EarI have had a really really tough time writing this article. I like the...
Tenderfoot: How to Write a Great Bug Report
I am an odd sort of person. Why? Because I love a well written and descriptive bug report. I love a case that includes clear and easy to follow reproduction steps. I love a written bug report that includes all the necessary information on versions, configurations, connections and other system details. Why? Because I believe in efficiency. I believe that as an engineer I have a duty to generate value to my employer or customer. Great bug reports are one part of our collective never-ending...
Who else is going to Sensors Expo in San Jose? Looking for roommate(s)!
This will be my first time attending this show and I must say that I am excited. I am bringing with me my cameras and other video equipment with the intention to capture as much footage as possible and produce a (hopefully) fun to watch 'highlights' video. I will also try to film as many demos as possible and share them with you.
I enjoy going to shows like this one as it gives me the opportunity to get out of my home-office (from where I manage and run the *Related sites) and actually...
Voltage - A Close Look
My first boss liked to pose the following problem when interviewing a new engineer. “Imagine two boxes on a table one with a battery the other with a light. Assume there is no detectable voltage drop in the connecting leads and the leads cannot be broken. How would you determine which box has the light? Drilling a hole is not allowed.”
The answer is simple. You need a voltmeter to tell the electric field direction and a small compass to tell the magnetic field...
What is Electronics
IntroductionOne answer to the question posed by the title might be: "The understanding that allows a designer to interconnect electrical components to perform electrical tasks." These tasks can involve measurement, amplification, moving and storing digital data, dissipating energy, operating motors, etc. Circuit theory uses the sinusoidal relations between components, voltages, current and time to describe how a circuit functions. The parameters we can measure directly are...
Linear Regression with Evenly-Spaced Abscissae
What a boring title. I wish I could come up with something snazzier. One word I learned today is studentization, which is just the normalization of errors in a curve-fitting exercise by the sample standard deviation (e.g. point \( x_i \) is \( 0.3\hat{\sigma} \) from the best-fit linear curve, so \( \frac{x_i - \hat{x}_i}{\hat{\sigma}} = 0.3 \)) — Studentize me! would have been nice, but I couldn’t work it into the topic for today. Oh well.
I needed a little break from...
Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine
Today’s topic is rounding in embedded systems, or more specifically, why you don’t need to worry about it in many cases.
One of the issues faced in computer arithmetic is that exact arithmetic requires an ever-increasing bit length to avoid overflow. Adding or subtracting two 16-bit integers produces a 17-bit result; multiplying two 16-bit integers produces a 32-bit result. In fixed-point arithmetic we typically multiply and shift right; for example, if we wanted to multiply some...
Chebyshev Approximation and How It Can Help You Save Money, Win Friends, and Influence People
Well... maybe that's a stretch. I don't think I can recommend anything to help you win friends. Not my forte.
But I am going to try to convince you why you should know about Chebyshev approximation, which is a technique for figuring out how you can come as close as possible to computing the result of a mathematical function, with a minimal amount of design effort and CPU power. Let's explore two use cases:
- Amy has a low-power 8-bit microcontroller and needs to compute \( \sqrt{x} \)...
Embedded Programming Video Course Shows How OOP Works Under the Hood
If you'd like to understand how Object-Oriented Programming (OOP) really works under the hood, here is a free video course for you:
OOP part-1: Encapsulation: This first lesson on Object-Oriented Programming (OOP) introduces the concept of Encapsulation, which is the ability to package data and functions together into classes. You'll see how you can emulate Encapsulation in C, what kind of code is generated, and how to debug such code. Next, you will translate the C design into C++ using...
Lost Secrets of the H-Bridge, Part IV: DC Link Decoupling and Why Electrolytic Capacitors Are Not Enough
Those of you who read my earlier articles about H-bridges, and followed them closely, have noticed there's some unfinished business. Well, here it is. Just so you know, I've been nervous about writing the fourth (and hopefully final) part of this series for a while. Fourth installments after a hiatus can bring bad vibes. I mean, look what it did to George Lucas: now we have Star Wars Episode I: The Phantom Menace and
VHDL tutorial
When I was first introduced to "Programmable Logic" several years ago, it was an answer to many of the challenges that I was struggling with. Though the parts were primitive by today's standards (simple PALs verses FPGA), they were an extremely cost effective tool addressing the need for specialized logic blocks.
I have continued to incorporate these powerful blocks into many of my latest designs. My current favorite part line is the Xilinx CoolRunner series (XC2Cxxx). In this...
Unit Tests for Embedded Code
I originate from an electrical engineering background and my first industry experience was in a large, staid defense contractor. Both of these experiences contributed to a significant lack of knowledge with regards to software development best practices. Electrical engineers often have a backwards view of software in general; large defense contractors have similar views of software and couple it with a general disdain for any sort of automation or ‘immature’ practices. While there...
Using the Beaglebone PRU to achieve realtime at low cost
Introduction
I work as an engineer in a synchrotron facility. A few weeks ago, I helped the people in charge of the power supply developments to integrate a realtime control algorithm on a prototype platform: a BeagleBone Black (BBB) running Linux. I had already worked with this board in the past, and I found it very interesting given its excellent resources versus price ratio (around 40 euros). This time, I was impressed by its realtime capabilities. I thought it would be a good idea to...
My Love-Hate Relationship with Stack Overflow: Arthur S., Arthur T., and the Soup Nazi
Warning: In the interest of maintaining a coherent stream of consciousness, I’m lowering the setting on my profanity filter for this post. Just wanted to let you know ahead of time.
I’ve been a user of Stack Overflow since December of 2008. And I say “user” both in the software sense, and in the drug-addict sense. I’m Jason S, user #44330, and I’m a programming addict. (Hi, Jason S.) The Gravatar, in case you were wondering, is a screen...
Linear Feedback Shift Registers for the Uninitiated, Part I: Ex-Pralite Monks and Finite Fields
Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.
— Évariste Galois, May 29, 1832
I was going to call this short series of articles “LFSRs for Dummies”, but thought better of it. What is a linear feedback shift register? If you want the short answer, the Wikipedia article is a decent introduction. But these articles are aimed at those of you who want a little bit deeper mathematical understanding,...
Introduction to Microcontrollers - Hello World
Embedded Hello World
A standard first program on an embedded platform is the blinking LED. Getting an LED to blink demonstrates that you have your toolchain set up correctly, that you are able to download your program code into the μC, and that the μC and associated circuitry (e.g. the power supply) is all working. It can even give you good evidence as to the clock rate that your microcontroller is running (something that trips up a great many people,...
Introduction to Microcontrollers - Interrupts
It's Too Soon To Talk About Interrupts!That, at least, could be one reaction to this chapter. But over the years I've become convinced that new microcontroller programmers should understand interrupts before being introduced to any complex peripherals such as timers, UARTs, ADCs, and all the other powerful function blocks found on a modern microcontroller. Since these peripherals are commonly used with interrupts, any introduction to them that does not...
Introduction to Microcontrollers - Further Beginnings
Embedded Programming BasicsThis tutorial entry will discuss some further embedded programming basics that you will need to understand before proceeding on to the LED blinky and other example programs. We will do this by looking at the general organization and types of instructions found in most microcontrollers, and how that organization and those instructions are reflected (or, in some cases, ignored) by the C programming language.
Basic CPU...Analog-to-Digital Confusion: Pitfalls of Driving an ADC
Imagine the following scenario:You're a successful engineer (sounds nice, doesn't it!) working on a project with three or four circuit boards. More than even you can handle, so you give one of them over to your coworker Wayne to design. Wayne graduated two years ago from college. He's smart, he's a quick learner, and he's really fast at designing schematics and laying out circuit boards. It's just that sometimes he takes some shortcuts... but in this case the circuit board is just something...
VHDL tutorial - A practical example - part 2 - VHDL coding
In part 1 of this series we focused on the hardware design, including some of the VHDL definitions of the I/O characteristics of the CPLD part. In part 2, we will describe the VHDL logic of the CPLD for this design.
With any design, the first step to gather the requirements for the job at hand. From part 1 of this article, I have copied two sections that address some of the requirements for the CPLD design.
The data acquisition engine has the...
Help, My Serial Data Has Been Framed: How To Handle Packets When All You Have Are Streams
Today we're going to talk about data framing and something called COBS, which will make your life easier the next time you use serial communications on an embedded system -- but first, here's a quiz:
Quick Diversion, Part I: Which of the following is the toughest area of electrical engineering? analog circuit design digital circuit design power electronics communications radiofrequency (RF) circuit design electromagnetic...10 Circuit Components You Should Know
Chefs have their miscellaneous ingredients, like condensed milk, cream of tartar, and xanthan gum. As engineers, we too have quite our pick of circuits, and a good circuit designer should know what's out there. Not just the bread and butter ingredients like resistors, capacitors, op-amps, and comparators, but the miscellaneous "gadget" components as well.
Here are ten circuit components you may not have heard of, but which are occasionally quite useful.
1. Multifunction gate (
VHDL tutorial - Creating a hierarchical design
In earlier blog entries I introduced some of the basic VHDL concepts. First, developing a function ('VHDL tutorial') and later verifying and refining it ('VHDL tutorial - part 2 - Testbench' and 'VHDL tutorial - combining clocked and sequential logic'). In this entry I will describe how to...
Byte and Switch (Part 1)
Imagine for a minute you have an electromagnet, and a microcontroller, and you want to use the microcontroller to turn the electromagnet on and off. Sounds pretty typical, right?We ask this question on our interviews of entry-level electrical engineers: what do you put between the microcontroller and the electromagnet?We used to think this kind of question was too easy, but there are a surprising number of subtleties here (and maybe a surprising number of job candidates that were missing...
Important Programming Concepts (Even on Embedded Systems) Part V: State Machines
Other articles in this series:
- Part I: Idempotence
- Part II: Immutability
- Part III: Volatility
- Part IV: Singletons
- Part VI: Abstraction
Oh, hell, this article just had to be about state machines, didn’t it? State machines! Those damned little circles and arrows and q’s.
Yeah, I know you don’t like them. They bring back bad memories from University, those Mealy and Moore machines with their state transition tables, the ones you had to write up...
Boot sequence for an ARM based embedded system -2
In the last post, we discussed about the startup execution sequence on an ARM based embedded system in broader terms. In this post, we are going to cover the details of a startup code.These details are also available through various ARM resources , however for the sake of completion of our discussion , here is - the flow the startup code for an ARM based embedded system.
Step 1: The reset
On startup, the processor will jump to fixed location ,(most ARM cores support two vector...
Success Story
A blog post has just broken the all-time record for the number of pageviews in 24 hours on the related sites. The blog post in question is titled Data Hiding in C and was written by Stephen Friederichs. It has been viewed by more than 7000 individuals since its publication a few days ago.
One reason that explains the success of this blog post is the wide appeal of the subject of the article (c programming) which allowed me to
Code Snippets Winners Announced
Wow, thanks a lot for all the code snippets - I am pleasantly surprised by the quality of the code that has been shared and I am very grateful.
Now, as you know, to give momentum to the section I had announced a special reward program for code snippets submitted by the end of March.
The partner members and I had a very hard time selecting the 5 "most useful" snippets out of the more than 50 who have been submitted.
Here's our selection:
Now on Twitter + More Code Snippets Incentives
Now on Twitter!
Better late than never, the three related sites (DSPRelated, FPGARelated and EmbeddedRelated) now have their Twitter accounts. If you are already on Twitter, please consider following. I'll make sure to keep the tweets interesting and informative. Plus, once in a while, I will tweet a link where the first x persons to visit will receive a gift (book, gift certificate, etc).
New Code Snippet Section
Following the success of the code snippet section on DSPRelated.com, I am happy today to announce the launch of the code snippet section on EmbeddedRelated.com.
If you have a piece of code that you would like to share with the Embedded Systems community, please go ahead and fill the form.
If the piece of code you submit is approved, you will be sent $10 through Paypal.
If...
Two jobs
For those of you following closely embeddedrelated and the other related sites, you might have noticed that I have been less active for the last couple of months, and I will use this blog post to explain why. The main reason is that I got myself involved into a project that ended up using a better part of my cpu than I originally thought it would.
edit - video of the event:
I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other...
October winner announced
If you are a regular visitor of EmbeddedRelated, you are most likely aware that I have been running monthly draws lately for users of the site who are helping me to clean up the archives by rating threads in the forums section.
For the month of August, the member "Cryptoman" won a iPad, and for the month of September, 10 members won $50 each.
For October, the winner of the new iPod Touch is the member with the username "hssathya".
The winner of the next draw will win...
Behold, the New Comments System!
I have just finished implementing a new system for commenting the blogs. It uses Ajax extensively, so the page won't reload if you post a comment. And it is a 'threaded' system, which means that if you post a reply to a comment, it will be attached to it.
What do you think? I personally love it. Please go ahead and test it with a quick comment.
Although it is better to be logged in to post a comment, non-registered users can also comment, but they will have...
Best Embedded Systems pdf Documents Out There
There are thousands of pdf documents related to Embedded Systems available online. In fact, when I do a search in Google for:
embedded systems filetype:pdf
I get 4,340,000 results! A huge mix of articles, promotional documents, theses, etc.
Out of these 4 millions+ documents, I suspect that there must be at least a few hundreds jewels that deserve to be given more visibility.
Today, I am asking for your help (again!) to build a directory of some of the most useful pdf files out...
New Discussion Group for Users of TI ARM based MCUs
If you are a user of an ARM based TI Microcontroller, please feel free to join the new "TI ARM processors MCUs" discussion group by sending a blank email to: tiarm-subscribe@yahoogroups.com This discussion group will be moderated, so you don't have to worry about receiving more spam than you probably already get. It usually takes a few weeks for a group to gain momentum, so don't worry if the activity level is low for a little while, but make sure to join so you don't miss the good...
New TI MCU Resource Center
I am happy to announce the publication of the new "TI MCU Resource Center" on EmbeddedRelated.com, where TI will regularly add videos and articles to keep you informed on their latest and greatest MCU related products.
To access the new section, you'll find a link in the main menu of the site at the top of the page.
