## Linear Feedback Shift Registers for the Uninitiated, Part II: libgf2 and Primitive Polynomials

July 17, 2017

Last time, we looked at the basics of LFSRs and finite fields formed by the quotient ring $GF(2)[x]/p(x)$.

LFSRs can be described by a list of binary coefficients, sometimes referred as the polynomial, since they correspond directly to the characteristic polynomial of the quotient ring.

Today we’re going to look at how to perform certain practical calculations in these finite fields. I maintain a Python library on bitbucket called...

## Went 280km/h (174mph) in a Porsche Panamera in Germany!

Those of you who've been following my blog lately already know that I am going through some sort of mid-life crisis that involves going out there to meet people and make videos.  It all started with Embedded World early this year, then continued at ESC Boston a couple of months ago and the latest chapter just concluded as I returned from Germany after spending a week at SEGGER's headquarters to produce a video to highlight their 25th anniversary.

## Embedded Toolbox: Windows GUI Prototyping Toolkit

In this installment of my "Embedded Toolbox" series, I would like to interest you in the free Windows GUI Toolkit called QWin for prototyping, developing and debugging embedded C or C++ code on Windows.

If you work on devices with non-trivial user interfaces consisting of LCDs (segmented or graphic), buttons, LEDs, etc., QWin could be just the tool for you. It has improved my productivity in such projects dramatically. I personally consider it a gem in my "Embedded...

## Linear Feedback Shift Registers for the Uninitiated, Part I: Ex-Pralite Monks and Finite Fields

July 3, 20171 comment

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,...

June 28, 20171 comment

Twenty years ago I read Code Complete by Steve McConnell. And then read it again. And again. And again. Of all the books I have read during my career, I believe this was the book that catapulted me from a young electrical engineer to a young and aspiring embedded software engineer. So to all the ‘tenderfoots’ embarking upon an embedded systems and especially embedded software and firmware career, this entry is for you.

## Embedded Toolbox: Programmer's Calculator

Like any craftsman, I have accumulated quite a few tools during my embedded software development career. Some of them proved to me more useful than others. And these generally useful tools ended up in my Embedded Toolbox. In this blog, I'd like to share some of my tools with you. Today, I'd like to start with my cross-platform Programmer's Calculator called QCalc.

## VERY Fast Japanese Sumo Robots

June 20, 20171 comment

For some reasons, I could not stop watching.  I would love to have the maker of one of these robots to blog about the project here on EmbeddedRelated.com, the sensors, microcontroller, algorithms and the challenges...  This would make for a very interesting read!  Do you know someone?

## Ten Little Algorithms, Part 6: Green’s Theorem and Swept-Area Detection

Other articles in this series:

## Going back to Germany!

A couple of blog posts ago, I wrote that the decision to go to ESC Boston ended up being a great one for many different reasons.  I came back from the conference energized and really happy that I went.

These feelings were amplified a few days after my return when I received an email from Rolf Segger, the founder of SEGGER Microcontroller (check out their very new website), asking if I would be interested in visiting their headquarters...

## ESC Boston's Videos are Now Up

June 5, 2017

In my last blog, I told you about my experience at ESC Boston and the few videos that I was planning to produce and publish.  Here they are, please have a look and any feedback (positive or negative) is appreciated.

Short Highlight

This is a very short (one minute) montage of some of the footage that I shot at the show & conference.  In future shows, I absolutely need to insert clips here and there of engineers saying a few words about the conference (why they...

## An overview of Linux Boot Process for Embedded Systems

This Text provides an insight in to the Embedded Linux Boot Process. Reader should have a basic Knowledge of Boot Process in general and should be familiar with Embedded Linux Boot Process.

.................PART-A................(1) Software components Involved in Embedded Linux Boot Process    (a) Bootloader    (b) kernel Image    (c) root file system - either an initrd image or a NFS location(2) Steps during Booting process of a conventional...

## 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...

## Introduction to Microcontrollers - Driving WS2812 RGB LEDs

This tutorial chapter is a bit of a detour, but I think an interesting and useful one.  It introduces a bit of assembly language programming, and demonstrates bit-banging a tight serial data protocol.  And it deals with RGB LEDs, which are just very fun in their own right, especially these new parts.  So I thought I'd post this to give readers time for some holiday lighting experimenting.

Back To The Future

Remember how we started this...

## Boot Sequence for an ARM based embedded system

Hello all,

Allow me to introduce myself. I am Deeksha and I come from plains of North India. My tryst with embedded technologies has been 5 years long and every single day I am amazed with the vastness and learning involved. The thing with embedded technologies is either you are into it, or you aren't. You cannot just hang around half-heartedly (I guess that holds true for every field, for that matter).You have to keep the learning and sharing process going on. And that is the reason I am...

## Introduction to Microcontrollers - Further Beginnings

Embedded Programming Basics

This 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...

## Important Programming Concepts (Even on Embedded Systems) Part I: Idempotence

There are literally hundreds, if not thousands, of subtle concepts that contribute to high quality software design. Many of them are well-known, and can be found in books or the Internet. I’m going to highlight a few of the ones I think are important and often overlooked.

But first let’s start with a short diversion. I’m going to make a bold statement: unless you’re a novice, there’s at least one thing in computer programming about which you’ve picked up...

## C++ on microcontrollers 1 - introduction, and an output pin class

This blog series is about the use of C++ for modern microcontrollers. My plan is to show the gradual development of a basic I/O library. I will introduce the object-oriented C++ features that are used step by step, to provide a gentle yet practical introduction into C++ for C programmers.  Reader input is very much appreciated, you might even steer me in the direction you find most interesting.

I am lazy. I am also a programmer. Luckily, being a lazy...

## Analyzing the Linker Map file with a little help from the ELF and the DWARF

When you're writing firmware, there always comes a time when you need to check the resources consumed by your efforts - perhaps because you're running out of RAM or Flash or you want to optimize something. The map file generated by your linker is a useful tool to aid in the resource analysis. I wanted to filter and sort the data generated in an interactive way so I wrote a C# WinForms application that reads the data from the map and presents it in a list view (using the awesome

## VHDL tutorial - A practical example - part 2 - VHDL coding

May 27, 2011

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...

## 10 Circuit Components You Should Know

November 28, 20111 comment

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 (

## 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

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).

@DSPRelated

## New Code Snippet Section

More incentives announced

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 December 5, 201223 comments 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. I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other as a parent of three kids. My job... ## October winner announced November 15, 20121 comment 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

June 14, 2010

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

April 1, 2010

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.

## Blogs Section Now Online!

September 18, 2007

I am happy to announce that the blog section is now online.

Last week, I sent an email to all the members of EmbeddedRelated.com to ask for embedded systems experts who would be interested in blogging on the site. The response was very positive and I have selected 10 highly qualified individuals who will soon be writing here about all sorts of embedded systems related subjects. I am currently in the process of receiving their info (bio, photo, username, etc) and creating their bloggers'...