Linear Feedback Shift Registers for the Uninitiated, Part VI: Sing Along with the Berlekamp-Massey Algorithm
The last two articles were on discrete logarithms in finite fields — in practical terms, how to take the state \( S \) of an LFSR and its characteristic polynomial \( p(x) \) and figure out how many shift steps are required to go from the state 000...001 to \( S \). If we consider \( S \) as a polynomial bit vector such that \( S = x^k \bmod p(x) \), then this is equivalent to the task of figuring out \( k \) from \( S \) and \( p(x) \).
This time we’re tackling something...
Linear Feedback Shift Registers for the Uninitiated, Part V: Difficult Discrete Logarithms and Pollard's Kangaroo Method
Last time we talked about discrete logarithms which are easy when the group in question has an order which is a smooth number, namely the product of small prime factors. Just as a reminder, the goal here is to find \( k \) if you are given some finite multiplicative group (or a finite field, since it has a multiplicative group) with elements \( y \) and \( g \), and you know you can express \( y = g^k \) for some unknown integer \( k \). The value \( k \) is the discrete logarithm of \( y \)...
Introduction to Deep Insight Analysis for RTOS Based Applications
Over the past several years, embedded systems have become extremely complex. As systems become more complex, they become harder and more time consuming to debug. It isn’t uncommon for development teams to spend more than 40% development cycle time just debugging their systems. This is where deep insight analysis has the potential to dramatically decrease costs and time to market.
Defining Deep Insight Analysis
Deep insight analysis is a set of tools and techniques that can be...
Linear Feedback Shift Registers for the Uninitiated, Part IV: Easy Discrete Logarithms and the Silver-Pohlig-Hellman Algorithm
Last time we talked about the multiplicative inverse in finite fields, which is rather boring and mundane, and has an easy solution with Blankinship’s algorithm.
Discrete logarithms, on the other hand, are much more interesting, and this article covers only the tip of the iceberg.
What is a Discrete Logarithm, Anyway?Regular logarithms are something that you’re probably familiar with: let’s say you have some number \( y = b^x \) and you know \( y \) and \( b \) but...
Linear Feedback Shift Registers for the Uninitiated, Part III: Multiplicative Inverse, and Blankinship's Algorithm
Last time we talked about basic arithmetic operations in the finite field \( GF(2)[x]/p(x) \) — addition, multiplication, raising to a power, shift-left and shift-right — as well as how to determine whether a polynomial \( p(x) \) is primitive. If a polynomial \( p(x) \) is primitive, it can be used to define an LFSR with coefficients that correspond to the 1 terms in \( p(x) \), that has maximal length of \( 2^N-1 \), covering all bit patterns except the all-zero...
Continuous Integration for Embedded Systems
It is no secret that anyone who wants to streamline project management, reduce risk and improve the quality needs some form of "automation" in SW development processes. What is commonly used in most companies as a tool for such automation is called Continuous Integration (CI). It is a good practice for embedded systems as well even though it is much harder to use CI for embedded systems compared to pure software development because embedded systems mostly depend on...
Finally got a drone!
As a reader of my blog, you already know that I have been making videos lately and thoroughly enjoying the process. When I was in Germany early this summer (and went 280 km/h in a porsche!) to produce SEGGER's 25th anniversary video, the company bought a drone so we could get an aerial shot of the party (at about the 1:35 mark in this video). Since then, I have been obsessing on buying a drone for myself and finally made the move a few weeks ago - I acquired a used DJI...
Tenderfoot: Embedded Software and Firmware Specialties
Once upon a time (seven years ago) I answered a question on Stack Overflow. Then Stephane suggested I turn that answer into a blog post. Great idea! This post dives deeper into the original question: “Is it possible to fragment this field (embedded software and firmware) into sub-fields?”
This post represents a detailed and updated response to my original Stack Overflow answer. I hope this post provides guidance and useful information to the “tenderfoots” in the...
Embedded Toolbox: Source Code Whitespace Cleanup
In this installment of my "Embedded Toolbox" series, I would like to share with you the free source code cleanup utility called QClean for cleaning whitespace in your source files, header files, makefiles, linker scripts, etc.
You probably wonder why you might need such a utility? In fact, the common thinking is that compilers (C, C++, etc.) ignore whitespace anyway, so why bother? But, as a professional software developer you should not ignore whitespace, because it can cause all sorts...
SEGGER's 25th Anniversary Video
Chances are you will find this video more interesting to watch if you take five minutes to first read the story of the week I spent at SEGGER's headquarters at the end of June.
The video is only a little more than 2 minutes long. If you decide to watch it, make sure to go full screen and I would really love to read your thoughts about it in the comments down bellow. Do you think a video like this succeeds in making the viewer want to learn more about the company?...
VHDL tutorial - A practical example - part 3 - VHDL testbench
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 described the VHDL logic of the CPLD for this design. In part 3, we will show the entire VHDL design and the associated tests used to prove that we have, in fact, designed what we started out to design.
First, let's pull all of the pieces of the prior design together into a...
Introduction to Microcontrollers - Beginnings
Welcome to this Introduction to Microcontroller Programming tutorial series. If you are looking to learn the basics of embedded programming for microcontrollers (and a bit of embedded hardware design as well), I hope these tutorials will help you along that journey. These are my first postings here, and I am writing this tutorial series because over the years I have seen countless newbies asking the same questions and tripping over the same stumbling blocks, and I thought I might be able to...
MSP430 Launchpad Tutorial - Part 2 - Interrupts and timers
What is an "interrupt"? It is a signal that informs our MCU that a certain event has happened, causing the interruption of the normal flow of the main program and the execution of an "interrupt routine", that handles the event and takes a specified action.
Interrupts are essential to avoid wasting the processor's valuable time in polling loops, waiting for external events (in fact they are used in Real-Time Operating Systems,
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
Adventures in Signal Processing with Python
Author’s note: This article was originally called Adventures in Signal Processing with Python (MATLAB? We don’t need no stinkin' MATLAB!) — the allusion to The Treasure of the Sierra Madre has been removed, in deference to being a good neighbor to The MathWorks. While I don’t make it a secret of my dislike of many aspects of MATLAB — which I mention later in this article — I do hope they can improve their software and reduce the price. Please note this...
MSP430 LaunchPad Tutorial - Part 4 - UART Transmission
Today we are going to learn how to communicate using UART with the Launchpad. For this purpose I will replace the default microcontroller that comes with the board with the MSP430G2553. It is the most powerful device in the MSP430 Value Line and it comes with an integrated hardware UART module, along with 16 Kb of Flash memory, 512 bytes of SRAM and an 8-channel, 10 bit ADC.
UART communication can be useful when dealing with sensors: as a basic example, we could...
How to Estimate Encoder Velocity Without Making Stupid Mistakes: Part I
Here's a common problem: you have a quadrature encoder to measure the angular position of a motor, and you want to know both the position and the velocity. How do you do it? Some people do it poorly -- this article is how not to be one of them.
Well, first we need to get position. Quadrature encoders are incremental encoders, meaning they can only measure relative changes in position. They produce a pair of pulse trains, commonly called A and B, that look like...
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...
MSP430 Launchpad Tutorial - Part 1 - Basics
TI's LaunchPad is a complete MSP430 development environment: all you have to do is download and install CCS IDE (login required), connect your G2231-ready LaunchPad to your computer with the included mini-usb cable, and you are ready to code!
Texas Instrument MSP430 LaunchPadSo, let's see how to start a new project in Code Composer Studio. This IDE is derived from Eclipse, so if you used it before you shouldn't have much problems.
We'll write a simple program that will...
Thermistor signal conditioning: Dos and Don'ts, Tips and Tricks
In an earlier blog entry, I mentioned this circuit for thermistor signal conditioning:
It is worth a little more explanation on thermistor signal conditioning; it's something that's often done poorly, whereas it's among the easiest applications for signal conditioning.
The basic premise here is that there are two resistors in a voltage divider: Rth is the thermistor, and Rref is a reference resistor. Here Rref is either R3 alone, or R3 || R4, depending on the gain...
Introduction to Microcontrollers - Beginnings
Welcome to this Introduction to Microcontroller Programming tutorial series. If you are looking to learn the basics of embedded programming for microcontrollers (and a bit of embedded hardware design as well), I hope these tutorials will help you along that journey. These are my first postings here, and I am writing this tutorial series because over the years I have seen countless newbies asking the same questions and tripping over the same stumbling blocks, and I thought I might be able to...
MSP430 Launchpad Tutorial - Part 2 - Interrupts and timers
What is an "interrupt"? It is a signal that informs our MCU that a certain event has happened, causing the interruption of the normal flow of the main program and the execution of an "interrupt routine", that handles the event and takes a specified action.
Interrupts are essential to avoid wasting the processor's valuable time in polling loops, waiting for external events (in fact they are used in Real-Time Operating Systems,
MSP430 LaunchPad Tutorial - Part 4 - UART Transmission
Today we are going to learn how to communicate using UART with the Launchpad. For this purpose I will replace the default microcontroller that comes with the board with the MSP430G2553. It is the most powerful device in the MSP430 Value Line and it comes with an integrated hardware UART module, along with 16 Kb of Flash memory, 512 bytes of SRAM and an 8-channel, 10 bit ADC.
UART communication can be useful when dealing with sensors: as a basic example, we could...
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...
How FPGAs work, and why you'll buy one
Today, pretty much everyone has a CPU, a DSP and a GPU, buried somewhere in their PC, phone, car, etc. Most don't know or care that they bought any of these, but they did.
Will everyone, at some future point, also buy an FPGA? The market size of FPGAs today is about 1% of the annual global semiconductor sales (~$3B vs ~$300B). Will FPGA eventually...
StrangeCPU #1. A new CPU
Summary: In this multi-part series I will share with you a design, implementation notes and code for a slightly different kind of a CPU featuring a novel token machine that resolves an 8-bit token to pretty much any address in a 32-bit or even 64-bit address space, using not much more than an adder.
Table of Contents:- Part 1: A new CPU - technology review, re-examination of the premises; StrangeCPU concepts; x86 notes.
Using the Beaglebone PRU to achieve realtime at low cost
IntroductionI 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...
VHDL tutorial - part 2 - Testbench
In an earlier article I walked through the VHDL coding of a simple design. In this article I will continue the process and create a test bench module to test the earlier design. The Xilinx ISE environment makes it pretty easy to start the testing process. To start the process, select "New Source" from the menu items under "Project". This launches the "New Source Wizard". From within the Wizard select "VHDL Test Bench" and enter the name of the new module (click 'Next' to...
Adventures in Signal Processing with Python
Author’s note: This article was originally called Adventures in Signal Processing with Python (MATLAB? We don’t need no stinkin' MATLAB!) — the allusion to The Treasure of the Sierra Madre has been removed, in deference to being a good neighbor to The MathWorks. While I don’t make it a secret of my dislike of many aspects of MATLAB — which I mention later in this article — I do hope they can improve their software and reduce the price. Please note this...
VHDL tutorial - A practical example - part 3 - VHDL testbench
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 described the VHDL logic of the CPLD for this design. In part 3, we will show the entire VHDL design and the associated tests used to prove that we have, in fact, designed what we started out to design.
First, let's pull all of the pieces of the prior design together into a...
Finally got a drone!
As a reader of my blog, you already know that I have been making videos lately and thoroughly enjoying the process. When I was in Germany early this summer (and went 280 km/h in a porsche!) to produce SEGGER's 25th anniversary video, the company bought a drone so we could get an aerial shot of the party (at about the 1:35 mark in this video). Since then, I have been obsessing on buying a drone for myself and finally made the move a few weeks ago - I acquired a used DJI...
SEGGER's 25th Anniversary Video
Chances are you will find this video more interesting to watch if you take five minutes to first read the story of the week I spent at SEGGER's headquarters at the end of June.
The video is only a little more than 2 minutes long. If you decide to watch it, make sure to go full screen and I would really love to read your thoughts about it in the comments down bellow. Do you think a video like this succeeds in making the viewer want to learn more about the company?...
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.
VERY Fast Japanese Sumo Robots
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?
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
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 HighlightThis 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...
Back from ESC Boston
NOT going to ESC Boston would have allowed me to stay home, in my comfort zone.
NOT going to ESC Boston would have saved me from driving in the absolutely horrible & stressful Boston traffic1.
NOT going to ESC Boston would have saved me from having to go through a full search & questioning session at the Canada Customs on my return2.
2017/06/06 update: Videos are now up!So two days...
Launch of Youtube Channel: My First Videos - Embedded World 2017
I went to Embedded World 2017 in Nuremberg with an ambitious plan; I would make video highlights of several exhibits (booths) to be presented to the *Related sites audience. I would try to make the vendors focus their pitch on the essential in order to produce a one to three minutes video per booth.
So far my experience with making videos was limited to family videos, so I knew I had lots of reading to do and lots of Youtube videos and tutorials to watch. Trade shows are...
Who else is going to Embedded World 2017 in Nuremberg?
These days I am particularly excited. In a little bit less than a month and a half, I will be travelling to Nuremberg in Germany to attend Embedded World, by far the biggest Embedded Systems trade show with over 1000 vendors displaying their products and services.
I have downloaded the Duolingo app and I'm trying to do a minimum of 30 minutes per day to learn some German. So far, I know that 'Frau' is a woman, 'Mann' is a man, 'Danke' is thank you and 'tschüss' is bye - still a...
New Comments System (please help me test it)
I thought it would take me a day or two to implement, it took almost two weeks...
But here it is, the new comments systems for blogs, heavily inspired by the forum system I developed earlier this year.
Which means that:
- You can easily add images, either by drag and drop or through the 'Insert Image' button
- You can add MathML, TeX and ASCIImath equations and they will be rendered with Mathjax
- You can add code snippets and they will be highlighted with highlights.js
- You can edit...
