Is it a Bug or an Error?

Michael Barr January 31, 20184 comments

Probably you’ve heard the story of how Adm. Grace Hopper attached a moth that was dislodged from a relay in the Harvard Mark II mainframe to an engineering notebook and labeled it the “First actual case of bug being found.”

Designers of electronics, including Thomas Edison, had been using the term bug for decades. But it was mostly after this amusing 1947 event hat the use of words like “bugs” and “debugging” took off in the emerging software realm.

So why is it that if a...

A Wish for Things That Work

Jason Sachs January 1, 20182 comments

As the end of the year approaches, I become introspective. This year I am frustrated by bad user interfaces in software.

Actually, every year, throughout the year, I am frustrated by bad user interfaces in software. And yet here it is, the end of 2017, and things aren’t getting much better! Argh!

I wrote about this sort of thing a bit back in 2011 (“Complexity in Consumer Electronics Considered Harmful”) but I think it’s time to revisit the topic. So I’m...

Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals

Jason Sachs December 29, 20171 comment

Last time we looked at the use of LFSRs for pseudorandom number generation, or PRNG, and saw two things:

  • the use of LFSR state for PRNG has undesirable serial correlation and frequency-domain properties
  • the use of single bits of LFSR output has good frequency-domain properties, and its autocorrelation values are so close to zero that they are actually better than a statistically random bit stream

The unusually-good correlation properties...

Linear Feedback Shift Registers for the Uninitiated, Part XI: Pseudorandom Number Generation

Jason Sachs December 20, 2017

Last time we looked at the use of LFSRs in counters and position encoders.

This time we’re going to look at pseudorandom number generation, and why you may — or may not — want to use LFSRs for this purpose.

But first — an aside:

Science Fair 1983

When I was in fourth grade, my father bought a Timex/Sinclair 1000. This was one of several personal computers introduced in 1982, along with the Commodore 64. The...

Linear Feedback Shift Registers for the Uninitiated, Part X: Counters and Encoders

Jason Sachs December 9, 2017

Last time we looked at LFSR output decimation and the computation of trace parity.

Today we are starting to look in detail at some applications of LFSRs, namely counters and encoders.


I mentioned counters briefly in the article on easy discrete logarithms. The idea here is that the propagation delay in an LFSR is smaller than in a counter, since the logic to compute the next LFSR state is simpler than in an ordinary counter. All you need to construct an LFSR is

Linear Feedback Shift Registers for the Uninitiated, Part IX: Decimation, Trace Parity, and Cyclotomic Cosets

Jason Sachs December 3, 2017

Last time we looked at matrix methods and how they can be used to analyze two important aspects of LFSRs:

  • time shifts
  • state recovery from LFSR output

In both cases we were able to use a finite field or bitwise approach to arrive at the same result as a matrix-based approach. The matrix approach is more expensive in terms of execution time and memory storage, but in some cases is conceptually simpler.

This article will be covering some concepts that are useful for studying the...

Linear Feedback Shift Registers for the Uninitiated, Part VIII: Matrix Methods and State Recovery

Jason Sachs November 21, 2017

Last time we looked at a dsPIC implementation of LFSR updates. Now we’re going to go back to basics and look at some matrix methods, which is the third approach to represent LFSRs that I mentioned in Part I. And we’re going to explore the problem of converting from LFSR output to LFSR state.

Matrices: Beloved Historical Dregs

Elwyn Berlekamp’s 1966 paper Non-Binary BCH Encoding covers some work on

Obsolete? Yes. Still in use? Yes. How do you use it? Ummm...

Ed Nutter November 14, 20175 comments

In today's world of constantly changing technology, quick parts availability, and seemingly endless options, some things can't change.  It isn't a big deal to wait a day or less for a computer upgrade to arrive.  It seems program size increases proportionally to hard drive size.  The old is discarded and replaced with the new.  Hard drives can hold terrabytes and even SD cards can hold gigabytes of information.

Now, suppose a system can't be changed.  It is still...

Linear Feedback Shift Registers for the Uninitiated, Part VII: LFSR Implementations, Idiomatic C, and Compiler Explorer

Jason Sachs November 13, 2017

The last four articles were on algorithms used to compute with finite fields and shift registers:

Today we’re going to come back down to earth and show how to implement LFSR updates on a microcontroller. We’ll also talk a little bit about something called “idiomatic C” and a neat online tool for experimenting with the C compiler.

Lazy Properties in Python Using Descriptors

Jason Sachs November 7, 2017

This is a bit of a side tangent from my normal at-least-vaguely-embedded-related articles, but I wanted to share a moment of enlightenment I had recently about descriptors in Python. The easiest way to explain a descriptor is a way to outsource attribute lookup and modification.

Python has a bunch of “magic” methods that are hooks into various object-oriented mechanisms that let you do all sorts of ridiculously clever things. Whether or not they’re a good idea is another...

Introduction to Microcontrollers - 7-segment displays & Multiplexing

Mike Silva August 14, 2014

Doing the 7 Segment Shuffle

The 7 segment display is ubiquitous in the modern world.  Just about every digital clock, calculator and movie bomb has one.  The treadmills at my gym have 6 or 7, each one displaying 3 or 4 digits.  What makes the 7-seg interesting is that it presents an opportunity to make a trade off between GPIO (output pins) for time.  Every 7-seg display requires 8 outputs (the 7 segments and usually either a decimal point or a...

Delayed printf for real-time logging

Yossi Kreinin October 25, 20133 comments

You often debug by adding a few printfs and looking at the logs. In some real-time/low-level contexts though, you don't have time for text formatting.

You don't want prints to affect timing too much, because then timing-related bugs you're chasing might disappear. And you certainly don't want the system to stop functioning altogether because prints cause it to miss real-time deadlines.

A common alternative to prints is more "raw" logging - an event buffer, where event is a union keeping...

The habitat of hardware bugs

Yossi Kreinin July 13, 20163 comments

The Moscow apartment which little me called home was also home to many other creatures, from smallish cockroaches to biggish rats. But of course we rarely met them face to face. Evolution has weeded out those animals imprudent enough to crash your dinner. However, when we moved a cupboard one time, we had the pleasure to meet a few hundreds of fabulously evolved cockroaches.

In this sense, logical bugs aren't different from actual insects. You won't find...

Two Capacitors Are Better Than One

Jason Sachs February 15, 20155 comments

I was looking for a good reference for some ADC-driving circuits, and ran across this diagram in Walt Jung’s Op-Amp Applications Handbook:

And I smiled to myself, because I immediately remembered a circuit I hadn’t used for years. Years! But it’s something you should file away in your bag of tricks.

Take a look at the RC-RC circuit formed by R1, R2, C1, and C2. It’s basically a stacked RC low-pass filter. The question is, why are there two capacitors?


Important Programming Concepts (Even on Embedded Systems) Part IV: Singletons

Jason Sachs November 11, 20142 comments

Other articles in this series:

Today’s topic is the singleton. This article is unique (pun intended) in that unlike the others in this series, I tried to figure out a word to use that would be a positive concept to encourage, as an alternative to singletons, but

Lost Secrets of the H-Bridge, Part III: Practical Issues of Inductor and Capacitor Ripple Current

Jason Sachs August 24, 20133 comments

We've been analyzing the ripple current in an H-bridge, both in an inductive load and the DC link capacitor. Here's a really quick recap; if you want to get into more details, go back and read part I and part II until you've got equations coming out of your ears. I promise there will be a lot less grungy math in this post. So let's get most of it out of the way:

Switches QAH and QAL are being turned on and off with pulse-width modulation (PWM), to produce an average voltage DaVdc on...

Introduction to Microcontrollers - More On Interrupts

Mike Silva September 25, 2013

A Little More Detail About The Interrupt Mechanism

It's time to look a little closer at what happens in an interrupt request and response.  Again this is in general terms, and different microcontroller designs may do things somewhat differently, but the basics remain the same.  Most but not all interrupt requests are latched, which means the interrupt event sets a flag that stays set even if the interrupt event then goes away.  It is this latched flag...

Byte and Switch (Part 2)

Jason Sachs May 7, 20118 comments

In part 1 we talked about the use of a MOSFET for a power switch. Here's a different circuit that also uses a MOSFET, this time as a switch for signals:

We have a thermistor Rth that is located somewhere in an assembly, that connects to a circuit board. This acts as a variable resistor that changes with temperature. If we use it in a voltage divider, the midpoint of the voltage divider has a voltage that depends on temperature. Resistors R3 and R4 form our reference resistance; when...

VHDL tutorial - A practical example - part 1 - Hardware

Gene Breniman May 18, 20111 comment

In previous posts I described some simple VHDL examples.  This time let's try something a little more complex. This is part one of a multiple part article.  This is intended to be a detailed description of one of several initial designs that I developed for a client.  This design never made it into a product, but a similar design was used and is currently being produced.  As a considerable amount of work was put into this effort, I decided to share this design...

Ten Little Algorithms, Part 4: Topological Sort

Jason Sachs July 5, 20151 comment

Other articles in this series:

Today we’re going to take a break from my usual focus on signal processing or numerical algorithms, and focus on...