Lazy Properties in Python Using Descriptors
Python descriptors let you outsource attribute lookup, and Jason Sachs walks through a practical use: lazy, cached properties. He presents a LazyProperty descriptor that defaults to a WeakKeyDictionary cache so computed results are stored on first access and automatically purged when objects are garbage collected. The post shows how to share caches by value using attrkey or swap cache classes for different use cases.
Linear Feedback Shift Registers for the Uninitiated, Part VI: Sing Along with the Berlekamp-Massey Algorithm
Jason Sachs breaks down the Berlekamp-Massey algorithm and shows how to recover an LFSR's minimal connection polynomial from a stream of output bits. The article mixes intuition, worked examples, and Python code to demonstrate the update rule, visual debugging tables, and when the solution is unique. Expect practical implementation notes, a complexity discussion, and a libgf2 example you can run in an IPython notebook.
Linear Feedback Shift Registers for the Uninitiated, Part V: Difficult Discrete Logarithms and Pollard's Kangaroo Method
Most discrete-log problems are hopeless by brute force, but clever algorithms cut that cost to feasible levels. This installment walks through baby-step giant-step, Pollard’s rho and kangaroo methods, and how Silver-Pohlig-Hellman and index calculus leverage group structure to speed attacks on GF(2^n) fields. Jason Sachs includes Python examples, heuristics, and complexity nuggets so you can see when each method is practical.
Linear Feedback Shift Registers for the Uninitiated, Part IV: Easy Discrete Logarithms and the Silver-Pohlig-Hellman Algorithm
Discrete logarithms can be either trivial or infeasible depending on how group elements are represented, and Jason Sachs shows a practical route when they are intentionally easy. This article walks through using LFSRs as fast counters, why a smooth group order matters, and how the Silver-Pohlig-Hellman algorithm plus the Chinese Remainder Theorem recovers exponents in GF(2) with small prime factors.
Linear Feedback Shift Registers for the Uninitiated, Part III: Multiplicative Inverse, and Blankinship's Algorithm
Jason Sachs walks through Blankinship's constant-space variant of the Extended Euclidean Algorithm and shows how to compute multiplicative inverses both modulo an integer and in GF(2)[x]. The article uses clear numeric and polynomial examples, Python snippets, and an LFSR finite-field example to show how the algorithm yields Bézout coefficients and inverses useful for discrete-log tricks and cryptographic contexts. Readers get a practical recipe for inverse computation.
Tenderfoot: Embedded Software and Firmware Specialties
This post revisits an earlier Stack Overflow answer and breaks embedded firmware into practical specialties, from assembly optimization and device drivers to DSP, IoT networking, security, UI, and systems architecture. It outlines the core skills, tools, and math each specialty demands, and explains how product constraints and industries shape those roles. Newcomers get clear guidance on where to focus their learning and career development.
Linear Feedback Shift Registers for the Uninitiated, Part II: libgf2 and Primitive Polynomials
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 called libgf2,...
Linear Feedback Shift Registers for the Uninitiated, Part I: Ex-Pralite Monks and Finite Fields
Jason Sachs demystifies linear feedback shift registers with a practical, bitwise view and the algebra that explains why they work. Readable examples compare Fibonacci and Galois implementations, show a simple software implementation, and reveal the correspondence between N-bit Galois LFSRs and GF(2^N) so you can pick taps and reason about maximal-length pseudorandom sequences.
How to Succeed in Motor Control: Olaus Magnus, Donald Rumsfeld, and YouTube
Jason Sachs turned frustration with algorithm-heavy motor-control app notes into a practical MASTERs class, now available on YouTube. He walks through building a fifteen-minute field-oriented control refresher, the hazards teams commonly miss, and the months of prep required to make a polished technical lecture. Read for a candid behind-the-scenes look at teaching motor control to engineers and tips you can apply to your next drive project.
Scorchers, Part 1: Tools and Burn Rate
Small purchases often pay for themselves faster than you expect, and Jason Sachs walks through the math to prove it. He shows how to compute a fully burdened labor rate, including taxes, benefits, overhead, holidays, and productive hours, then compares that rate to the price of common tools. The practical conclusion is simple: if a sub-$100 utility saves about an hour of productive work, just buy it.
3D printing for embedded development
Used mostly for creating little plastic objects, the desktop 3D printer is not an obvious addition to the embedded developer's toolbox. However, if you're looking for more reasons to get one, or already have one that's mostly gathering dust, here are a couple of embedded-related ways to get more value out of it.
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 1)
Jason Sachs argues the 2021 semiconductor shortage was not a single surprise but a set of structural imbalances exposed by COVID-19. He connects long lead times, constrained 200mm fabs and mature-node economics to why automotive features like heated seats became scarce, and shows how bullwhip dynamics and inventory practices amplified the problem. This first part uses concrete anecdotes and simple games to make the supply-chain lessons tangible.
What I Learned From Crashing and Burning in Grad School
Have you ever felt so consumed by something that it started to crowd other parts of your life? So obsessed with success in a particular area that you could hardly think about anything else? I found myself in exactly that spot in 2018 when I first started graduate school; I wanted to succeed so badly that I worked myself to the bone and I let even my marriage and my health suffer in service to it. This state of being is, believe it or not, NOT conducive to success, in neither the long-term nor the short-term. But it took two authors and one pivotal book for me to understand that, to see the pit I had dug for myself, and to begin the path back out. In this blog, I want to share with you my journey in the hopes that you can avoid the mistakes I made.
Baking in Process Improvements
Jason Sachs uses a backyard cookie-baking session with his niece to illustrate practical process improvements engineers can apply. He documents batch-by-batch tweaks — temperature, dough placement, and a pipelined scooping step — that raised throughput and improved quality, then connects the lesson to pilot projects and small automations like a Python script for JIRA. The piece makes the case for quick experiments and a culture that rewards refinement.
Supply Chain Games: A Warning on Tariffs
Jason Sachs warns that the 2025 tariff surge could amplify an existing semiconductor inventory glut and destabilize automotive and industrial supply chains. He lays out why steep, rapid tariff changes cannot be absorbed by years-long fab lead times, sticky proprietary ICs, or quick part substitutions. Read this to understand practical risks, likely timing, and what engineers and buyers should watch over the next two to three years.
How to Include MathJax Equations in SVG With Less Than 100 Lines of JavaScript!
Jason Sachs recounts a simple hack to get MathJax equations inside SVG without heavy dependencies or complex tools. His approach renders MathJax in temporary HTML divs, captures the resulting SVG nodes, and swaps them into SVG
Scorchers, Part 1: Tools and Burn Rate
Small purchases often pay for themselves faster than you expect, and Jason Sachs walks through the math to prove it. He shows how to compute a fully burdened labor rate, including taxes, benefits, overhead, holidays, and productive hours, then compares that rate to the price of common tools. The practical conclusion is simple: if a sub-$100 utility saves about an hour of productive work, just buy it.
Scorchers, Part 4: Burned by the Happy Path (Simon Says)
Designs that only work along the happy path break in real use, causing frustration and sometimes safety risks. Jason M. Sachs uses everyday examples from microwaves to car Auto Park logic to show how mutable software and physical state create brittle behavior. He outlines practical firmware fixes such as clear state machines, sensor or user-driven resynchronization, soft-start delays, and a ‘‘Drunken Happy Path’’ fuzzing approach to find real-world failure modes.
Tenderfoot: Embedded Software and Firmware Specialties
This post revisits an earlier Stack Overflow answer and breaks embedded firmware into practical specialties, from assembly optimization and device drivers to DSP, IoT networking, security, UI, and systems architecture. It outlines the core skills, tools, and math each specialty demands, and explains how product constraints and industries shape those roles. Newcomers get clear guidance on where to focus their learning and career development.
Massive Open Online Courses ( Transforming education )
Jayaraman Kiruthi Vasan outlines why MOOCs have become a practical way for embedded engineers and programmers to learn from top universities without quitting jobs. The post highlights platform options like Coursera, edX, Udacity and Khan Academy, explains how on-demand video lectures and clear prerequisites make targeted upskilling feasible, and points to DSP and Python courses useful for embedded design.
Oh Robot My Robot
Oh Robot! My Robot! You’ve broken off your nose! Your head is spinning round and round, your eye no longer glows, Each program after program tapped your golden memory, You used to have 12K, now there is none that I can see, Under smoldering antennae, Over long forgotten feet, My sister used your last part: The chip she tried to eat.
Oh Robot, My Robot, the remote controls—they call, The call—for...
A Wish for Things That Work
Jason Sachs revisits his long-running gripe with poor user interfaces, cataloguing annoyances from his Toyota Prius dashboard to desktop apps and browsers. He mixes sharp, real-world examples with a short, practical wishlist for 2018 aimed at making embedded displays, update behavior, security cues, and developer tools noticeably less frustrating for engineers and end users alike.
Linear Feedback Shift Registers for the Uninitiated, Part IX: Decimation, Trace Parity, and Cyclotomic Cosets
Taking every jth bit of a maximal-length LFSR uncovers a surprising algebraic structure. Jason Sachs walks through cyclotomic cosets, shows why decimation by powers of two preserves minimal polynomials, and connects LFSR output to trace parity and simple bitmask parity computations. The article uses hands-on Python with libgf2, Berlekamp-Massey, and state recovery so you can reproduce and automate these analyses.
Python Code from My Articles Now Online in IPython Notebooks
Jason M. Sachs has published the Python code from his EmbeddedRelated articles as standalone IPython notebooks. He automated extraction of example code and pushed the notebooks to a public Bitbucket repository under the Apache license, and they are viewable via nbviewer. The post lists available notebooks and asks readers to link back to EmbeddedRelated and share feedback on how they used the code.
Book Review: "Turing's Cathedral"
The early days of electronic computing are explored through George Dyson's Turing's Cathedral, which traces the IAS machine, John von Neumann, and Princeton's Institute for Advanced Study from 1940 to 1958. Jason Sachs praises Dyson's archival access and narrative detail, especially on hardware like vacuum tubes and delay lines, but warns the book's software explanations feel vague and would have benefited from diagrams.
Reading and Understanding Profitability Metrics from Financial Statements
Whoa! That has got to be the most serious-minded title I’ve ever written. Profitability Metrics from Financial Statements, indeed. I’m still writing Part 2 of my Supply Chain Games article, and I was about to mention something about whether a company is profitable, when I realized something that didn’t quite fit into the flow of things, so I thought I’d handle it separately: how are you supposed to know what I mean, when I say a company is profitable? And how am I...
Massive Open Online Courses ( Transforming education )
Jayaraman Kiruthi Vasan outlines why MOOCs have become a practical way for embedded engineers and programmers to learn from top universities without quitting jobs. The post highlights platform options like Coursera, edX, Udacity and Khan Academy, explains how on-demand video lectures and clear prerequisites make targeted upskilling feasible, and points to DSP and Python courses useful for embedded design.
Musings on Publication — and Zero Sequence Modulation
Publishing technical content involves more than writing, it requires tools, reviewers, and patience. Jason Sachs walks through his lean workflow for posting to EmbeddedRelated, contrasts it with the multi-person review cycles at semiconductor companies, and points out a neat trick for checking PDF metadata. He also highlights a Microchip tutorial on Zero Sequence Modulation that includes a 3-D HTML5 interactive viewer to make space vector concepts easier to grasp.
3D printing for embedded development
Used mostly for creating little plastic objects, the desktop 3D printer is not an obvious addition to the embedded developer's toolbox. However, if you're looking for more reasons to get one, or already have one that's mostly gathering dust, here are a couple of embedded-related ways to get more value out of it.
Painting with Light to Measure Time
When Jason Sachs needed to verify a first-order sigma-delta LED dimming implementation but had no oscilloscope, he turned to long-exposure "light painting" to turn time into space on a photograph. By sweeping the camera across blinking LEDs he captured pulse trains, read the bit patterns from the light trail, and confirmed the result with a tiny Python accumulator model. The post shares practical tips on timing accuracy, exposure, and avoiding ambient-light artifacts.
