Definite Article: Notes on Traceability
Electronic component distibutor Digi-Key recently announced part tracing for surface-mount components purchased in cut-tape form. This is a big deal, and it’s a feature that is a good example of traceability. Some thing or process that has traceability basically just means that it’s possible to determine an object’s history or provenance: where it came from and what has happened to it since its creation. There are a...
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.
Linear Feedback Shift Registers for the Uninitiated, Part XVIII: Primitive Polynomial Generation
Jason Sachs walks through how to find primitive polynomials for GF(2) LFSRs, moving from naive exhaustive checks to smarter synthetic constructions. The article compares sieve and constructive methods, shows practical optimizations like parity checks and companion-matrix updates, and demonstrates decimation plus Berlekamp-Massey to generate all primitives from one seed; it also teases a novel Falling Coyote Algorithm for additional speedups.
Linear Feedback Shift Registers for the Uninitiated, Part XVII: Reverse-Engineering the CRC
Jason Sachs shows how to pry CRC parameters out of a black-box oracle and reimplement the checksum yourself. By canceling the affine offsets, probing single-bit basis messages, and treating per-bit outputs as LFSR sequences, you can recover the generator polynomial, bit and byte order, and init/final XOR values. The post includes working Python code, a 4-message shortcut, and real-world tests such as zlib CRC32.
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 XI: Pseudorandom Number Generation
Jason Sachs breaks down when linear feedback shift registers make good pseudorandom sources and when they fail. He shows why LFSR output bits look very different from full-state integer samples, explains their two-valued autocorrelation and quasi-random behavior, and gives practical guidance on when an LFSR is acceptable for fast hardware bit generation and when you should use a proper PRNG instead.
Linear Feedback Shift Registers for the Uninitiated, Part X: Counters and Encoders
Jason Sachs shows how linear feedback shift registers can be practical counters and compact absolute encoders, and why the choice of polynomial matters. He explains using primitive and reducible polynomials to get long but decode-friendly periods, demonstrates a 48-bit example, and lays out a De Bruijn chain-code encoder that turns an extra track into quick absolute resynchronization. Read to learn implementation tradeoffs and decoding strategies.
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.
Linear Feedback Shift Registers for the Uninitiated, Part VIII: Matrix Methods and State Recovery
Matrix methods for LFSRs look intimidating, but Jason Sachs walks through companion-matrix representations and shows why they matter for time shifts and state recovery. He derives lookahead masks from powers of the companion matrix, then translates those matrix insights into efficient bitwise and finite-field algorithms. The article includes two simple state-recovery methods and working Python/libgf2 examples you can run and adapt.
Linear Feedback Shift Registers for the Uninitiated, Part VII: LFSR Implementations, Idiomatic C, and Compiler Explorer
Jason Sachs takes LFSR theory back to real hardware, showing multiple C implementations and dsPIC33E assembly to squeeze cycles out of Galois LFSR updates. He digs into idiomatic C pitfalls like rotate idioms, demonstrates tricks using unions and 16/32-bit views, and shows when inline assembly with SL/RLC and conditional-skip instructions pays off. The article also uses Compiler Explorer and supplies an MPLAB X test harness for verification.
nRF5 to nRF Connect SDK migration via DFU over BLE
This writeup contains some notes on how I was able to migrate one of my clients projects based on the nRF5 SDK, to nRF Connect SDK (NCS) based firmware, via a DFU to devices in the field over BLE.
Levitating Globe Teardown, Part 2
Tim Wescott opens up a budget levitating globe and shows why it seems magical: a massive 30 mm rare-earth magnet and a deliberately cheap magnetic circuit. He documents a bolt used as the flux core, a likely microcontroller and hall sensor in the head, very fine winding in the electromagnet, and a single-transistor unidirectional drive. Part 3 will measure forces and sensor voltages to build a better controller.
Margin Call: Fermi Problems, Highway Horrors, Black Swans, and Why You Should Worry About When You Should Worry
Jason Sachs walks through practical strategies for choosing engineering margin, from split-second Fermi estimates to industry-grade safety factors. He blends highway and boiler anecdotes with a MOSFET thermal example to show why probabilistic thinking, experiments, and documentation matter when you must decide fast or later justify your choices. Read this to learn how to balance conservatism, cost, and risk in real projects.
Linear Feedback Shift Registers for the Uninitiated, Part XI: Pseudorandom Number Generation
Jason Sachs breaks down when linear feedback shift registers make good pseudorandom sources and when they fail. He shows why LFSR output bits look very different from full-state integer samples, explains their two-valued autocorrelation and quasi-random behavior, and gives practical guidance on when an LFSR is acceptable for fast hardware bit generation and when you should use a proper PRNG instead.
Basic hand tools for electronics assembly
Though the software tools vary with different microcontrollers, many hardware tools are the same.
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.
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.
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.
Linear Feedback Shift Registers for the Uninitiated, Part VII: LFSR Implementations, Idiomatic C, and Compiler Explorer
Jason Sachs takes LFSR theory back to real hardware, showing multiple C implementations and dsPIC33E assembly to squeeze cycles out of Galois LFSR updates. He digs into idiomatic C pitfalls like rotate idioms, demonstrates tricks using unions and 16/32-bit views, and shows when inline assembly with SL/RLC and conditional-skip instructions pays off. The article also uses Compiler Explorer and supplies an MPLAB X test harness for verification.
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...
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 4)
The chip shortage didn't end with 2021, it moved into older process nodes where cars and industrial gear live. In this installment Jason Sachs explains why mature-node and trailing-edge capacity remain tightly constrained, how NCNR commitments and price increases are reshaping supplier behavior, and what companies like NXP and Microchip are doing to cope. He warns the imbalance could take multiple semiconductor cycles to fix.
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.
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.
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 X: Counters and Encoders
Jason Sachs shows how linear feedback shift registers can be practical counters and compact absolute encoders, and why the choice of polynomial matters. He explains using primitive and reducible polynomials to get long but decode-friendly periods, demonstrates a 48-bit example, and lays out a De Bruijn chain-code encoder that turns an extra track into quick absolute resynchronization. Read to learn implementation tradeoffs and decoding strategies.
Linear Feedback Shift Registers for the Uninitiated
Jason Sachs assembled an eighteen-part deep dive into linear feedback shift registers, connecting the simple shift-register circuit to finite-field algebra and practical tools. The series walks through primitive polynomials, Berlekamp-Massey state recovery, libgf2-based analysis, discrete-log methods, and real-world uses from PRNGs and Gold codes to Reed-Solomon and CRC reverse-engineering. It’s a single reference for engineers who want both theory and working code.
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.
nRF5 to nRF Connect SDK migration via DFU over BLE
This writeup contains some notes on how I was able to migrate one of my clients projects based on the nRF5 SDK, to nRF Connect SDK (NCS) based firmware, via a DFU to devices in the field over BLE.
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.
