Monte Carlo Integration
Monte Carlo integration looks deceptively simple, estimate an area by throwing random points at it and counting hits. Jason Sachs uses that idea to approximate pi, compare error scaling, and then show why the same approach becomes far more useful in higher dimensions. He also demonstrates a stratified sampling trick that improves accuracy by spending samples where they matter most.
You Don't Need an RTOS (Part 4)
In this fourth (and final!) article I'll share with you the last of the inter-process communication (IPC) methods I mentioned in Part 3: mailboxes/queues, counting semaphores, the Observer pattern, and something I'm calling a "marquee". When we're done, we'll have created the scaffolding for tasks to interact in all sorts of different the ways. Additionally, I'll share with you another alternative design for a non-preemptive scheduler called a dispatch queue that is simple to conceptualize and, like the time-triggered scheduler, can help you schedule some of your most difficult task sets.
You Don't Need an RTOS (Part 3)
In this third article I'll share with you a few cooperative schedulers (with a mix of both free and commercial licenses) that implement a few of the OS primitives that the "Superduperloop" is currently missing, possibly giving you a ready-to-go solution for your system. On the other hand, I don't think it's all that hard to add thread flags, binary and counting semaphores, event flags, mailboxes/queues, a simple Observer pattern, and something I call a "marquee" to the "Superduperloop"; I'll show you how to do that in the second half of this article and the next. Although it will take a little more work than just using one of the projects above, it will give you the maximum amount of control over your system and it will let you write tasks in ways you could only dream of using an RTOS or other off-the-shelf system.
Finite State Machines (FSM) in Embedded Systems (Part 4) - Let 'em talk
No state machine is an island. State machines do not exist in a vacuum, they need to "talk" to their environment and each other to share information and provide synchronization to perform the system functions. In this conclusive article, you will find what kind of problems and which critical areas you need to pay attention to when designing a concurrent system. Although the focus is on state machines, the consideration applies to every system that involves more than one execution thread.
You Don't Need an RTOS (Part 2)
In this second article, we'll tweak the simple superloop in three critical ways that will improve it's worst-case response time (WCRT) to be nearly as good as a preemptive RTOS ("real-time operating system"). We'll do this by adding task priorities, interrupts, and finite state machines. Additionally, we'll discuss how to incorporate a sleep mode when there's no work to be done and I'll also share with you a different variation on the superloop that can help schedule even the toughest of task sets.
Finite State Machines (FSM) in Embedded Systems (Part 3) - Unuglify C++ FSM with DSL
Domain Specific Languages (DSL) are an effective way to avoid boilerplate or repetitive code. Using DSLs lets the programmer focus on the problem domain, rather than the mechanisms used to solve it. Here I show how to design and implement a DSL using the C++ preprocessor, using the FSM library, and the examples I presented in my previous articles.
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.
You Don't Need an RTOS (Part 1)
In this first article, we'll compare our two contenders, the superloop and the RTOS. We'll define a few terms that help us describe exactly what functions a scheduler does and why an RTOS can help make certain systems work that wouldn't with a superloop. By the end of this article, you'll be able to: - Measure or calculate the deadlines, periods, and worst-case execution times for each task in your system, - Determine, using either a response-time analysis or a utilization test, if that set of tasks is schedulable using either a superloop or an RTOS, and - Assign RTOS task priorities optimally.
Unraveling the Enigma: Object Detection in the World of Pixels
Exploring the realm of embedded systems co-design for object recognition, this blog navigates the convergence of hardware and software in revolutionizing industries. Delving into real-time image analysis and environmental sensing, the discussion highlights advanced object detection and image segmentation techniques. With insights into Convolutional Neural Networks (CNNs) decoding pixel data and autonomously extracting features, the blog emphasizes their pivotal role in modern computer vision. Practical examples, including digit classification using TensorFlow and Keras on the MNIST dataset, underscore the power of CNNs. Through industry insights and visualization aids, the blog unveils a tapestry of innovation, charting a course towards seamless interaction between intelligent embedded systems and the world.
Finite State Machines (FSM) in Embedded Systems (Part 1) - There's a State in This Machine!
An introduction to state machines and their implementation. Working from an intuitive definition of the state machine concept, we will start with a straightforward implementation then we evolve it into a more robust and engineered solution.
You Don't Need an RTOS (Part 1)
In this first article, we'll compare our two contenders, the superloop and the RTOS. We'll define a few terms that help us describe exactly what functions a scheduler does and why an RTOS can help make certain systems work that wouldn't with a superloop. By the end of this article, you'll be able to: - Measure or calculate the deadlines, periods, and worst-case execution times for each task in your system, - Determine, using either a response-time analysis or a utilization test, if that set of tasks is schedulable using either a superloop or an RTOS, and - Assign RTOS task priorities optimally.
Finite State Machines (FSM) in Embedded Systems (Part 1) - There's a State in This Machine!
An introduction to state machines and their implementation. Working from an intuitive definition of the state machine concept, we will start with a straightforward implementation then we evolve it into a more robust and engineered solution.
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.
Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter
Jason Sachs shows how a single-pole IIR low-pass filter, implementable in one line y += alpha * (x - y), tames noise in embedded signals without floating point. The post explains how to compute alpha from tau and delta-t, practical tradeoffs like phase lag and oversampling, and fixed-point pitfalls including how many extra state bits you need to avoid quantization. Short, practical, and code-ready.
Elliptic Curve Cryptography - Basic Math
An introduction to the math of elliptic curves for cryptography. Covers the basic equations of points on an elliptic curve and the concept of point addition as well as multiplication.
You Don't Need an RTOS (Part 2)
In this second article, we'll tweak the simple superloop in three critical ways that will improve it's worst-case response time (WCRT) to be nearly as good as a preemptive RTOS ("real-time operating system"). We'll do this by adding task priorities, interrupts, and finite state machines. Additionally, we'll discuss how to incorporate a sleep mode when there's no work to be done and I'll also share with you a different variation on the superloop that can help schedule even the toughest of task sets.
Ten Little Algorithms, Part 3: Welford's Method (and Friends)
Jason Sachs takes a practical look at Welford's method, a numerically stable online algorithm for computing mean and sample variance without storing large batches. He demonstrates Python implementations, shows why the naive sum and sum-of-squares approach suffers catastrophic cancellation, and why Welford is a better fit for memory- and CPU-constrained embedded systems. Jason then turns Welford into simple filters for tracking time-varying noise and discusses heuristic fixes and tradeoffs.
Finite State Machines (FSM) in Embedded Systems (Part 4) - Let 'em talk
No state machine is an island. State machines do not exist in a vacuum, they need to "talk" to their environment and each other to share information and provide synchronization to perform the system functions. In this conclusive article, you will find what kind of problems and which critical areas you need to pay attention to when designing a concurrent system. Although the focus is on state machines, the consideration applies to every system that involves more than one execution thread.
You Don't Need an RTOS (Part 3)
In this third article I'll share with you a few cooperative schedulers (with a mix of both free and commercial licenses) that implement a few of the OS primitives that the "Superduperloop" is currently missing, possibly giving you a ready-to-go solution for your system. On the other hand, I don't think it's all that hard to add thread flags, binary and counting semaphores, event flags, mailboxes/queues, a simple Observer pattern, and something I call a "marquee" to the "Superduperloop"; I'll show you how to do that in the second half of this article and the next. Although it will take a little more work than just using one of the projects above, it will give you the maximum amount of control over your system and it will let you write tasks in ways you could only dream of using an RTOS or other off-the-shelf system.
Ten Little Algorithms, Part 7: Continued Fraction Approximation
In this article we explore the use of continued fractions to approximate any particular real number, with practical applications.
Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter
Jason Sachs shows how a single-pole IIR low-pass filter, implementable in one line y += alpha * (x - y), tames noise in embedded signals without floating point. The post explains how to compute alpha from tau and delta-t, practical tradeoffs like phase lag and oversampling, and fixed-point pitfalls including how many extra state bits you need to avoid quantization. Short, practical, and code-ready.
Ten Little Algorithms, Part 3: Welford's Method (and Friends)
Jason Sachs takes a practical look at Welford's method, a numerically stable online algorithm for computing mean and sample variance without storing large batches. He demonstrates Python implementations, shows why the naive sum and sum-of-squares approach suffers catastrophic cancellation, and why Welford is a better fit for memory- and CPU-constrained embedded systems. Jason then turns Welford into simple filters for tracking time-varying noise and discusses heuristic fixes and tradeoffs.
Ten Little Algorithms, Part 1: Russian Peasant Multiplication
Jason Sachs revisits a centuries-old multiplication trick and shows why it still matters. He lays out Russian Peasant Multiplication with simple Python code, then reveals how the same shift-and-add pattern maps to GF(2) polynomial arithmetic and to exponentiation by squaring. The post mixes historical context with practical bitwise techniques that are useful for embedded and low-level math work.
From Baremetal to RTOS: A review of scheduling techniques
Jacob Beningo walks through five common embedded scheduling techniques, showing how each scales from a single super loop to a full RTOS. He highlights practical trade-offs for round-robin, interrupt-driven, queued, cooperative, and RTOS approaches so you can spot when timing becomes fragile and when added complexity is justified. This primer sets up the next post on when to adopt an RTOS.
You Don't Need an RTOS (Part 1)
In this first article, we'll compare our two contenders, the superloop and the RTOS. We'll define a few terms that help us describe exactly what functions a scheduler does and why an RTOS can help make certain systems work that wouldn't with a superloop. By the end of this article, you'll be able to: - Measure or calculate the deadlines, periods, and worst-case execution times for each task in your system, - Determine, using either a response-time analysis or a utilization test, if that set of tasks is schedulable using either a superloop or an RTOS, and - Assign RTOS task priorities optimally.
Finite State Machines (FSM) in Embedded Systems (Part 1) - There's a State in This Machine!
An introduction to state machines and their implementation. Working from an intuitive definition of the state machine concept, we will start with a straightforward implementation then we evolve it into a more robust and engineered solution.
Ten Little Algorithms, Part 4: Topological Sort
Jason Sachs detours from signal processing to make topological sort feel practical and even a little funny, using a Martian Stew recipe to illustrate dependencies and cycles. He walks through two canonical algorithms, Kahn’s method and the depth-first-search variant, compares adjacency-list and matrix graph representations, and provides complete Python implementations so you can run and inspect cycle detection and ordering yourself.
Ten Little Algorithms, Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
Today we will be drifting back into the topic of numerical methods, and look at an algorithm that takes in a series of discretely-sampled data points, and estimates the maximum value of the waveform they were sampled from.
Elliptic Curve Cryptography - Basic Math
An introduction to the math of elliptic curves for cryptography. Covers the basic equations of points on an elliptic curve and the concept of point addition as well as multiplication.
Practical CRCs for Embedded Systems
Stephen Friederichs shows a practical way to get correct CRC code quickly by using PyCRC to generate C implementations, then verifying them on the desktop and an AVR ATMega328P. The post walks through the common generation algorithms, how to self-test with the standard "123456789" check value, and a real timing comparison that exposes the speed versus memory tradeoffs for embedded systems.
