Webtagr - Technology News Summarizer

Is 0.999... Really Equal to 1? A Mathematical Controversy

2025-06-02

This article delves into the long-standing debate surrounding whether the infinitely repeating decimal 0.999... is exactly equal to 1. While mathematically proven to be equal, many find this counterintuitive. The article analyzes common proofs, highlighting their shortcomings in terms of student comprehension, particularly concerning the multiplication of infinite decimals. It further explains the absence of infinitesimals and infinity in the real number system, introducing hyperreals to demonstrate why the difference between 0.999... and 1 is an infinitesimal, equivalent to zero in the real numbers. Ultimately, the article concludes that the intuitive feeling of a difference between 0.999... and 1 isn't contradictory; this difference simply holds no significance within the real number system used daily.

(lcamtuf.substack.com)

Misc infinite decimal

The Decibel (dB): A Scientific Unit Gone Mad

2025-05-22

The decibel (dB), a seemingly simple unit for measuring sound, is surprisingly complex and confusing. It's not a unit in the conventional sense, but rather a logarithmic scale representing a change in magnitude. The article delves into the history and application of the bel and decibel, highlighting the ambiguity arising from its context-dependent nature. Different fields use dB differently, leading to inconsistencies and misunderstandings. The author uses the example of microphone sensitivity to illustrate the inherent confusion, arguing for a more standardized and less ambiguous approach to this widely used unit.

(lcamtuf.substack.com)

Tech decibel scientific unit measurement

Drawing the Sierpinski Triangle with Bitwise Operations: A Stunning Bit Twiddling Hack

2025-05-10

This article unveils a stunning bit manipulation trick: generating the famous Sierpinski triangle fractal using only a simple bitwise AND operation (&). The author meticulously breaks down the bitwise operation, revealing the underlying mathematical principles. It shows how the inherent fractal nature of binary counting and iterative block removal, achieved through bitwise manipulation, generates the classic Sierpinski triangle. This technique cleverly leverages the binary operation capabilities of computers, simplifying the seemingly complex process of generating graphics into concise code, resulting in an astonishingly elegant solution.

(lcamtuf.substack.com)

Development

What is Electricity? From Atomic Structure to Conductivity

2025-02-23

This article provides a clear and accessible explanation of electricity. Starting with the Bohr model of the atom, the author explains the arrangement and behavior of electrons within atoms and discusses key concepts in quantum mechanics such as quantization and the Pauli exclusion principle. The article further explains the different behaviors of electrons in insulators and conductors, and how electric current is generated. The author uses plain language, avoiding complex mathematical formulas and jargon, making it easy for readers to understand the fundamental principles of electricity.

(lcamtuf.substack.com)

Tech electricity basics atomic structure conductivity

Relativity and the Origin of Magnetic Fields

2025-02-06

This article provides an intuitive explanation of the origin of magnetic fields, avoiding the typical textbook approach of simply introducing 'B-fields' or 'H-fields'. Using a thought experiment involving a spaceship and flashing lights, the author elegantly explains how relativistic length contraction accounts for the appearance of magnetic fields when electrons move in a wire. The key insight is that while a stationary observer sees a constant electron density, an observer moving with the electrons perceives a lower electron density and a higher positive ion density, resulting in a net electric field pulling it towards the conductor – the essence of a magnetic field.

(lcamtuf.substack.com)

Tech Relativity Magnetic Fields Electromagnetism

A Surprisingly Rich History of Calculators

2025-01-31

This article traces the surprisingly rich history of calculators, from ancient abacuses and counting rods to modern electronic devices. Using a personal collection of antique calculators, the author details the evolution from mechanical marvels like Pascal's adder and Leibniz's multiplier, through slide rules, hand-cranked calculators, and finally, the electronic calculator. The story highlights key technological advancements and limitations at each stage, culminating in the miniaturization and widespread adoption of handheld calculators, even integrated into wristwatches. However, the rise of smartphones ultimately relegated the standalone calculator to a niche product.

(lcamtuf.substack.com)

Tech calculator history mechanical calculators electronic calculators

Copper Pours on PCBs: Fashion or Necessity?

2025-01-30

The widespread use of copper pours in modern PCB design has sparked discussion. This article explores the reasons behind this trend, going beyond mere aesthetics. From early 8-bit computer motherboards to today's smartphones, PCB design has evolved dramatically. Copper pours not only improve signal integrity in high-speed electronics but also reduce RF emissions, aiding compliance with regulations like FCC Part 15. However, the mechanism involves inductance and common-mode chokes; copper pours manage return current paths to lower impedance, reducing interference and radiation. But copper pours aren't always necessary; for most hobby projects, it's not a critical concern. The article concludes by cautioning about the careful consideration required when working with high-speed interfaces, and the potential increase in shunt capacitance.

(lcamtuf.substack.com)

Hardware PCB design copper pours signal integrity

UI Hell: The Case of the Four-Function Calculator

2025-01-24

This article delves into the surprisingly complex UI design of a seemingly simple four-function calculator. Starting with the basic components—ten digit keys, operators, and an equals sign—the author reveals hidden complexities. Issues like handling continuous operations, negative number input, implicit equals, and the legacy 'K-constant' feature are explored. These seemingly minor details lead to inconsistencies and user confusion, highlighting the challenges in designing even the simplest of devices. The author uses humor and diagrams to illustrate the intricate logic and historical evolution of calculator UI, prompting reflection on the design nuances often overlooked in everyday objects.

(lcamtuf.substack.com)

Design Calculator

Mystery Solved: The 'Evil' RJ45 Dongle Was Just Old Tech

2025-01-17

A tech blogger investigates a Chinese-made RJ45-to-USB dongle accused on social media of containing malware. Through reverse engineering, the author discovers the dongle uses a publicly available, signed driver for a clone of the Realtek RTL8152B chip. The onboard flash memory stores the driver, essentially acting as a 'software-defined' CD-ROM. The conclusion? The dongle itself is harmless, just employing an outdated method of driver delivery. The article, written in a lighthearted tone, highlights misinterpretations and overreactions in cybersecurity, emphasizing the importance of security, particularly for critical infrastructure and strategic businesses.

(lcamtuf.substack.com)

Tech hardware reverse engineering

C Programming's Dark Corners: Exploiting Obscure Syntax

2025-01-10

This article delves into the lesser-known corners of C syntax, showcasing techniques like function renaming using `typedef` and `asm` keywords, bypassing compiler checks with forward parameter declarations, and employing function declarations as `for` loop iterators. The author uses a series of mind-bending code examples to illustrate the flexibility and complexity of C, prompting reflection on the boundaries of the C standard and compiler implementations. The article is written with humor and is best suited for those with prior C programming experience.

(lcamtuf.substack.com)

Development Coding Tricks

Say Goodbye to Obsolete Op-Amps: A Guide to Modern Alternatives

2025-01-07

This article critiques the widely used but outdated LM741 and LM324/LM358 op-amps, recommending superior, user-friendly modern alternatives such as the Microchip MCP6272, MCP6022, and Texas Instruments OPA2323, TLV3542, and OPA2356. It details crucial parameters to consider when choosing an op-amp, including supply voltage range, maximum output current, rail-to-rail I/O (RRIO), input stage type (FET vs. bipolar), gain-bandwidth product, slew rate, and noise. The author emphasizes that many parameters are often overblown in hobbyist projects.

(lcamtuf.substack.com)

Development op-amp analog circuit design electronics components

The Hydraulic Analogy: A Detriment to Electronics Education

2024-12-30

Many introductory electronics textbooks use the hydraulic analogy to explain circuits, comparing electric current to water flow and batteries to pumps. However, the author argues this analogy is deeply flawed, especially when explaining semiconductor components like JFETs and MOSFETs. The analogy fails to accurately represent their characteristic curves, ultimately hindering learning. The author advocates abandoning this inaccurate analogy and instead learning electronics from more fundamental principles.

(lcamtuf.substack.com)

Development electronics education hydraulic analogy

The Marvelous Disappearing Capacitor: A Clever Trick to Improve Photodiode Amplifier Performance

2024-12-12

This article introduces a clever technique to improve the performance of photodiode amplifiers: bootstrapping. The parasitic capacitance of a photodiode limits its ability to amplify rapidly changing signals. In a traditional transimpedance amplifier (TIA), this capacitance reduces bandwidth. The article analyzes the working principle of a TIA, explaining how the photodiode's parasitic capacitance affects circuit performance. The author presents a bootstrapped circuit using an op-amp and JFET, which effectively eliminates the parasitic capacitance by keeping the voltage across the photodiode terminals virtually the same, significantly improving bandwidth. The article also discusses a variant AC-coupled bootstrapped circuit and provides relevant formulas.

(lcamtuf.substack.com)

Hardware photodiode bootstrapping transimpedance amplifier