2026年7月14日

Audio Frequency Analyzer: five-band spectrum display

Five Bands, Twenty Hertz to Twenty Kilohertz: How to Read an Audio Frequency Analyzer

By xiezixing 2026年7月14日

A spectrum analyzer turns your ears into a screen you can defend in a mix review. Here is what the five-band display actually tells you — and the three traps that make it lie.

Entropy Calculator poster — Shannon, Min-Entropy, Strong/Medium/Weak rating and CPU-vs-GPU cracking times for sample inputs

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Measuring Cryptographic Strength with an Entropy Calculator

By xiezixing 2026年7月14日

Length is not a security metric. Use Min-Entropy to measure how unpredictable a password, key, or token really is — and how long it would take an adversary with 10⁶ to 10¹² guesses/sec to crack it.

Dice Probability Calculator cover with title and stats row

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Why Dice Probability Doesn’t Behave the Way Your Gut Says

By xiezixing 2026年7月14日

Two six-sided dice have 36 ordered outcomes. Sum 7 hits 1/6 of the time. The triangular histogram is your mental model for craps, Yahtzee, Catan robber rolls, and every D&D attack roll.

CRC32 Checksum tool — IEEE 802.3 32-bit fingerprint for ZIP, PNG, gzip, and Ethernet integrity

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The 32-bit Fingerprint Your Computer Uses a Billion Times a Day: A CRC32 Field Guide

By xiezixing 2026年7月14日

CRC32 is not a hash. It is the cheapest integrity check in computing, and the reason ZIP, PNG, gzip, and Ethernet all know when something went wrong.

Significant Figures Sandbox — 5 rules, 3 modes, 4 traps mental model

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Five Rules That Decide Whether Your Measurement Is Honest: The Significant Figures Sandbox

By xiezixing 2026年7月14日

Count, round, and propagate significant figures with a sandbox that grades each digit and walks you through the rules — built for chemistry and physics students who keep getting 0.005030 wrong.