Why Your Hex Converter Lies to You: Two's Complement, the 53-Bit Wall, and Radix Magic

This story was originally published on HackerNoon at: https://hackernoon.com/why-your-hex-converter-lies-to-you-twos-complement-the-53-bit-wall-and-radix-magic.
An in-depth exploration of two's complement, sign extension traps, IEEE-754 precision limits in JavaScript, and why Radix 36 is the superior choice for URL-safe
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This story was written by: @eliasmiller. Learn more about this writer by checking @eliasmiller's about page, and for more stories, please visit hackernoon.com.

Why hardware never stores a minus sign and how two's complement actually calculates negatives; how arithmetic and logical bitshifts (>> vs >>>) introduce silent network packet bugs; the 53-bit precision limit that collapses large integers in JavaScript; and why Radix 36 beats Base-64 for URL slugs and distributed IDs.