https://makertube.net/videos/watch/b2f2bd20-5c32-4556-aa80-5a198917f337 Why does Python tell you that 0.1 + 0.2 = 0.30000000000000004? The answer is IEEE 754 - the floating-point standard baked into every CPU on the planet. In this video we go under the hood: from the limits of fixed-point arithmetic, through scientific notation in binary, to hand-converting 3.14 into its 32-bit IEEE 754 representation - and then proving it in C with a union hack that reads the raw bits directly out of memory. We also look at what happens at the edges: divide by zero, and rather than a crash you get infinity. Divide zero by zero and you get NaN - Not a Number. IEEE 754 doesn't just define the happy path, it defines all the weird paths too. ━━━━━━━━━━━━━━━━━━━━━━━━ 📌 CHAPTERS ━━━━━━━━━━━━━━━━━━━━━━━━ 0:00 The 0.1 + 0.2 Problem 1:01 Fixed-Point Arithmetic 5:57 Scientific Notation & the Birth of Floating Point 6:48 The IEEE 754 Standard 7:01 Converting 3.14 to a 32-bit Float 11:12 Proving it in C 13:24 Edge Cases: Infinity and NaN 15:20 Why IEEE 754 Changed Everything ━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 LINKS & RESOURCES ━━━━━━━━━━━━━━━━━━━━━━━━ ☕ Support the channel on Patreon (+ 24hr early access, no ads): https://www.patreon.com/ncot_tech Scientific Calculator - Thirunavukkarasye-Raveendran, CC BY 4.0 https://creativecommons.org/licenses/by/4.0, via Wikimedia Commons Intel 486 DX2 Die shot - This file was derived from: Intel 80486 DX2 die.JPG by Pauli Rautakorpi CC BY 3.0 Music by Karl Casey @ White Bat Audio Tue, 02 Jun 2026 17:30:17 GMT https://validator.w3.org/feed/docs/rss2.html PeerTube - https://video.eientei.org https://video.eientei.org/lazy-static/avatars/d78575d1-24d3-4192-a1fb-bccf471ac353.png https://makertube.net/videos/watch/b2f2bd20-5c32-4556-aa80-5a198917f337 All rights reserved, unless otherwise specified in the terms specified at https://video.eientei.org/about and potential licenses granted by each content's rightholder. https://video.eientei.org/w/o6DgKtxsYbUcueACenFwNc;threadId=40488 https://video.eientei.org/w/o6DgKtxsYbUcueACenFwNc;threadId=40488 Mon, 01 Jun 2026 04:40:42 GMT btw the weird addition of 127, is to divide the exponent in half, so half of it is the positive exponent and the other half the negative (the fractions). To honest, I don't remember the generic formula right now.

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