A Working Library

Applied Computing

The handful of plain ideas that make a computer actually compute — taken one at a time, from the first principle all the way down to the silicon that runs it.

Here's a funny thing about the machine on your desk: underneath the apps and the abstractions, it's really a small handful of ideas, each one wearing a dozen disguises. So that's what we'll do here — take them one at a time. Build each one up from nothing, find the single move that makes it useful, and then chase it all the way down to the hardware, into the places it earns its keep: numbers, memory, parallelism, the strange new arithmetic that trains the learning machines. And we won't just talk about it — every section is yours to poke at. Read the idea, then grab a slider and watch the bits move.

Contents

Floating Point

Computers store finite bits; the real numbers are infinite. So every way of writing a real on a machine is a lossy compression — the only question is which reals you keep. Floating point is the answer the whole world settled on: binary scientific notation, packed into a sign-exponent-mantissa layout, co-designed with the hardware so the bits sort like integers, round predictably in silicon, and degrade gracefully at the edges. It's why 0.1 + 0.2 ≠ 0.3, and why deep learning set loose a whole zoo of new number formats.
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More ideas on the way — one disguise at a time.

Applied Computing

Floating Point