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
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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. -
The Transistor
There is no such thing as a digital transistor. The thing on the chip is an analog switch — leaky, lopsided, and unable to reach the rails you ask of it: an N-type pulls a node cleanly to
0but stalls halfway pulling it to1. Almost everything follows from that one imperfection — why we pair complementary devices into CMOS, why every gate is forced to invert, why a whole computer can be built from copies of a singleNAND, and why speed and power both come down to one knob: voltage. -
More ideas on the way — one disguise at a time.