Inside a chip a digit is a voltage on a wire, and every wire wobbles: noise, heat, parts getting old. Cut the voltage into ten levels and a small wobble pushes a six into a seven. Cut it into two and the same wobble changes nothing: it's clearly high or clearly low.

In 1945 ENIAC still counted in tens. A year later, planning the next machine, Arthur Burks, Herman Goldstine and John von Neumann chose two: "we do not attempt to measure gradations of charge at a particular point in the Selectron but are content to distinguish two states." (They also valued binary for simpler, faster arithmetic.)

Our simplified simulation: one million digits each way through the same wire with the same wobble (4% of the range), each digit read as the nearest level. Ten levels: about 15 in every 100 read wrong. Two levels: not one in a million. The wobble's size is our choice; the point is what the same wobble does to each.

Some drives today read sixteen levels in a single cell to fit more in. That only works when the wobble is kept tiny.

Computers don't count in twos because they're simple. They count in twos because two is hard to get wrong.

What else did you assume computers do because they're "simple"?

Sources: our own simulation, 2026; Arthur W. Burks, Herman H. Goldstine and John von Neumann, Preliminary discussion of the logical design of an electronic computing instrument, 1946; John von Neumann, First Draft of a Report on the EDVAC, 1945; Moore School of Electrical Engineering, Report on the ENIAC, 1946; Kioxia, US patent 11,264,090, 2022.
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