• You don't build a custom chip.

    You design a custom board with the chips on it, get some prototypes and assemble them and test. Then you work with one of the assembly places to get it produced. There are a bunch of places specializing in runs of various sizes. Lots of places will pre-program your chip (or you could do it yourself). Notice how Digikey et. al. offer to pre-program many microcontrollers.

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