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Depends on how many people die in the apocalypse.

In general, tech requires specialization. (You don't have people who are devoting most of their time to something else who are also producing critical components of our tech tree - the exception being some open-source components.)

Specialization requires enough people that you can put at least one person in each specialty (plus enough to grow food to feed all those specialists).

So you can't create CPUs below a certain population level, whether or not the people remember the scientific knowledge that it all requires.



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