I imagine civilisation would wind back to around the 18th century, because we would understand things like fertilizers, calculus and how to make steel, but could not immediately use that knowledge to produce steam trains, bicycles or saxophones.
So, assuming an accelerated pace of development thanks to some of this knowledge surviving I'd say 50 years give or take.
Do you have books with the existing computer engineering literature in them and just no fabs, or do you have to rediscover boolean logic and information theory?
You can work backwards from "Semiconductor fabrication", which (I guess) would look something like:
Microfabrication > Computation > Manufacturing > Electrical Engineering > Chemical Engineering > Metalworking > Power generation > Basic tools
As to how long this would take, that feels very speculative. Did anyone print a copy of Wikipedia?
There are many books on rebuilding a civilization. I think this is too complicated of a question to answer in a meaningful way. If by apocalypse you mean a true reset of almost everything and only some humans survived but no information was in tact, probably several thousand years or more likely never.
People could draw on cave walls their memories of this civilization. CPU's have a complicated supply chain and there are a myriad of experts that specialize in specific parts of the motherboard, CPU, memory, etc... There is not a single person that has the all inclusive knowledge of engineering a CPU. This assumes we also have people that can refine all the minerals used to craft the parts, the energy requirements to do so and people remain that know how to do this. I assume an apocalypse means we lost many of the people that carry specialized knowledge so most of the R&D would have to be restarted from scratch, again assuming that only some humans survived and all data is gone, power is gone, libraries are gone, etc... This assumes this R&D is the priority of the survivors, which it would not be. Even if all this information was archived on the moon or satellites, nobody would know how to retrieve it and that is assuming any of the survivors even know of it. Current satellites would probably de-orbit in a few generations or sooner. Someone here more knowledgeable could comment on satellites not under active management by people or ground control automation systems.
I personally think their priority will just be survival, probably for quite a few generations. If we are being honest with ourselves, many people today would not survive on a scorched and tattered earth. Most would not even survive in the wild without an apocalypse. By the time a sub-set of the survivors pass hunting & gathering great filter, then agrarian and eventually industrial, all the tribal knowledge would have long since aged out. Maybe there could be campfire stories of the SeaPeaYou's, HighScrapers and falling Spams from the SkyNets. I know this sounds negative but I think this is the best case scenario.
My personal take-away from this thought exercise is to make the most of computers to augment life improvement and life enjoyment while I can and not depend on them.
There's a long and deep infrastructure dependency that needs to exist that would take a long time for all-knowing hunter gatherers to get in place.
But: it's even harder to imagine existing high-tech equipment destroyed, worldwide. A significant % would likely survive. Remember there's like 100B+ cpu's in the world out there.
Starting from there, it would be more like a logistics bottleneck. Like when Covid pandemic hit, or that ship got stuck in the Suez canal. Possibly worse. But manageable.
In short: an event catastrophic enough to nuke that 'installed base', would be extinction-level where "will any humans survive?" would be more relevant than "can we make new cpu's?".
Of course we depended on some machines, raw materials and especially a mono crystalline silicon wafer.
I think it is notable, that we did not really depend on an existing computer. Of course a SAW filter is simple, but the 6502 was still made with a similar technique. So if the material science is up to par again a microprocessor is a smaller step than one might think.
There's a lot we take for granted in civilization. Once those layers are peeled back you're competing for territory with animals and scrounging for survival. Being able to manipulate bits will be extraneous, and really only emerged because of the sheer number of people that are alive right now. With 8Bn people, you get a lot of geniuses.
A better question would be: "how long until you could have a 24/7 source of electricity?"
My guess would be in the hundreds of years from the stone age, assuming we remember those technologies were possible, and we bootstrapped as fast as possible. In practise, you can imagine calamity would breed religious anchors that could weigh us down another thousand years.
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.
This refers to galactic civilisation. The interesting part is: it depends a lot on how much you pass over, anticipating the downfall.
There is a parallel to deploying software: how good are your instructions, if you can’t be there to fill in the blanks?
Anyway, can’t stop thinking in the Delorean’s chip of Back to the Future 3.
Water wheels for a start, then dams, hydroelectric power and industrial revolution around the corner in just a year. Then ethanol/corn fueled engines and we'll be sailing/flying in no time. Trains will go electric right away instead of steam/diesel/gas. A small country with smart people and good leadership would easily build the first computer and nuclear bomb in less than a decade. From there, world domination.
Someone joked that the tribe that protects him will have a major advanage...
I suppose the deeper question is how long until we Factorio our way into being able to prodce all the chemicals and devices involved in the process. I'd love to read an in depth analysis of that question!
Then we can breadboard one[0].
If we lose our ability to produce these extraction and refinement tools (or energy becomes too expensive to extract before we have sufficient alternatives), we'll be locked into a subsistence based existence for hundreds of millions of years until the world reserves of coal and oil are slowly replenished.
No energy = no post-industrial goods (and mass starvation due to lack of fertilizer), and definitely no CPUs.