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Whats the smallest computer you could make?
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RJSV:
Hello Typematrix!    OOPs,  shot my mouth off (again);  I had meant to say,  you could have a processor using non-silicon technology, where it is the case that its easier to do MATH functions by table lookup, rather than actual ALU logic.  A decimal mode multiplier, for example, can perform a multiply by placing the two input digits together, concatenating into an address, such as '42',  when doing a 4 times 2 multiply.   (The answer would be '08', as a two digit result.)
   Of course any table lookup method must have a well behaved input, such as SINE wave lookup, using zero though 90 degrees.  Obviously, an 'inverse SINE' lookup table does not appear practical, as the input values aren't going to show a sequential form, for the pointer to the table values.  Still,  there can be some powerful lookups done,  such as SINE lookup, producing 3 digits of result for each angle of input.
    While development of the mechanical computer was most focus on 'imitation' of electronic gates and existing bus architectures one of the more interesting MEMs developments had implemented a transistor function using a vibrating column, used to transfer single electrons as it gets close to either side (electrode).  I believe that development was being done as a university physics dept.
   Mostly, practical systems are going to have layers, as the network folks say;  and I would say the layers are for data transfer (gate layer), next are layer(s) doing the micro-code, as in the 6502 instruction set, for example.  Next up is going to start to be operating systems.   My approach, to a mechanical system, would be to get upwards a couple layers, to where a user does not know or need to know
what the signal level hardware is or is doing.  Thus some students could stick to learning software,  rather than delving into the physics of the gates.
   I was convinced, and still am, that the students, learning on a mechanical gate system, would come up with things I would never have thought of !
   Typematrix,  I think this question you've asked is one of the best, in this blog system !
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