Computers that operate exclusively on boolean algebra

I was wondering if there are any computers that operate exclusively on boolean operations. For example, no add, sub, mult, or div in the instruction set (although these could be emulated with the appropriate boolean code). Rather, the cpu would work by comparing 2 bits at a time, with instructions like and, or, xor. I realize that no modern computer would operate like this, but have any historical computers had an instruction set something like this?

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You can build one on a breadboard using rather large digital components and LED lights, like this: cs.princeton.edu/courses/archive/spr06/cos116/FSM_Tutorial.pdf While I no longer deal with hardware directly, I do not regret taking some classes in digital circuitry. – Job Mar 11 '12 at 5:14
The Digi-Comp, whose CPU has three 1-bit registers - mindsontoys.com/kits.htm?dc1_main.htm – DarenW Oct 31 '12 at 5:30

Even nowadays you can find examples of such processors, for example in complex interlocking systems.

However, these processors are not off-the shelf, and typically the production numbers are so low that in the end these end up being implemented in programmable logic (such as FPGA).

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Böhm-Jacopini result states that every program can be implemented using sequence, repetition, and selection.

So using ONLY booleans makes no sense but if there are repetition control statements such as a FOR or WHILE loop and sequence any computable function can be expressed.

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Try labview's free download. It's pretty close to where you want to be, which is hardware. Circuit design has some tools that, like labview, abstract away some details in order to push up the bar on productivity, but underneath it all, it's all zeros and ones. Quarutus is another, similar option for building circuits that operate exclusively on boolean logic to accomplish some rather simple tasks. But it does help in understanding how computers in general operate.

All computers operate exlusively on boolean logic, this is just some lower-level options for building up your own ideas in a simple format. This does pay off if you're interested in, say, embedded systems.

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"All computers operate exlusively on boolean logic" is not at all true. – Pubby Mar 11 '12 at 5:18
I didn't realize that. Any links back you up? – Droogans Mar 11 '12 at 6:06
Those links point to computers that are modeling bit-wise logic using things other than silicon and copper. I saw nothing of another base besides binary. Is there another number system used in computing? – Droogans Mar 11 '12 at 19:33
en.wikipedia.org/wiki/Ternary_computer uses Ternary logic rather than Binary logic – Scott Rickman Jun 12 '14 at 13:57