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?
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).
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.
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.