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The really old TI-83's actually used a physical Z80, coupled with some fancy memory mapping hardware to let it access all of it's "ROM". While this doesn't really apply to our example since the memory isn't Flash, the concept is similar. TI just found cheaper ways to implement these schemes. They kinda ... stuck with us.I figure that this information is only valid for your good ol' Ti-73's, TI-83+/84+(SE)s and perhaps a select few other calculators. You'd have to ask around for how the Ti-89 calcs work, though I think they work in a similar way. The Nspire is completely different and ... well. I'm not the person to ask.
TI did some good programming work on their calculators
The TI-89 and other 68k calcs have 24-bit memory addressing, so there is no need for swapping any memory cause that's 16MB of space to use. The OS is run from the Flash ROM (I think the Flash is fast enough to handle it, since the processor runs at ~15MHz or less; I don't know the exact details but different models have different processor speeds). Normal programs are loaded into RAM. I have no idea what happens with applications.