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There's a project I've been working on: put a DIP z80 into a TI-83+.

There's a couple things that are easier with full-size logic:
- making blinkenlights
- making a front panel
- messing with the address space so that things like cp/m could run
- adding IO ports (real serial port, more GPIO, etc)

Anyway, here's the semi-finished product:

(sending an OS was of course the first thing I did because I'm definitely sure it's stable and not at all going to break on some weird flash thing)
And the two sides of the back:

As Runer112 pointed out on IRC, it "looks eerily like actual surgery"

Every other wire in those bundles is a ground wire. Before, I had tried this without the ground wires, and crosstalk was unsurprisingly the biggest issue. I used 80-pin IDE cable for the wires, which worked pretty well. I would have preferred something with a little higher melting point on the insulation, though. The yellow tape is kapton tape, to prevent any parts of the wires which had de-insulated from touching the board.
Very impressive and fiddly by the looks of it!

You mentioned adding extra functionality such as LED's and other stuff attached to GPIO - do you have any specific plans?
I'm thinking of maybe adding a front panel, something like the Cactus or Cosam.

I think by simply disconnecting A15 from the ASIC, and pulling the ASIC's A15 input high, you could trick it into giving the CPU RAM at address 0, which would allow you to run CP/M in 32k of memory. I'm not sure how I/O would work, though.

EDIT:
I've been experimenting with the clock circuit to see if I can use something other than the built-in RC tank, but I'm getting... strange, seemingly unrelated results. When I hook up a 5V square-wave @ 6 Mhz, the calc gets stuck in the stat-> edit lists menu, and seems to refresh the screen ~twice a second.

When hooking up a 'scope to the stock RC circuit, it appears as if the calculator is in low-power mode most of the time, and by continuing to pulse the clock, it's brought out of low-power mode... at least that's my working theory.

Also, somewhat surprisingly, an NMOS Z80 works, at least assuming I've identified my SGS Z80ACPUB1 correctly.
  
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