Added indication of access to the I2C bus (in fact, access to FRAM) - an LED that lights up when the SCL line is low. The quick-and-dirty approach to connect the LED through a 2 kOhm resistor did not pass at all - there was not a single memory module on the bus - it turned out to be too strong pull-up, although it worked after 4.7 kOhm, but in 7407 there are free pins, so through this buffer it turned out more reliable.

Hello, sir! You may hex-file upload to Arduino with avrdude -> link to hex-file for version 3.8 - in Firmware topic of project description.
This project is opened circuit, but closed source of firmware.

I did a redesign of the project (see picture on the top).
Evaluated the influence of the size of the instruction cache on the real speed of the "nanocomputer" operation using the example of the speed of thinking the first move by the machine in MICROCHESS (results for the TURBO mode, the video image was not drawn):
without cache - 291 seconds;
4-byte cache (too small, overhead does not pay off and degrade speed) - 580 seconds;
cache 8 bytes (optimum) - 21 seconds !!!;
cache 16 bytes (too large, the overhead does not pay off) - 26 seconds.