HACK III is my largest Minecraft computer to date. It is very loosely based on the HACK architecture. This computer has a seven-function, 16-bit ALU. It is Turing complete and can process at a clock speed of 40 ticks (fastest test). Two seven segment displays are connected to the computer to provide numeric output.
HACK III can support up to 32K RAM and 64K ROM. Currently, it only has internal CPU RAM (no external chips yet) and 256 bytes of ROM (the long chip sticking out).
At the time of its construction, HACK III was Minecraft's largest and most powerful computer. I'm not certain if this record still holds or not.
The forum thread can be found here:
Watch the second video for a more detailed explanation of the computer. Also, note that some of the screenshots above are from before the seven segment displays were added.
Single Player Commands