The four-registers system is almost conplete, two boards assembled, tested and debugged and are working as expected. The only thing yet to do is to connect the boards propery, and hopefully it will be done without additiinal trouble. Here is how it all looks like as of now:

On the left half are the registers themselves, and in the corner is support circuitry for register contents indicators (blue leds in the same corner of right half). On the right board are control circuits -- switches and buttons, and three 2-to-4 decoders (demultiplexers) for choosing the registers I want to do operation on. There is circuitry for choosing which register to set to 1, to enable to be written to from bus and which to enable output to bus. Reset is global and is applied at once for all registers.