I just wired and tested one diode array used for decoding the 1 of 10 signal to the what the seven segment displays need. It took a long time.
The parallel multiplier was going to use diode arrays as well, but I am not keen on using 40 relays and 768 diodes. I looked into the double dabble algorithm and it actually seems pretty simple to do with eight +3 adding circuits with no output carry. Best guess is maybe 60-80 relays for a parallel multiplier and double dabbler, which will also cut down the amount of relays required in the adder.
I'm hoping to make at least 4 single digit additions or multiplications per second, which would allow for a complete 8 digit by 8 digit addition to be made in 2 seconds and a multiplication to be made in 32 seconds.
Also I think I may need four registers, not three.
And just like that, I have run out of relays.