Here’s my solution (it’s the one from the book):
And here’s the link:
http://www.lodev.org/jstumble/?board=0e0reerlrfxrreerl00eelrr0ere0llerrr0eer0lieelleel
Description: The two bits on top set up a 4-ball cycle. The first ball subtracts one from register B. The second ball adds the 1’s place of register A to register C. The third ball is thrown out (it doesn’t do anything). The fourth ball adds the 2’s place of register A to register C. When register B underflows, the computer stops.
I think this is the picture for challenge 55 again, not 56. The book solution, and the solution the link points to, use 32 parts.
I agree with Samuel that the image here isn’t the image for challenge 56.
I also think it’s worth noting that this design doesn’t address what happens in the case of overflow. Maybe the challenge statement could have a note added to it saying that the solution should work in cases where the result is less than or equal to 7? Or you could explicitly handle overflow by adding an interceptor, like this:
https://www.lodev.org/jstumble/?board=0e0reerlrfxrreerl00eelrr0ere0llerrr0eel0lielileel_16_16