That is quite a bit more messy than it needs to be.
and it's kind of messy because I didn't plan anything
One step ahead of you.
Most of the complication arose from me forgetting about various things. For instance, I wasn't handling carry properly on the bit 1 adders, so certain combinations would give improper result. This is one of the reasons why I have 5-block high staircases and a bunch of gates sticking out of the back of the "machine."
All in all, this could have been made smaller and neater if I had planned it, but like I said, I didn't plan it at all. I literally threw together one adder, made sure it worked, then threw another one in. The carry logic, particularly for result bit 2, is probably more complex than it needs to be.
But, again, it works fine, and that was the sole objective. Considering it's my first redstone machine
ever, I don't think it's too hideous. I can work on making a better adder another time, and I probably will.
I've got a 1bit adder set up in one of my worlds. What really gets interesting is when you try to make a proper circuit that does something useful (like say, set all the right turns in your rail system so you can select a destination)
Yeah, I was kind of inspired to mess with redstone when I saw a video of someone who set up an elaborate subway system.