Note that you can click on any of the Digital Simulator pictures to download the .DSS file. If you have Digital Simulator (get it here) you can test these out and be impressed. I chose Digital Simulator because it's free for students, and did what I needed it to. It's not real stable, and I couldn't figure out how to expand the design to more than a page (this is supposedly possible), but it works and if you like toying around with this kind of thing, you'll probably want something that doesn't cost a thousand dollars nor expires in 30 days. It has its quirks, but it does the job, so who's complaining? "I like the pretty lights." :)

OK, those rectangles with circles in them are switches. In the upper left, from top down, they represent the following inputs: A, B, Control1, Control2. Also in the middle of the top is the carry-in bit.
The big (4-square) circles represent lights, which will show the output. The one on the upper-right is the output bit, and the one further down and left is the carry bit.

My hand drawn schematics! I'm rather proud of these, so treat 'em kindly. The first one is the leftmost or top breadboard:

Aren't these cool? If you look closely at each chip, I've drawn in where the ins and outs are, and those numbers with circles around them by each gate correspond to a copy of my original schematic where I went through and numbered each gate. Makes tracing the logic a *lot* easier. Here's the right, or lower, breadboard:

Here is something I whipped together to test out my sketch of how the ALU would look when assembled using the chips I have (hence the clustering of gates):

The wires criss-cross to all hells, and sometimes they overlap making it almost impossible to follow with the "naked eye." However, it worked (ok, it didn't, see note below) in the simulator, which is great. I have this sketched out on paper, and the circuit is actually fully assembled as I created this schematic, but it doesn't quite work yet. This proves it's a wiring or chip problem, not a logic one. I'm not quite sure if that's good or bad...

Well, turns out that the impossible-to-follow schematic actually *didn't* work correctly, as the not-B function was disabled. So I redid the whole thing, this time using almost all diagonal lines, so it is technically possible to follow w/the "naked eye." Good luck if you try, though. Anyhow, the not-B works fine, so it was just a glitch. As for the real thing, it's still sitting there looking very impressive, and glaring random lights at me. Time to re-check all of the wiring again and pray a whole bunch. Here's the "new" schematic:

Yeah, a bit messy looking isn't it? Hey, it works though...