4-bit ALU

This is the beginning of DupinComp. Though I don't quite know all the parts I need or the final design, I'm impatient, so I'm building the ALU before finishing the book. I haven't done any electrical engineering before, and I know very little about electricity, so I'm starting off with a 4-bit ALU. If it ends up not working, or I end up frying anything, then I've wasted less time and money than if I wired the 16-bit ALU I'll eventually need.  Here are all the components I'm using:

3 840 hole breadboards
3 spools of wire (1 green, 1 red, 1 black)
1 Arduino UNO (power supply)
2 DIP 8 slide switches (CTS 206-8)
4 NAND gates (sn74ls00n)
4 AND gates (sn74ls08n)
1 OR gate (sn74ls32n)
4 MUX gates (sn74hct157n)
1 Full Adder (sn7483n)

*Note: This list may change, if I find I need more parts

Though I planned out what I needed based on a design I had already tested with software, I'm tweaking it a little bit. Once I've written it down in HDL (hardware description language, for those who haven't read the book), I'll probably upload it.