Seriously? A 1 bit "full adder" is too complicated to build with discrete gates? If you are going to show people how to build a discrete 4 bit ALU then you really need to own it and at least build it with simple gates, if not transistors if you want to seriously own the discrete bit. As you can see in this reference (https://en.wikibooks.org/wiki/Microprocessor_Design/Add_and_...) a single bit full adder is 2 xor, 2 and, and an or gate. For for a four bit addr, that is 8 XOR (2 chips), 8 AND (2 chips), and 4 OR (1 chip), so 5 chips instead of one MSI 4 bit adder.