NOR (like NAND) is a universal logic gate. You can build any other logic gate out of just NORs.
For this ALU, you’d presumably write a subroutine that computed XORs in terms of NORs, and then use that as a primitive for building an adder.
For this ALU, you’d presumably write a subroutine that computed XORs in terms of NORs, and then use that as a primitive for building an adder.
To me it's not really an ALU either, since the NOR gate doesn't really do the job I expect from an ALU.