Build a 3 bit full adder using only XOR gate? I don't know if this is the right place to ask this, but I'm trying to design the logic for a simple calculator and I was wondering how can you build/design a 3 bit full adder using only XOR (one or the other but not both) gates and no AND or OR gates as well. How can it be done using only XOR operation?

To implement 1 bit full adder you need 2 XOR gates 2 AND and 1 OR gate. You can construct a NOT gate using XOR, but the other crucial operation, OR, cannot be constructed with it. If it was possible, you could make yourself AND gates using 3 NOT's and 1 OR, and then pretty much have everything you need to make a full adder.