I suppose it depends on how you define your number system. I + I = II, I + II = III, I + III = IV, etc.
Seems a bit complicated, even base 10 is too complicated, so let's use base 2.
00 + 00 = 00
01 + 00 = 01
10 + 00 = 10
00 + 01 = 01
00 + 10 = 10
So far it just looks like we can OR these numbers together and all will be fine.
01 + 01 = 10
Oh. It seems that OR isn't quite good enough.
Let's look at some single bit calculations then.
0 OR 0 = 0
1 OR 0 = 1
0 OR 1 = 1
1 OR 1 = 1
What we actually want is f(1, 1) to return 0.
So what about XOR?
0 XOR 0 = 0
1 XOR 0 = 1
0 XOR 1 = 1
1 XOR 1 = 0
Looks good! But with two bit numbers?
01 XOR 01 = 00
We need a way of carrying the bit. You know where this is going. What operation haven't we mentioned yet? AND.
So when we're doing our calculations, we actually need 3 inputs instead of 2, and 2 outputs instead of 1 to accommodate for this carry bit.
Here's a logic diagram for our full adder:
Minecraft has redstone. Redstone is essentially electronics. A line of dust functions like a wire, a torch on the side of a block works like a NOT gate, and from that you can make all the other kinds of gate. There is no OR gate in minecraft since a signal propagates both ways.
Here are some builds of the different gates: