In the video below, a team built two computers out of dominoes. The first was capable of adding any two numbers between 0 (zero) and 7 (seven). The second computer they built was capable of adding any two numbers between 0 (zero) and 15 (fifteen).
The computer you are using right now, deep under the covers, does everything in terms of binary addition. What about the other operations you ask?
- Multiplication is just repeated addition: 8 x 4 is the same as 8+8+8+8.
- Subtraction is just addition with negative numbers: 8-4 is the same as 8+(-4)
- Division is just repeated subtraction: 12/4 is the same as subtracting 4 from 12 until you have nothing left. So if you start with 12, subtract 4 you have 8. Then subtract 4 again (from 8) leaving 4. Then subtract 4 one more time (from 4) leaving 0 (zero). So 3 times you subtracted 4 from 12, so 12/4=3.
So with addition your computer can do everything. Of course, your computer does it much faster than setting up and toppling dominoes.
For more about computers built out of dominoes, Domino Addition on the Numberphile channel. If you're really really interested, stay to the very end of the video for even more.