 This time, I'm just going to go through a number of examples in various bases. I'll start off with a common example in base 16, which is to add DEAD to BEEF. So, F plus D will give me 1C. And the easy way to do this is to recognize that I've got this F. It's 1 less than 10. I'm just going to take something from my D and put it over with my F. That'll give me 10. And whatever is left is what I'll put down below. So, my result is here is 1C. So I write down the C, carry the 1. Now, 1 plus E puts me in the same position I was in before, where I've got this F down here. So I'll borrow something from the A, put it with the F. Now I've got 9 here and a 10 down here. So I'll write down the 9, carry a 1. Now I've got 2E is in a 1, so I can say either one of them is in an F, borrow something from the other. I'm left with 1D. So there's my 1D. Now I've got 1 plus D gives me E, which is not quite as nice to work with as F, but it's pretty close. So I need to subtract 2 from my B. B is 11. 11 minus 2 is 9. So this will also give me 9, carry a 1. Then my 1 just comes down. And these strategies will work in any base that we're interested in. So I can also do addition and say base 5. If I have that number in base 2 and I want to add another number in base 5, so 2 plus 4 doesn't give me 6 because I don't have any 6's in base 5. I have 11 instead. So write down 11. 3 plus 4 plus 1 would normally give me 8, but again I don't have any 8's in base 5. I have to represent this as 10 plus 3. So I'll write down the 3, carry the 1. 1 plus 4 is 10. 10 plus 2 is 12. 1 plus 1 plus 3 is 5, which is again 10. So I get 1, 0, 2, 3, 1 for my answer in base 5. But I can do that same problem and say base 6, and I'll get a slightly different number. So 2 plus 4 is 10 in base 6. So I'll write down a 0, carry a 1. 1 plus 3 is 4. 4 plus 4 is 12. So write down a 2, carry a 1. 4 plus 2 is 10. Plus 1 is 11. And then 1 plus 1 plus 3 is 5. So I get a number that's about half the size in base 6, as it is if I do that same arithmetic in base 5. Again I can move up one more base. Look at this problem in say base 7. And again the main concern is remembering what base I'm in, so I remember what 10 is. 2 plus 4 is 6 this time, because I have 6's in base 7. 3 plus 4 is 10 because I'm in base 7. And now I've got 1 plus 4 plus 2 is also 10. And then 1 plus 1 plus 3 is 5. So my base 7 number isn't too different from my base 6 number. And if I move up to doing this in octal, I would have, and now I'm looking for blocks of 8. So 2 plus 4 is 6. 3 plus 4 is 7. So I now have 7's in base 8. 4 plus 2 is 6. And then 1 plus 3 is 4. Now because I didn't carry anything, if I increase the base any further, I'm going to end up doing the same arithmetic, nothing's going to change anymore. So this won't get any more interesting. But as long as there was some carrying to do, there was some potential for some interesting change to happen there.