 Let's try some more examples in arbitrary bases. I have a number in say base nine. I add another number in base nine. Again, I'm going to be looking for blocks of nine because nine is my ten in this case. So seven plus seven is not fourteen. It will actually be fifteen because it will give me a nine and a five. So I'll have a five carry a one. Now I've got one plus three plus four is eight. Eight is less than nine, so it's part of, it is an acceptable digit. I've got eight plus six. I can borrow one from my six, put it with my eight, which will make a ten. That'll leave me with five down here and a ten up here. So I'll have five carry a one. Now one plus eight is nine, so there's a ten. And that leaves me with a six to write down, then one plus zero plus zero is one. So if I've got two numbers in base five that I'd like to add together, one plus four is ten. One plus four is ten, plus three gives me three carry a one. One plus four is ten, plus three gives me three carry a one. One plus two is three, plus one is four. So there's that number in base five. I've got two numbers in base seven that I'd like to add together. I can borrow one from my five, put it with my six, that will make a ten. Then I'm left with four, so I'll have a four carry a one. One plus five gives me six again, so I'll borrow one from my four. That will leave me with three and another ten. Now I have one plus two plus three is six. Six is less than seven, so I don't have any carrying. Then one plus six gives me seven, which is a ten. I do two numbers in binary. Now my ten is two, so one plus one gives me ten. I'll zero carry a one. One plus zero plus one gives me ten again. One plus one plus one is eleven. One plus zero is one, and one plus one is ten. There's another number in base five. So four plus three isn't seven, because I don't have sevens in base five. I actually have five plus two, so it will give me twelve. One plus one plus three gives me ten, and one plus four gives me ten plus two. Now I have three plus two is ten, plus one is eleven in base five. I can also do things and say base twelve. So four plus seven is eleven, and eleven is smaller than twelve. Eleven is one of the digits that I've got available, and that's the digit B. Now nine plus eight is seventeen, but I'm working in base twelve, so I have a twelve plus a five. So I'll write down the five and carry the one. One plus B gives me twelve, so that's ten, leaving me with two, and I'll carry a one. Now I've got one plus A gives me B, so I want to borrow something from my other A, leaving me with nine and a ten. I'll write down a nine, carry a one.