 This time we're going to look at the multiplication method for converting between bases. The multiplication and division methods comprise the other pair of strategies for converting between bases. And the multiplication method, like the addition method before, allows us to do our arithmetic in the destination base instead of the source base. A lot of students prefer the multiplication and division methods because they're very procedural. We're going to work through an algorithm and we're just going to do it repeatedly until we run out of digits to work with. So the multiplication method tells you to take our solution, multiply by the source base, and then add in the most significant digit from our original number, and remove it from the original number at the same time, and then just repeat this process until we run out of digits to work with. So if I start with a number, say in base two, I might be interested in knowing what this number is in base ten again. So I'll be doing my arithmetic in the destination base, which is nice. I know how to do arithmetic in base ten. And when I start out, my solution is zero. I don't have anything in my solution. So I'm just going to go to the second part, which says to take this number and add it to my solution. So I take this one, and I'm going to copy it into my solution. I'm going to remove this one from my original number. So this one has been used. I'm not going to need to come back to it. So now I have something in my solution, and I'm going to go back to the beginning of my algorithm and start again. So now I'm going to multiply this by two. So one times two gives me two. And then I'm going to add in the next bit. So zero, and I'll add zero to this, which will give me two. But I'll still go back to the beginning, and I'm going to multiply this by two again. So two times two is four. Then I'm going to add in the next bit. So this time I have a one. Gives me five. And I'll cross out this one. Five times two gives me ten. And then I add in another bit. Gives me ten still. Now I'm going to go back and multiply by two again. Gives me twenty. I'm going to add one. Move the one. Multiply by two. Add zero. Multiply by two. And add one, which gives me eighty-five. Now I've run out of bits in my original number, so I can't go through my number anymore and do any more computation. I'm done. Eighty-five is my final solution in decimal.