 The multiplication method allows us to do our arithmetic in the destination base. So it'll be good for converting numbers from, say, binary to decimal, or octal to decimal, or hexadecimal to decimal. So if I take a number like 0, 1, 1, 0 in binary, and I want to convert this to decimal, going to start with an empty solution and multiply by 2, so obviously it gives me 0. And now I'll add in the first bit, 0 plus 1 gives me 1. Now I can multiply by 2, it will give me 2, add in the second bit. And I can multiply by 2, give me 4, add in the third bit. It will give me 5, multiply by 2, it will give me 10. Add the fourth bit, gives me 11, and I'll multiply by 2. It will give me 22, add 0, and it gives me 22. And since I have no more bits, I'm not going to go back and do the multiplication again, I will just say that my solution is 22. And if I look at my number line, that is what I see. So if I take this same number and I start in octal, it would be 26. And I'm going to do the same thing. So I'll start with an empty solution and I will multiply by my base. It will give me 0, but now I can add in the first digit. This gives me 2, and then I can multiply by my base again. It gives me 16, and I'll add the 6. And that gives me 22 in base 10 again. So the same number in hexadecimal is 16. So if I start with 16 in hexadecimal, then I'll start with a zero for my solution, and I'll multiply by 16. So of course, give me zero. Now I'll add the first digit, which will give me 1. And now I can multiply by 16, which gives me 16. I'll add 6 to that, and I'll get 22 in base 10 again. If I take a different number out of here, say 11011, base 2, I'll do the same thing. I can really kind of skip this first step and just start by taking this first bit. So I'll have 1 times 2 gives me 2 plus 1 is 3 times 2 is 6. My third bit is a 0, multiply by 2 gives me 12, fourth bit is a 1. This will give me 13 times 2 is 26, plus 1 is 27 in base 10. And this is what I get for this number. So the octal version of it is 33. So we can work with that. So I'll take this first digit again, and I will multiply by 8. That will give me 24 in base 10, and I'll add the 3 to get 27. Hexadecimal is 1b. So I'd start with a 1, multiply by 16, gives me 16. And now I want to add b, but I don't have any b's in base 10. So I need to convert the b into base 10. B in base 10 is 11. So I add 11 to 16 and get 27 in base 10.