 So the subtraction method is pretty much the flip side of the addition method. We're going to be doing the same sorts of things, but pretty much just in reverse. So the idea here is that we're going to be subtracting exponents of the destination base. So where the addition method allows you to do your arithmetic in the destination base, subtraction method will allow you to do your arithmetic in the source base. So this will make it a whole lot easier to convert from, say, decimal to binary, decimal to base 86. Because all of those were starting in decimal and converting to something else. So this time, instead of finding exponents and then adding them all together, we're going to be trying to find exponents and subtract them. So if I start with a number like 47 in base 10, perhaps I want to convert this to base 2. So the first thing I'm going to do is try to look for exponents of base 2 in my decimal number. So I know a bunch of exponents in base 2. I know that 64 is one of them, but 64 is bigger than 47. So I'm not going to be able to subtract 64 from 47. So I'll go to the next lowest exponent, which is 32. 32 is smaller than 47. So I'll subtract off 32. This would leave me with 15. So the next smallest exponent in base 2 is 16. But again, 16 is larger than 15, so I can't do that subtraction. Instead, I'll go to the next smallest exponent, which is 8. Since 8 is smaller than 15, I'll subtract off 8. So leave me with 7. Now divide 8 by 2, that's 4. So 4 is smaller than 7. So I'll subtract 4. Next smallest exponent is 2. 2 is smaller than 3. That leaves me with 1. 1 is also an exponent of 2. So I could subtract 1 and get 0 out. So now I just need to figure out what all of these exponents are in base 2. And then I can write this number in base 2. So 1 is really easy. That's 1 times 2 to the 0. 2 then is 1 times 2 to the first. 4 is 1 times 2 squared. 8 is 1 times 2 cubed. And then 32 is 1 times 2 to the fifth. So now I'm going to want to take all of those, turn those back into a regular number. So I'll have 1. I don't have a 2 to the fourth, so I'll put in a 0. I do have a 2 cubed, then I have a 2 squared, a 2 to the first, and a 2 to the 0. So there is my number in binary. And the basic idea is I'm looking for all of these exponents of 2 that I pretty much already know. So this method works really well if you know those exponents of 2. If you don't know the exponents of the base that you're converting to, then this method is going to be a whole lot harder to use.