 For this example, I'm going to be converting these two decimal numbers into binary. So I'll start with the 13.625. So I mentioned I'm going to break this into two parts. I'll convert the 13 separately from the .625. So 13 in binary is 1101. This number chances are you'll just memorize after a while. But now I have the .625. If you are used to looking at some of these fractions, you might be able to see what that is automatically. But otherwise, we'll want to work through our algorithm. My fraction here is .625. So I'll write this down. And my algorithm says to multiply this by the destination base. I'm converting this to binary, so my destination base is 2. So I get 1.25 as my result. Next thing it tells me to do is to take this whole part of my result and move it up here. So I now have 1101.1. I now go back and multiply this by 2 again. This will give me 0.5. And I will take this 0 and copy it up here as my second bit. Now I'll multiply the .5 by 2. That will give me 1.0. And I would take this 1 and copy it up here as the third bit. Now I can continue multiplying this by 2, but my answer is always going to be 0 from now on. Which should make sense because adding more 0s to the end of a fraction will not change its value. I can have as many 0s here as I'd like, but I'll have the same number. So 13.625 is 1101.101 in binary. So if you'd like to confirm this, you can see that this is 8 plus 4. I don't have any 2s. I have a 1. This is 1 half, 2 to the minus first. 2 to the minus second would be 1 fourth. This is 1 eighth. So 8 plus 4 plus 1 is 13.5 plus .125 gives me .625. Our second example is negative 6.5625. So again, I'll do the negative 6 parts separately from the .625. This negative 6 is minus 110 in binary. Now I want to do the .5625. So I will write down that fraction. Since I'm converting this to binary, I'm going to be multiplying by 2 again. So I'll multiply this fraction by 2, and I get this number out. So I will take this one and move it up here as the next bit in my binary number. And then I will multiply whatever's left by 2. .125 times 2 is .25. So I have a 0. And I would take this 0 and move it up here. Now I want to multiply .25 by 2. That will give me .5. So I will take this 0 and move it up here as my third bit in the fraction. Now I'll multiply this by 2 one more time. I get 1.0. And I take this 1 and move it up here. So there is negative 6.5625 in binary. I've got a 1 half bit and a 1 sixteenth bit. Together those add up to .5625. And then on this side I have negative 6.