 So this time I'll do a couple examples with larger numbers. We start with 48 and decimal. We want to convert this to binary. So we need to find exponents of 2. We have 2, 4, 8, 16, 32, 64. 64 is bigger than 48, so we'll go back to 32. And we'll put a 1 in our 32 position. 48 minus 32 gives me 16. So our next exponent down is actually 16. So I will put a 1 in the 16 position. That leaves me with 0. So I'm going to fill in zeros in all my other positions. I have an 8, a 4, a 2, and a 1 position. So I put zeros in all of those, and I get 11 and 4 zeros. And that is exactly what I see up for 48. So if I want to convert 48 from decimal to octal, well, I'm going to be looking for exponents of 8. So I have 1, 8, 64. Again, 64 is bigger than 48. So I'm going to look for something times 8, which fits into 48. Well, I know 6 times 8 is 48, so I will subtract 48. And write down 6 in my 8th position. Now, I don't need anything else. I'm left with 0 there, so I'll just put a 0 in the 1's position. And I get 60 in octal, which is also what I see for 48. The last one is hexadecimal. And here, I'm looking for powers of 16. So I have 1, 16, and 256. So I'm going to have to make do with multiples of 16. And 3 times 16 will give me 48. So again, I'll subtract 48. Left with 0. So I'd write down the 3 in hexadecimal, and then 0 for the 1's position. Trying another large number, I can look at, say, 10,000. So to convert to binary, I'm going to be looking for powers of 2 again. I know I have 81, 92, and then the next one up would be 16, 384. So clearly, I'm going to want to take out the 81, 92. And I'm going to put that in the 81, 92's position. That's a really big position. And we're going to have lots of places to follow it. So here, I have 0 minus 2. Well, I'm going to have to borrow something all the way over here, 0. This would be a 10. Borrow from that, now it's a 9, 9, 9. So now I have a 10 in my 1's position. 10 minus 2 will give me 8. 9 minus 9 is 0. And minus 1 is 8. 9 minus 8 is 1. So I have 1808 left. So 4096, I can't pull out of this. So I'll put a 0 there. 2048, nope. 1024, yes. Subtract, I'll get 4. I'll have to borrow something from my 8 here. It's a 7. That's a 10. 10 minus 2 is 8. 7 minus 0 is 7. 1 minus 1 is 0. So I put a 1 in my 1024 position. Going one more exponent down, I have 512, which is less than 784. So I've got a 1 there. 4 minus 2 is 2. 8 minus 1 is 7. 7 minus 5 is 2. So next exponent down is 256, which will also fit. And I'll have to borrow something. So 12 minus 6 will give me 6. 6 minus 5 will give me 1. And 2 minus 2 will give me 0. So I put a 1 in my 256 position. Going down, I'd have 128, which is clearly bigger than 16. So I'll put a 0 there. Next one down is 64. So another 0, 32, another 0. And then 16. So I can subtract a 16. And that'll leave me with 0, but a 1 in the 16's position. Now I need to fill in the rest of my positions. So I have an 8's position, 4's, 2's, and a 1's. Now if I break this up into blocks, I should see that it matches what I get for 10,000. If I try this again for octal, I'm probably going to need to know a few more exponents of octal. But I'll start with my 10,000. And I'm going to look for powers of 8. So I know that I have 1, 8, 64. Now I'm going to need to go up past that. So I'm going to write down my powers of 8. I have 1, 8, 64, 5, 12, 40, 96. And then whatever else I'd have would be bigger than 10,000. So I'm going to start with this 40, 96. And I can pull two of these out of 10,000. So I'll subtract 81, 92. And I will write down 82 in my 4,096 position, which is my 1, 5th position. So 10 minus 2 leaves me with 8, 9 minus 9 is 0, 9 minus 1 is 8. And 9 minus 8 is 1. So you can actually see we ended up over here. Same place again. We're just working with some different numbers this time. So the 1808, I'm going to look for multiples of 5, 12. I think I can pull three of those out of here. I'll put a 3 in the 5, 12 position. So 3 times 5, 12 will give me 15, 36. If I subtract that, 8 minus 6 gives me 2, 7, 10. 10 minus 3 gives me 7. 7 minus 5 gives me 2. So now I'm down to this 272. Should be able to pull some 64s out, maybe four of them. So 64 times 4, 6 times 4 would give me 24 plus 16 give me 256. So I'll write down a 4 in my 64th position. And this will leave me with 16. 16 then is 2 in my 8th position and leaves me with 0 for my 1's position. So if I compare this with my number in my slide, I'll discover I've put the wrong number in the slide and don't need to go change that. Now that we have the right number in the slide, we can try this again for base 16. So again, I will start with 10,000 in decimal. And I'm going to be looking for powers of 16. So I would have 1, 16. Know that I've got 256. Then I need to find more powers of 16. Looks like whatever my next position is over here, that would be much larger than I need. So I'm going to look for blocks of 4096 and my 10,000. And as we saw before, I've got two of those. It gives me 81,92. So I will write down a 2 in my 4096th position, which this time is the fourth position. So as before, this leaves me with 1,808 once I do my subtraction. Now I need to find a multiple of 256 in my 1,808. Well, four of these gets me about 1,000. And that should leave me with about enough for three more. So I think I can get seven of these out of here. So if I do 256 times 7, 6 times 7 is 42. 7 times 5 is 35. 9. And 7 times 2 is 14. Plus 3 is 17. So I can get 7, 256 is out of my 1,808. So I will put a 7 in my 256 position. Now I'll do this subtraction. I'll need to borrow here. So 8 minus 2 is 6. 10 minus 9 is 1. That leaves me with a 16. And I can get 116 out of there. So I would put a 1 in my 16's position. And I've got nothing left. So I will put a 0 in the 1's position. And I get 2710 for my hexadecimal number, which is what I'd find in my slide this time.