 So far we've looked at converting integers between bases. But we might also be interested in converting real numbers. As before, we'll have four different methods of converting between arbitrary bases. And also a more specific method that works between powers of bases. Our addition and subtraction methods work exactly the same as they did before. We will have positive exponents representing all the numbers in the whole number part of our real number. Then we get negative exponents for all the numbers in our fraction. If you compare the multiplication and division methods that we have with the ones we used for integer conversions, you'll notice that before the multiplication method allowed you to do your arithmetic in the destination base and the division method allowed you to do it in the source base. Here they've been switched. That means that if we're using the multiplication and division methods, we're going to want to break our number into two parts. We'll use one strategy to convert the whole number part of our number and a different strategy to convert the fraction part. Basic ideas aren't too much different. We'll do a whole lot of multiplication or division. But the precise details of the methods are a little bit different. Our conversion methods between bases such as binary and octal or binary and hexadecimal will pretty much work the same as they did before. We just have to do our conversion relative to, say, the octal point or the hexadecimal point. We will be looking for groups of three or four bits moving out from that point. So for our whole number part, we'd look for groups of, say, four, then four, then four. On the fraction side, we look for a group of four and a group of four and then a group of four. Pretty straightforward. Just be sure not to work from one end to the other all the way.