 The two's complement format is the method that we currently use for representing integers in computers. It's harder to read and write than the sign-in magnitude format, but it actually makes our arithmetic work out nicely. We won't have to worry about special cases between positive numbers and negative numbers. We can actually just do our arithmetic exactly the way we would expect, and things just happen to work out. But it does end up being a lot harder to read and write than we might like. Our positive numbers are still really easy. You just write down the positive number using however many bits you've got. Again, it will have lots of zeroes on the left-hand side, and we'll use the most significant bit as an implicit sign bit. Again, we won't specifically set this to be a sign bit, but it will be zero if we have a positive number and one if we have a negative number. So if we do want to represent a negative number, we would start by converting the number to binary, write that in binary using however many bits we've got, say 32, and then we would apply the two's complement operation to that number. The two's complement operation will allow us to convert a number between positive and negative representations, and what it will have us do is flip all of the bits in our number, so we'll change all of our zeroes to ones, all of our ones to zeros, and then go back and add one more to this number. Again, it's a little odd and convoluted, but it does make the arithmetic work out. And when our focus in the hardware is on processing the numbers, that's what we're really interested in. This method allows us to do our computation much faster than we otherwise could.