# IEEE representation

by Maylis
Tags: ieee, representation
 PF Gold P: 575 Between any powers of 2, are there 2^52 representable numbers? I just guessed on that one. Is the number of representable numbers between 2^3 and 2^4 2^52 as well?? Or how do you determine that log2(eps(1)) ans = -52 so the distance between 1 and the next representable number is 2^ -52, now I see that one. I think I discovered a pattern for determing the value of eps(x). So you just express x as a power of 2, if its a whole number, then you do 2^x-52, and that is eps(x). If yoy have something that is not expressed as a power of 2, then you just go back to the lower number that can be, so eps(5) = eps(4) So eps(4), 4 is 2^2, so eps(4) is 2^(2-52) = 2^-50. So now, I can say with some confidence I understand F.1, F.3, and F.4. Now where I am stuck is F.2 and F.5. Edit: I might be able to justify F.5 now, let's give this a whirl So I know eps(2^52) is 1, because 2^(52-52) is 0, hence 2^0 = 1. So, everything in between there also has an eps(x) = 1. That means you can have ##2^{52}, 1+2^{52}, 2+2^{52},3+2^{52} ....2^{53}##. So there are 2^52 numbers in between 2^52 and 2^53. So I guess what you should do to find the number of representable numbers is subtract the highest number from the lowerst number in the interval, then divide by eps(lower interval)?? ##2^{53} - 2^{52} = 2^{52}/1 = 2^{52}## representable numbers So to create another example, the number of representable numbers between [4 8). eps(4) = 2^(2-52) = 2^-50 spacing between. ##8-4 = 4##, so ##4/2^{-50} = 4*2^{50}## representable numbers between 4 and 8