1. The problem statement, all variables and given/known data
Calculate the roundoff error using the function |x - fl(x)| - roundoff error.
fl(x) is the floating point representation of the value 0.2 (x = 0.2).
2. Relevant equations
See above.
3. The attempt at a solution
This isn't actually a assignment or exercise, it's actually a worked example from a set of notes we have and there's just a jump in the example from one part to another which I could use some help understanding. So, after finding fl(0.2) = (1.1001....10011010)2 x 2^-3 (52 bits long)
0.2 = 1.1001...100110001)2 x 2^-3 (52 bits long).
|0.2 - fl(0.2)| = |-1 + (0.1001)2| x 2^-52 x 2^-3.
This is where I lost track. What's been done to turn the left hand side into the right and where has that -1 come from?
Calculate the roundoff error using the function |x - fl(x)| - roundoff error.
fl(x) is the floating point representation of the value 0.2 (x = 0.2).
2. Relevant equations
See above.
3. The attempt at a solution
This isn't actually a assignment or exercise, it's actually a worked example from a set of notes we have and there's just a jump in the example from one part to another which I could use some help understanding. So, after finding fl(0.2) = (1.1001....10011010)2 x 2^-3 (52 bits long)
0.2 = 1.1001...100110001)2 x 2^-3 (52 bits long).
|0.2 - fl(0.2)| = |-1 + (0.1001)2| x 2^-52 x 2^-3.
This is where I lost track. What's been done to turn the left hand side into the right and where has that -1 come from?
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