Floating Point Representation
3 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Suppose we are in a floating-point regime where the mantissa had 3 digits and the exponent has one digit.
Then, 0 = .000e-9 is relatively isolated from next two positive numbers .100e-9 and .101e-9. Which are 10e-12 apart.
This is from Hamming's book on numerical methods, but how is .100e-9 the next positive number, why not .001e-9?
3 Kommentare
James Tursa
am 7 Aug. 2011
@Walter: OP has stated a decimal digit system, so hidden bit & normalization is not applicable.
Walter Roberson
am 7 Aug. 2011
Okay on the hidden bit, but I think normalization is still a factor.
You seldom want a system that has a distinct zero for every different exponent value (e.g., 000E-9 000E-10).
You seldom want a system that has three different representations for some values, such as 100E-12 010E-11 001E-10
IEEE 754, referenced in the tags, *requires* normalization of binary values, except for the extremely small denormalized numbers, which it has special rules for.
IEEE 754 did adopt an optional decimal representation; my recollection at the moment is that it uses normalization as well, but I would need to cross-check that.
Antworten (1)
James Tursa
am 7 Aug. 2011
1) What does this have to do with MATLAB?
2) How can you have numbers in the e-9 and e-12 range with only one exponent digit? Is this some type of decimal digit floating point system you are talking about? If so, what is the exponent bias? How can you get negative exponents in e-9 range with only one digit?
In short, please explain the floating point format you are talking about in detail.
2 Kommentare
James Tursa
am 7 Aug. 2011
Obviously you don't think so, but I do. Why isn't 0.001e-10 or 0.001e-11 or 0.001e-12 the next positive number? The exponent bias *does* make a difference to me, and I can't answer your question without knowing this.
Siehe auch
Kategorien
Mehr zu Logical finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!