That is, floating-point cannot represent point coordinates with atomic accuracy in the other galaxy, only close to the origin. Small values, the ones close to zero, can be represented with much higher resolution (1 femtometre) than distant ones because greater scale (light years) must be selected for encoding significantly larger values.
The example also explains that using scaling to extend the dynamic range results in another contrast with usual fixed-point numbers: their values are not uniformly spaced. But, because 9 digits are 100 times less accurate than 9+2 digits reserved for scale, this is considered as precision-for-range trade-off. Now, one number can encode the astronomic and subatomic distances with the same 9 digits of accuracy. Instead of these 100 bits, much fewer are used to represent the scale (the exponent), e.g. Assuming that the best resolution is in light years, only 9 most significant decimal digits matter whereas 30 others bear pure noise and, thus, can be safely dropped.
distances between galaxies, there is no need to keep all 39 decimal places down to femtometre-resolution, employed in particle physics. For instance, to represent large values, e.g. The idea of floating-point representation over intrinsically integer fixed-point numbers, which consist purely of significand, is that expanding it with the exponent component achieves greater range.
The typical number that can be represented exactly is of the form: Significant digits Ã- base exponent The base for the scaling is normally 2, 10 or 16. The numbers are, in general, represented approximately to a fixed number of significant digits (the mantissa) and scaled using an exponent. In computing, floating point describes a method of representing an approximation to real numbers in a way that can support a wide range of values. A diagram showing a representation of a floating point number using a mantissa and an exponent.
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