The Antonov Saleev variant of the Sobol sequence generates numbers between zero and one directly as binary fractions of length w, from a set of w special binary fractions, V _ i, i = 1, 2, \ dots, w called direction numbers.
12.
What's weird is that I can store an N bit binary integer in somewhere between N / 3 and N / 4 decimal digits-but a binary fraction takes N digits-even though there is the same amount of " information " present in both cases.
13.
I was thinking about binary fractions with N bits after the binary point . . . but with Double precision floating-point format, numbers are represented as " mantissa " x 2 " exponent " . . . where the mantissa is in the range 1 to 2 and has 53 bits.
14.
This is correct; the information content of a three-digit decimal is approximately 9.966 bits; the same message could have been encoded in the binary fraction 0.10001010 ( equivalent to 0.5390625 decimal ) at a cost of only 8 bits . ( The final zero must be specified in the binary fraction, or else the message would be ambiguous without external information such as compressed stream size .)
15.
This is correct; the information content of a three-digit decimal is approximately 9.966 bits; the same message could have been encoded in the binary fraction 0.10001010 ( equivalent to 0.5390625 decimal ) at a cost of only 8 bits . ( The final zero must be specified in the binary fraction, or else the message would be ambiguous without external information such as compressed stream size .)
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