On Mon, 19 Jun 2006, Hans-Christoph Steiner wrote:
On Jun 19, 2006, at 3:36 PM, Mathieu Bouchard wrote:
if you include the sign as part of the mantissa, then it's 24 bits. you need slightly more than 7 digits to cover all that range. you also need to take the space taken by writing the decimal point.
0111 1111 1111 1111 1111 1111 (23-bits) = 8388607, not counting the sign, why would you need more than 7 digits to represent 8388607 in decimal?
Because the most significant bit of the mantissa, not counting the sign, is implicit and assumed to be 1 in almost all cases, except zero, NaN and Infinities. Therefore mantissas don't range from 0 to 8388607, they range from 8388608 to 16777215. However, when writing in decimal ascii representation, that bit is always explicit. For numbers 1<=x<2, for example, x is always printed starting with "1", which can be considered as a completely wasted digit.
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