[PD] 23bit t_float vs. 20bit display in Pd's integer representation

[Mathieu Bouchard]

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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