Posted: Mon Feb 19, 2007 1:48 pm
You guys really make my head hurt...! That was impressive. Does it translate into English? And, maybe, words of less than one syllable? <shudder>
Forum to post messages about Bree and Danielbeast
https://lg15.cassieiswatching.com/forum/
https://lg15.cassieiswatching.com/forum/viewtopic.php?t=6465
to change see what crazy Hexidecimal I get but I am having trouble with it... Maybe you can figure it out Deagol. There is more on WikipediaFloating-point numbers are typically packed into a computer datum as the sign bit, the exponent field, and the significand (mantissa), from left to right. For the common (IEEE standard) formats they are apportioned as follows:
sign exponent (exponent bias) significand total
single 1 8 (127) 23 32
double 1 11 (1023) 52 64
While the exponent can be positive or negative, it is stored as an unsigned number that has a fixed "bias" added to it. A value of zero, or all 1's, in this field is reserved for special treatment. Therefore the legal exponent range for normalized numbers is [-126, 127] for single precision or [-1022, 1023] for double.
When a number is normalized, its leftmost significand bit is known to be 1. In the IEEE single and double precision formats that bit is not actually stored in the computer datum. It is called the "hidden" or "implicit" bit. Because of this, single precision format actually has 24 bits of significand precision, while double precision format has 53.
For example, it was shown above that π, rounded to 24 bits of precision, has:
sign = 0 ; e=1 ; s=110010010000111111011011 (including the hidden bit)
The sum of the exponent bias (127) and the exponent (1) is 128, so this is represented in single precision format as
0 10000000 10010010000111111011011 (excluding the hidden bit) = 40490FDB in hexadecimal
The real question is...which half?deagol wrote:Ha, that's it! Remove the comma and you get 333, the triple trinity, or a half-beast... Wink
Excellent! Finally someone understands my postBalmung wrote:Hey what if you did it backwards?
33.001
33+1/1000
[33, 1000]
or
3.3001
...
[3,3,3,99,1,2,3]
:big ol' freakin wink:
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[I'm pretty quick to pick up on math stuff]
Code: Select all
abcdefghijklmnopqrstuvwxyz
20000000011111111112222222
72345678901234567890123456
p i z z a i c e c r e a m s p i n a r t
[16, 9,26,26,27] [ 9, 3, 5] [ 3,18, 5,27,13] [19,16, 9,14] [27,18,20]
2665473/165448 149/16 98571/32266 39001/2046 9767/361
Code: Select all
a c k n o w l e d g e
[27, 3,11,14,15,23] [12, 5, 4, 7, 5]
4549815/166516 9521/781
Using ascii (decimal) code requires smaller chunks:
[97,99,107] [110,111,119,108] [101,100,103,101]
1027725/10594 156959863/1426791 105101005/1040501
Nope, there's no ambiguity (with a caveat), and that's critical for it to work as code. Every continued fraction has a unique real number in decimal, and every real number has a unique continued fraction, as well as a trivial variant.Balmung wrote:is it possible for a continued fraction to convert to a decimal, and then when you convert it back to a continued fraction, you get a different set of numbers? kind of like how 2/4 goes to .5 then 1/2
Code: Select all
S A N T A N E L L A D R O P
[19,01,14,20,01] [14,05,12,12,01] [04,18,15,16]
6299/316 11329/798 17657/4354
When decoding 6299/316 11329/798 17657/4354, you'd probably stop at:
[19,01,14,21] [14,05,12,13] [04,18,15,16]
S A N U N E L M D R O P
Or you might decide to take the extra step:
[19,01,14,20,01] [14,05,12,12,01] [04,18,15,15,01]
S A N T A N E L L A D R O O A
Code: Select all
S A N T A A N E L L A A D R O P A
[19,01,14,20,01,01] [14,05,12,12,01,01] [04,18,15,16,01]
12299/617 21792/1535 18756/4625