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Old 2011-08-23, 14:20   #1
fivemack
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Default Where did that 37 come from

At a party yesterday, my friend Simon commented that it was silly to display baud-rates in hex, since decimal 38400 comes out in hex as 0x9600 and causes confusion.

That is, 9600 is a number for which 'read as if it were in hex' and 'multiply by four' are the same operation.

154231124 is a number for which 'read as if it were in hex' and 'multiply by 37' are the same operation. Likewise 224321889 [41] 187605873 [35] and 17996800 [22].

multipliers I have observed are 4, 6, 10, 16, 22, 25, 35, 37, 40, 41 (twice! 224321889 and 789458685), 42, 56, 61 (1365665301), 64, 65 (3502669923), 66 (1067455668), 67 (4251168226) ...

this is an unnatural set of numbers but I suppose read-as-if-it-were-in-hex is an unnatural operation.

of course 11702482 [25] implies 117024820 [40] and 1170248200 [64]
187605873 [35] implies 1876058730 [56]

Last fiddled with by fivemack on 2011-08-24 at 18:10
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Old 2011-08-23, 20:20   #2
xilman
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Quote:
Originally Posted by fivemack View Post
At a party yesterday, my friend Simon commented that it was silly to display baud-rates in hex, since decimal 38400 comes out in hex as 0x9600 and causes confusion.

That is, 9600 is a number for which 'read as if it were in hex' and 'multiply by four' are the same operation.

154231124 is a number for which 'read as if it were in hex' and 'multiply by 37' are the same operation. Likewise 224321889 [41] 187605873 [35] and 17996800 [22].

multipliers I have observed are 4, 6, 10, 16, 22, 25, 35, 37, 40, 41 (twice! 187605873 and 789458685), 42, 56, 61 (1365665301), 64, 65 (3502669923), 66 (1067455668), 67 (4251168226) ...

this is an unnatural set of numbers but I suppose read-as-if-it-were-in-hex is an unnatural operation.

of course 11702482 [25] implies 117024820 [40] and 1170248200 [64]
187605873 [35] implies 1876058730 [56]
And, of course, Halloween is the same as Christmas Day.

(Yes, the old ones are the best.)


Paul

31 OCT == 25 DEC
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Old 2011-08-23, 20:38   #3
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Quote:
Originally Posted by fivemack View Post
At a party yesterday, my friend Simon commented that it was silly to display baud-rates in hex, since decimal 38400 comes out in hex as 0x9600 and causes confusion.

That is, 9600 is a number for which 'read as if it were in hex' and 'multiply by four' are the same operation.

154231124 is a number for which 'read as if it were in hex' and 'multiply by 37' are the same operation. Likewise 224321889 [41] 187605873 [35] and 17996800 [22].

multipliers I have observed are 4, 6, 10, 16, 22, 25, 35, 37, 40, 41 (twice! 187605873 and 789458685), 42, 56, 61 (1365665301), 64, 65 (3502669923), 66 (1067455668), 67 (4251168226) ...

this is an unnatural set of numbers but I suppose read-as-if-it-were-in-hex is an unnatural operation.

of course 11702482 [25] implies 117024820 [40] and 1170248200 [64]
187605873 [35] implies 1876058730 [56]
I'm confused ?? is there a link to an explanation somewhere of what is meant ?
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Old 2011-08-24, 02:27   #4
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Originally Posted by science_man_88 View Post
I'm confused ?? is there a link to an explanation somewhere of what is meant ?
9600 * 4 = 38400, and 0x9600 (the way programmers write 9600_16 or "9600 in hexadecimal") is also 38400 = 0 * 16^0 + 0 * 16^1 + 6 * 16^2 + 9 * 16^3.
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Old 2011-08-24, 19:36   #5
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Originally Posted by CRGreathouse View Post
9600 * 4 = 38400, and 0x9600 (the way programmers write 9600_16 or "9600 in hexadecimal") is also 38400 = 0 * 16^0 + 0 * 16^1 + 6 * 16^2 + 9 * 16^3.
thanks should I make a pari code to figure out sequences ?
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Old 2011-08-24, 22:27   #6
fivemack
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I've taken this in C++ code to about 2.5e12 for several bases, so probably there's little point writing very much pari. The smallest working-example for base 11 is amusingly enormous (it's a tripling). Next interesting question is whether there are better search techniques than just counting.

You're looking for a short vector in the integer lattice perpendicular to some other vector, but I'm not sure how you encode 'non-negative' for lattice problems; might well be able to do dynamic programming and get an answer for any given multiplier much more quickly than just counting.
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Old 2011-08-29, 06:01   #7
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Quote:
Originally Posted by xilman View Post
And, of course, Halloween is the same as Christmas Day.

(Yes, the old ones are the best.)


Paul

31 OCT == 25 DEC
Would you care to explain how Halloween is the same as (or equivalent to) Christmas Day? The spoiler answer didn't help me.

The problem posed by fivemack is a very interesting one. The question is: Did he really hear such a problem at a party? :-)

Last fiddled with by gd_barnes on 2011-08-29 at 06:07
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Old 2011-08-29, 06:05   #8
LaurV
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that's 31 (octal) is 25 (decimal), a very old joke. But the problem is quite interesting, and I would also like to read some math behind. I stucked my ears into it, but without any relevant result.
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Old 2011-08-29, 08:16   #9
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It's like:

"There are 10 kinds of people in the world β€” those who understand binary and those who don't."
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Old 2011-08-29, 15:50   #10
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Quote:
Originally Posted by fivemack View Post
You're looking for a short vector in the integer lattice perpendicular to some other vector, but I'm not sure how you encode 'non-negative' for lattice problems; might well be able to do dynamic programming and get an answer for any given multiplier much more quickly than just counting.
This is something I've wondered about for quite a while: has there been any work on 'constrained' lattice reduction? i.e. finding a small vector in a lattice even though conventional 'approximate orthogonalization' techniques are not allowed? This has a lot of bearing on several aspects of NFS polynomial selection...

I also wonder if the best one can do involves techniques that look like the branch-and-bound techniques from integer programming.
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Old 2011-08-29, 22:30   #11
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Quote:
Originally Posted by LaurV View Post
that's 31 (octal) is 25 (decimal), a very old joke. But the problem is quite interesting, and I would also like to read some math behind.
Thanks. That explains it.

Quote:
Originally Posted by LaurV View Post
I stucked my ears into it...
I think the English phrase that you are looking for is "I put my head to it". :-)

Quote:
Originally Posted by kar_bon View Post
It's like:

"There are 10 kinds of people in the world β€” those who understand binary and those who don't."
That's funny. I had not heard either one of these before.
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