Re: magic integer converter number 62?
Re: magic integer converter number 62?
- Subject: Re: magic integer converter number 62?
- From: email@hidden
- Date: Fri, 23 Feb 2001 23:53:05 -0500
On Fri, 23 Feb 2001 09:54:03 -0500, Deivy Petrescu <email@hidden> asked,
>
The explanation did not convince me.
>
First: it should work the same with 61 or 62 or show a pattern work
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not work every 2 powers of 2.
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Second: Paul originally argued that 62 +2 = 64 and that was what was
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going on. He was right. It does not explain, on the contrary shows
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another problem, namely, the expression:
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set b to ((x + (2.6 - (2.6 mod 1))) - x) as integer
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should, according to the rules of precedence, be computed inside
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out. That is, one should get 0.6 (or its periodic representation in
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binary) before adding or subtracting from x. Since, if one changes
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the number 2.6 to 3.6, 61 works fine and so does -67, this indicates
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that there are some sums going on before the due time.
I think the problem is that you aren't considering that this is floating point
format, with a fixed number of mantissa bits. Since you are subtracting 0.6
from 2.6, there is a misalignment.
In binary, to 24 significant bits, (with the "123456789012345678901234" label to
help keep the bit count right.)
12 3456789012345678901234
2.6 = 10.1001100110011001100110
123456789012345678901234
0.6 = 0.100110011001100110011010
(Note the rounding up. The last two significant bits are [01][10011...]
rounded to [10][00000...])
Line these up and subtract them, and you get
12 3456789012345678901234
10.1001100110011001100110
- 0.100110011001100110011010
---------------------------
1.111111111111111111111110
123456789012345678901234
which rounds to 24 bits as
1 23456789012345678901234
1.111111111111111111111110
---------------------------
1.11111111111111111111111
Or, 2 - 2^-23.
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My Graphing Claculator shows 2 to the power 1024 is infinity. Looking
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at the binary expansion for .10 or .60, I do not have a clue as to
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why 62 works and 61 doesn't. IEEE or not.
2^1024 is a bit more than 10^307. That's a
yotta-yotta-yotta-yotta-yotta-yotta-yotta-yotta-yotta-yotta-yotta-yotta-exa-bit.
Actually, using the exact binary prefixes, its a
yobba-yobba-yobba-yobba-yobba-yobba-yobba-yobba-yobba-yobba-yobba-yobba-ebi-bit.
Moore's Law tells us you'll be able to buy a disk this size in 994 18-month
time periods, or on 23 February, 3492. That's a Wednesday.
--
Scott Norton Phone: +1-703-299-1656
DTI Associates, Inc. Fax: +1-703-706-0476
2920 South Glebe Road Internet: email@hidden
Arlington, VA 22206-2768 or email@hidden