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From: Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups: comp.lang.javascript
Subject: Re: IEEE 754
Date: Fri, 29 Aug 2014 23:27:24 +0100
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"Christoph M. Becker" <cmbecker69@arcor.de> writes:

> Ben Bacarisse wrote:
>
>> Gene Wirchenko <genew@telus.net> writes:
>> 
>>>      Yes.  The value closest to 123.45 can be represented exactly.
>> 
>> Sure.  To be specific, for IEEE 754 double, it's 7B.733333333334 in hex.
>> Using enough decimal digits to see what happening, that's about
>> 
>>   123.45000000000000284217...
>
> According to John's fine IEEE 754 double format calculator[1] that is
> correct.  The hexadecimal representation is 405edccccccccccd, by the
> way.

Sure, but that's the bit representation of the double.  If I've got it
right, 7B.733333333334 is the number in plain base 16 which might be
helpful in calculators that can do hex.

However, I can see that it might have helped to show the bit
representation of these:

>>  The three candidates are centred
>> on 12345:
>> 
>>   12344.999999999998181011...
>
> Correct.  Hexadecimal representation: 40c81c7fffffffff
>
>>   12345.000000000000000000...
>
> Correct.  Hexadecimal representation: 40c81c8000000000
>
>>   12345.000000000001818989...
>
> Correct.  Hexadecimal representation: 40c81c8000000001
>
>> and 12345.0 is the closest.

...as it might have made what's going on clearer.

-- 
Ben.