[Sussex] Challenge

[Geoff Teale]

Steve Dobson wrote:
-------------------
> But you saw my approach without seeing the error :-)

I saw the 0000.1 if thats what you meant - it threw me at first, but I
assumed you were using it because you couldn't represent it in base 2 :)
 
<snippage>
> I'm going to argue that it does represent 0.1(base 10) in 
> binary!  

Sorry.. I should have been more explicit. So yes, your right it is a
representation of it in base 2.

<snippage of some very good arguements with which I will not disagree>

> Your challenge was to "in base 2 prove that the following base 10
> equation is correct: 10 * 0.1 = 1".  In base ten 0.1 can be represent
> as: ..., 10.0*10^-2, 1.0*10^-1, 0.1*10^0, 0.01*10*2, ... Neither
> is more or less valid than the others and no accuracy is lost in them
> either.  I therefore set my floating point number representation to be
> 1.0 * 10 ^ <int-mantissa>.

Hmmm.. the challenge was:

>>Computer scientists often say that 10 times 0.1 very rarely equals 1.0
All
>>I want you to do is come up with a wholly accurate binary representation
of
>>the number 0.1 that can be used by normal floating point operators without
>>the use of "fudge factors".  The proof is simple, it must in base 2 prove
>>that the following base 10 equation is correct:
>>
>>10 * 0.1 = 1.0

So yes, you meet the required proof, though the depth and rigour may be
lacking, this stands as a very good argument indeed!

> I do _not_ offer this number representation to solve the general case
> of x * y = z, or for that mater to represent any number as it is clear
> limited by my restriction that the mantissa must be equal to 1.0 for
> all numbers and the exponent has to be an integer.  The only number
> that can be represented in my representation class without loss of
> accuracy are powers of 10.  As this includes 10, 1 & 0.1 which were
> all I needed for your proof.

Wisely done sir!  You found a scemantic hole and pushed an equation through
it, very nice ;)

> As I said: Mine is a point of Horsham Best! [Unless anyone 
> else can offer
> a ?better? solution. :-)

Indeed..

-- 
GJT
Free Software, Free Society. 
http://www.fsf.org   http://www.gnu.org


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