09/20/2006

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Another student writes:

Dr. Patt,

I also have a question about promblem 3. In one of your lectures you
mentioned that when the exponent field of the floating point
is all ones, the number is considered nonsense
but you also mentioned it could be considered infinity

Ooops!  You left out the rest of the sentence.  The exponent field containing
all 1s is used to represent nonsense, AND it is also used to represent + and
- infinity, DEPENDING on the bit pattern in the fraction field.

That is, if the exponent field is all 1s (11111111) and the fraction field
is all 0s (00000000000000000000000), then the value is infinity (+ or -
depending on what?).  If the exponent field is all 1s and the fraction field
is NOT all 0s, then what is represented is one of the nonsense values, such
as 0/0, infinity - infinity, arcsin(2), for example.

....is infinity the same as nonsense?

No.  For example, you studied trigonometry, right?  What is the tangent of
90 degrees?  Is that nonsense?

The point is that the symbol infinity has great value in mathematics, and
can be manipulated like finite numbers.  For example  3/(infinity) = 0.

For example, a continued fractions evaluation.  What is the value of:

2
--------------------
6
3   +  -----------
4
5  + ---
0

On the other hand, what is: 0/0 - 6/0 + arcsin(2)?  Yup, nonsense!

Hope that helps.
Yale Patt

Thanks so much!!

<<name withheld to protect ...>>
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