09/20/2006

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 ...>>