CHAPTER 01.05: FLOATING POINT REPRESENTATION: Background : Part 3 of 3
So what I would like you to do as homework is that we have four places . . . we have four places for the mantissa in this example, right? So if I put . . . if I take 5 . . . if I take 5 times 10 to the power 2 minus . . . 2 minus 4, and what do I get? I get 0.05. So what you are finding out here is that, if I take this 4 and put it right here, I get 5 times 10 to the power 2 . . . 2 minus 4, I get 0.05. Does this formula have something to do with how much relative true error I'm going to get in every case? Will it be less than 0.05 percent? So if I look at any other number for the same example, will I always get the value of the relative true error less than 0.05 percent? So you might have hit on something here, that if I have m number of places for the mantissa, then the amount of relative true error which I'm going to get in representing any of the numbers which can be represented will be less than or equal to 5 times 10 to the power 2 minus m, where m is the number of places you have, or number of . . . not bits, I should say, no, I should say places, you have for representing the mantissa. So that's your homework, and I want you to look at it. And that's the end of this segment.