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a) Correct! b) This seems to be correct, but I have to say, this representation for exponents is very strange. A four digit exponent plus a sign bit lets you represent an exponent between $-1111_2$ t …

I may be misunderstanding the question, but I don't think we have enough information to tell. Consider, for example: $$A = \left\{ \frac{1}{4}, \frac{1}{2}, \frac{3}{4} \right\}$$ and: $$P(x) = \l …

Note: In the interest of making this somewhat self-contained, I am using terminology from the most recent versions of the IEEE-754 standard. Prior to 2008, "subnormal numbers" were called "denormal nu …

Since this is CS and not Stackoverflow, I'm going to assume that you're asking a question about numeric analysis, and (to keep things simple) IEEE-754 floating point in particular. In that case, the a …

Even though absolute comparisons may not converge, you should be able to narrow the argument into at least one of several partially overlapping ranges, such that you have a technique that works in tha …

The first thing you should understand is why central differencing gives you a more precise solution. Consider the Taylor expansion of $f$ around $x$: $$f(x + h) = f(x) + h f'(x) + \frac{1}{2} h^2 f''( …