The way it was always taught for me is like “oh, well, floating point is just scientific notation, right? Except it’s binary, not base 10, have fun
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Which gives no understanding about the actual numbers floats can represent!
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I like the window + offset analogy. Mantissa identifies a value between two successive powers of two, exponent tells you which "window" you're in.
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you could even bring Farey sequences https://en.m.wikipedia.org/wiki/Farey_sequence … into it to better explain it visually
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I think because we teach scientific notation in high school? I was taught floats as “like a * 10^b but binary” but this only tells representation and not limitations.
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I always describe fixed-point as rational numbers with a constant denominator. I've never explained floating point that way though, for no particular reason. I wonder if describing it both ways, stressing the equivalence, might also be helpful for some.
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floats are just like fixed-point, except they're not fixed to any particular point >.>
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Because it would have to flip between a/b and a*b according to the sign of the exponent. And also because the actual binary representation is less obvious that way.
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The mantissa and exponent fields map more directly to a × 2^b. Also, some operations on the scientific notation are a lot easier on paper / in your head. That's my guess.
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because of how they're spec'd presumably?
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