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@@ -503,4 +503,51 @@ this confirms that the approximation we found is the same as the float represent
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## Experience Report Evidence
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## Questions After Today's Class
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## Questions After Today's Class
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### Why can't systems just interpret decimal numbers like humans can?
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Because it has to be represented mechanically or electrically for it to be a machine.
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### My question is how bad can the approximations get when calculating floats? How much precision gets lost when dealing with fractional numbers?
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The quality of the approximation varies depending on the particular number.
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At the bottom of
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[float exposed](https://float.exposed/0x3ff0000000000000) you can see how close the next value is.
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For 1 (the link above) the next number is a little more than 2.22e-16 away.
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For [1532.625](https://float.exposed/0x44bf9400) the next value is 1.22e-4 away.
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For [4503599627370497.0](https://float.exposed/0x4330000000000001) to [9007199254740991.0](https://float.exposed/0x433fffffffffffff)the next value is 1.0 away, that is we can only represent integers between those two values, nothing in between.
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### Did the people that came from an academia background typically design and implement these low-level systems or people in industry?
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A lot of this work was deep collaborations between academia and industry. Some of it occured in universities, some of it was at places like Bell Laboratory. That was a research instittue inside of the for profit Bell Telephone Company.
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### How can I practice what we learned today for better understanding?
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This is a hard topic and it will come back up in CSC411.
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Also, I recommend reading these notes carefully, and trying the float.exposed site.
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### Does this process of going through all the bits increase in time with more bytes? Or is there a set number of bits?
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This standard is a fixed size of 64 bits, but ther are others with different numbers of bits.
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### How different was the initial standard from the one that exists today?
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The initial standard defined fewer basic formats, more were introduced in 2008. Official IEEE standards are not free so they're slightly harder to read easily.
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### How are we able to assign 0.1 to a variable despite that?
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We do not actually get a .1 for doing math. It is close, but not exact. Unless your programming environment has a different base type.
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