So not everything is about getting 20+ decimal places of precision. Integers are great, sometimes they are enough, sometimes they are *ALMOST* enough (and, well, sometimes they aren't enough). For example, in music I can have notes that take one beat, notes that take up multiple beats...or notes that take a beat and a half, or others that take a half a beat. I don't ever need to worry about a note that takes 3.071253 beats. If I could represent fractions down to maybe 1/16 of a beat, that would be plenty. That was kind of a side track. What I'd like is numbers that fit in a 16 bit int. I want to be able to represent numbers that can represent about 3 places past the decimal point (about 10 bits past the binary point), and I need to have at least +/- 2PI of range. Let's go for 5 bits on the left of the binary point and 11 bits to the right...so we can represent numbers from 15something to -16 range with a resolution of 1/2048. For this numbering scheme, find the four digit hexadecimal representations (as close as can be represented) for: 1,-1,2,-2, pi,-pi,2pi,-2pi,pi/2 and -pi/2.
So not everything is about getting 20+ decimal places of precision. Integers are great, sometimes they are enough, sometimes they are *ALMOST* enough (and, well, sometimes they aren't enough).
For example, in music I can have notes that take one beat, notes that take up multiple beats...or notes that take a beat and a half, or others that take a half a beat. I don't ever need to worry about a note that takes 3.071253 beats. If I could represent fractions down to maybe 1/16 of a beat, that would be plenty.
That was kind of a side track. What I'd like is numbers that fit in a 16 bit int. I want to be able to represent numbers that can represent about 3 places past the decimal point (about 10 bits past the binary point), and I need to have at least +/- 2PI of range. Let's go for 5 bits on the left of the binary point and 11 bits to the right...so we can represent numbers from 15something to -16 range with a resolution of 1/2048.
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For this numbering scheme, find the four digit hexadecimal representations (as close as can be represented) for: 1,-1,2,-2, pi,-pi,2pi,-2pi,pi/2 and -pi/2.
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