base:fixed_point_arithmethic

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+ | ====== Fixed point arithmethic ====== | ||

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+ | A fixed-point number representation is a number that has a fixed number of digits before and after the radix point (e.g. " | ||

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+ | In terms of binary numbers, each magnitude bit represents a power of two, while each fractional bit represents an inverse power of two. Thus the first fractional bit is ½, the second is ¼, the third is ⅛ and so on. | ||

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+ | 8:8 Fixed Point representation is the most straightforward approach (in fact the only sane approach when coding on the c64). | ||

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+ | for example: | ||

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+ | < | ||

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+ | represents the number: | ||

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+ | integer part: | ||

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+ | < | ||

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+ | fractional part: | ||

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+ | < | ||

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+ | giving us: | ||

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+ | < | ||

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+ | It's easyer to think of a 8.8 fixed number in a way that you have a 1 byte integer part, and a 1 byte fractional part where the fractional part represents a number which is: fractional part* 1/ | ||

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+ | Repeating the example above: | ||

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+ | < | ||

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+ | < | ||

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+ | You may totally forget about fractional parts and just threat the two 8 bit numbers as a straight representation of numbers from 0-65536: a 16 bit number when working with numbers like this. In reality a fixed point number will be always just a bunch of bits, and what makes it fixed point is only how you think about it. :) | ||

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base/fixed_point_arithmethic.txt · Last modified: 2015-04-17 04:31 (external edit)