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 — base:fixed_point_arithmethic [2015-04-17 04:31] (current) Line 1: Line 1: + ====== Fixed point arithmethic ====== + + A fixed-point number representation is a number that has a fixed number of digits before and after the radix point (e.g. "." in English decimal notation). + + 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. + + 8:8 Fixed Point representation is the most straightforward approach (in fact the only sane approach when coding on the c64). + + for example: + + + integer.fractional + + 00001101.01010000 + + + represents the number: + + integer part: + + 1*2^3+1*2^2+0*2^1+1*2^0 + + fractional part: + + 0*(2^-1)+1*(2^-2)+0*(2^-3)+1*(2^-4) + + giving us: + + 1*2^3+1*2^2+0*2^1+1*2^0  +  0*(2^-1)+1*(2^-2)+0*(2^-3)+1*(2^-4) = 13.3125 + + 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* 1/256. + + Repeating the example above: + + + integer.fractional + + 00001101.01010000 + + + %01010000 = 80 decimal => 80*1/256 = 0.3125 + + + 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. :) + + 