Formulas for blending modes

Hi,
I want to truly understand layer blending modes so I can use them better and predict their impact. I know from Bruce Fraser's books that the formula for the Multiply Mode is:
     result = (top_pixel * bottom_pixel) / 255
This is great for me (I have a BS in Math). The question is: how are the other modes calculated? For instance, i am having trouble figuring out the Color Burn Mode...
Thanks,
Juan Dent

Color burn is a little easier to calculate in CMYK because the numbers are expressed as %
Base % / (1 – Blend %)
For example, bottom layer is 40M. Make a layer above with Color Burn, fill with 50M
.4 / (1 – .5) = .8
The color result is 80M
Because of this relationship, if the base % is half of the blend % the color result matches the blend color:
.25 / (1 – .5) = .5
You could probably arrive at a reliable result using a similar formula in RGB, but the numbers get crunched differently when dealing with 0 - 255
To get multiply in CMYK I always use
(Base % + Blend %) –  (Base % x Blend %)
So if bottom layer is 40M. Layer above is multiply, 50M
(.4 + .5) – (.4 x .5) = .7
Perhaps this formula is wrong somehow but it seems to work for me.

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