xor and color inversion?

What is the inversion of colors algorithm ? How can we implement this?

For example

Black->White
Blue-&g开发者_如何学Got;Yellow

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You do this:

RInv = 255 - R
GInv = 255 - G
BInv = 255 - B

which can be done with XOR as follows:

RInv = R xor 255
GInv = G xor 255
BInv = B xor 255

The xor works because we want the sum of R and RInv to be equal to 255:

RInv = 255 - R
=> RInv  + R = 255

and, since a xor on binary numbers is an addition over the Galois field mod 2, we get:

C = A xor B
=> C xor B = A xor B xor B = A
RInv = 255 xor R
RInv xor R = 255