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The screen shot above shows the AND mask (in black and white) and the color XOR mask (Exclusive Or) and the resulting icon which has been painted transparently to the screen using these two masks. In order to achieve this transparency in the image, first the AND mask is applied to the screen. Now the AND operation is true if, and only if, both operands are true. So then 1 AND 1 = 1 (or true if you want to think in terms of logic). Any other combination of the values of 0 and 1 returns 0. (1 AND 0 = 0; 0 AND 0 = 0). The value of White is '11111' (etc, up to the number of bits in the color depth). Black however consists of all zeros ('0000' etc). When the AND mask is applied to the screen pixels only in those places where the AND mask is white will the screen pixels be included. You can think then of a kind of 'hole' shaped like the icon left on screen (all zeros where the AND operation failed, and thus black).
An OR operation is true if either one or the other of the operands is true (or 1). So 1 OR 0 = 1 as well as 1 OR 1 = 1. An EXCLUSIVE OR (XOR) is true if, and only if, one of the operands is true (either one but not both) so then 1 XOR 0 = 1 ( or true) but 1 XOR 1 = 0 and 0 XOR 0 = 0 (or false). Now the AND map left a 'black hole' on the screen shaped like the icon as described above. The color XOR mask consists of an Icon fitted to shape this 'black hole' in the screen pixels surrounded by a black area, as you can see in the screen shot above. When the XOR operation is applied to the screen pixels under this black area, the screen pixels pass the test and show through, and when the XOR operation is applied to the Icon (sitting over the black area left by the AND operation above) then the icon pixels pass the XOR test and show through. The result of these two logical operations on the pixels is the transparent image of an Icon shown on the right of the graphic.
A Unified Field Theory
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The Unified Field Theory
is also available as a zip file -> unified.zip
Introduction :The Pioneer Effect and the New Physics. A brief description of the new physics required to explain the 'Pioneer Effect', which is the constant deceleration of space craft as they fly through space.

