Comparing bitmaps to assign color to pixels

[Albdamned]

Is there a way to compare two different black and white images (png). These two tone images that are exactly the same dimensions. Is there a way to have adobe compare the two images (perhaps as layers), and assign a color based on the values comparision? I would also like to distinguish between the pixels that are different, based on how the difference layers (is it white and black, or black and white).

[c.pfaffenbichler]

Please post the images. 

The Blend Mode »Difference« comes to mind. 

Edit: 

[Albdamned]

Thanks for your post. I will try this out with a red and green pic layer. I should have time later today. I would be happy to give jpeg versions of them, as BMP is not supported. The only reason I mentioned the bmp is the pixel map nature. I am more interested atm in getting the process down at the moment. I can give you examples that would work as a fun place holder. Both of thes images are blown up (102 times), and the grey has been dithered black. Based on 4 possible combination of overlapping pixels (black/black, black/white, white/black, white/white), I would like 1 of 4 colors.

[c.pfaffenbichler]

Why the upsampling? 

Why the dithering? 

Why is the one image colorful and the other not? 

Please provide undamaged images. 

What is the actual point of the exercise? 

[Albdamned]

So it isn't a matter of unsampling but formating the file for this site. 
I am dithering because I want an absolute binary (on/off) function of the pixels on each layer.

like I said, this was meant more as a sample. the image that I used was the 25 by 25 sprite, blown up and dithered.
I dont want to get into why I am doing this but it requires very specific control over the colors. I also would like to mention I realized I made and error in my description, I had not considered the white nature of paper.

[c.pfaffenbichler]

This setup with two instances of two different Smart Objects would yield four different values for the combinations black-on-black, black-on-white, white-on-white and white-on-black. 

A one-instance per Smart Object-approach is possible, though. 

[c.pfaffenbichler]

For the second case I forgot to change the name of »x2« – the actual Blend Mode is »Linear Burn« (edit) and the two Curves Layers are not identical. 

[Albdamned]

I think the smart object is the ticket. The way I was thinking was to give different values (all with just cyan) to the 3 colors (Black from layer 1, black from layer 2, and white from either layer), and then use the conentration  to determine the colors. I have created a truth table that would take these 6 values, and convert it into the desired colors. Please note the colors in the table are not meant to be considered the colors I am using (excel does weird things with colors). I will try the guidance you have given.

I was trying to index the colors but it resulted in photoshop taking liberities that compromised the result. (with the truth table, you can look at 2 pixels, and see what the result should be).

I appreciate your efforts, and would like to apologize if my verbiage is off or I am being difficult with my exactness. I would like to explain that I have a background with philosophy and computers, (If it wasn't obvious with the truth table lol). I have a strong understanding in "if this, then that", which is 99% of what a computer does. I can usually navigate photoshop but becomes frustrated when there isn't a more code level adjustments like this. Ideally, I wish I could look at a spreadshead and enter formulas to cause the changes. If there was an easy way to convert a png to a CSV and vice-versa i would be set lol.

[c.pfaffenbichler]

I appreciate the effort you put into the table with the boolean values but the issue is no more clear to me now. 

Please post actual examples. 

Are there three images (for Cyan, Magenta, White) that need to be combined to create an output image? 

@jazz-y has posted a couple of Scripts lately that utilize RAW data to evaluate colors; this data could be used to create a csv but the time-factor obviously depends on the actual images (pixel dimensions etc.). 

[c.pfaffenbichler]

By translating the black in three images to different brightnesses (see the Solid Color Layers in the screenshot) it is possible to combine the images in such a way that each of the eight combinations of white/black assumes a different shade of gray. 

A Gradient Map Adjustment Layer could then be used to change each of those shades to the one you actually want. 

[Albdamned]

Hey there,
I wanted to give an update as I did work through the process. Blend mode was the ticket.
My methodology:

Create 2 high def images that are absolutely black and white (using dithering pattern). I played with the modes a lot, indexing makes all this fast. Once done though settle the mode on rgb

On two different layers, convert the two image black and white pixels with the following values via select color and fill. The goal is to make a monochromatic red picture

Picture 1 white: 40R 0G 0B       Black: 80R 0G 0B

Picture 2 white 40R 0G 0B        Black: 160R 0G 0B

Now when using blend mode, you need to do Linear Dodge, these just add values together (I had to shift from cymk to rgb for this which is a pain for printing but not insurmountable, just another step). I then shifted to index color (you have to make sure it is exact with all the settings, adobe tries to be super helpful sometimes but this time it doesnt help! lol). This will create a dark to red image with 4 values, i then chose the values I wanted and made the pic I am attaching. The beauty in this is that under the right conditions the image will shift from one to the other. I am going to using this effect, for a lot more than just pokemon but it seemed like a fun way to work on it.

[Albdamned]

Here is an idea I had for this whole process. I have detailed a few uses for this but a high def image at this point is not different than the Pokémon sprites. One thing I didn't mention. I had to add those values of the red color. That told me which color to match with what. Big time/ink saver!