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We know that in the RGB system we have three primary colors and each of them has a value from $0$ to $255$ (or $256$ values in total). So all possible colors are $256^{3}=16777216$.

But in the CMYK system we have four primary colors and each of them has $101$ values (from $0$ to $100$). So in this case all possible colors should be $101^{4}=104060401$ which is far more than all possible colors in the RGB system.

So does CMYK system provide more colors? (but of course we can perceive only $16777216$ colors because of our vision which only perceives three primary colors)

Also another question: In RGB system the hexadecimal codes again provide $16777216$ colors; because we have from 00 to FF for each primary color (again $256$ possible codes). But for CMYK system the total possible colors differ from $104060401$ when using hex codes. Because the code range is from 00 to 64 ($85$ total codes) for each primary color and the total number of possible colors is $85^{4}=52200625$ which is again more than the possible colors of RGB system. But why are the number of colors differ in CMYK system when using values and hex codes?

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  • $\begingroup$ Scientists estimate that humans can distinguish up to 10 million colors. $\endgroup$
    – user1703
    Sep 11, 2023 at 17:00

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You are focusing far too much on the number of color codes in common implementations. There is no reason that RGB must have 256 values per component, and no reason that CMYK must have 101 values per component. Within any system, we can choose to store more bits and therefore discriminate more finely between colors. And if we don't have enough bits, dithering is an option.

The true difference between RGB and CMYK is that they each encode color in a way that suits the limitations of a particular display technology.

  • RGB color representation suits television, computers, and other video displays that are directly emitting colored light. It can represent any color that is some mix of the red, green, and blue primary colors — any color that those displays can present.

    However, there are still some colors that cannot be displayed by RGB monitors. Not because they are in-between the existing codes, but because they are outside the gamut defined by the choice of three primary colors. It's impossible to make a display that emits all possible colors unless each pixel could individually tune the wavelengths of light it emits.

  • CMYK color is used for printing — for putting ink on paper.

    The limitation of printing is that the image is formed by light hitting the ink pigments and being absorbed; the color that we see is everything but those absorbed colors. But when we make a color that is not a primary color, by the printer spraying or pressing a mixture of those inks onto the paper, not all of the paper is covered by each one. The result of this is that a color made by mixed inks will always be a little “muddy”. If you try to make black out of CMY, you will not succeed; you will get a dark brown color instead. Thus, the black (K) additional element is needed, and people designing for print use CMYK so that they are working within the limitations of the technology.

    Thus, the gamut of CMYK is typically smaller than RGB — though both may contain colors the other does not. If you use RGB to design for printing, you will often be unpleasantly surprised by your colors being less vibrant because the RGB colors you chose cannot be made by CMYK inks.

You cannot meaningfully compare CMYK and RGB on the basis of the number of distinct colors; it's the gamut that matters — the boundaries of the space of representable colors.

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  • $\begingroup$ Yes, and there is no super good reason. Other than dominating your output blacks. To base your design in CMYK space, as long as you are aware of the gamit difference. You can always comvert your RGB to your devices specific CMYK when you need it. Then deal with blacks separately if you really need. $\endgroup$
    – joojaa
    Sep 22, 2023 at 5:45

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