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How does windows send colour data to printer and how does printer translate the data into ink proportions?

e.g. If I have some text in MS Word with font colour of some RGB values and my printer has CMYK colour cartridges and I print the text.
In that case, how does windows convey the colour data to printer and how does the printer decide correct proportion of CMYK inks to reproduce the colour?

My question does not just limit to windows. It can be applicable to any OS which supports printers.

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It depends on the printer.

If the printer supports PostScript, the application/driver can send the colour data in just about any colour format you like: RGB, CMYK, indexed colour, greyscale, etc. The printer will convert it into CMYK, adjusted for the particular inks/toners used in the printer. The adjustment is done with internal colour tables that adjust not only for the actual ink colours, but also for various perceptional models. The printer also adjusts the resolution so you can, for example, send the printer a 100dpi image and print it at 300dpi. All up, this makes PostScript the preferred way to print colour.

PCL5 and PCL6 printers can use RGB, CMYK and greyscale colour models. The printer does the conversion to ink dots on the paper. Colour adjustments are very limited in PCL and are mostly done in the driver.

GDI printers (also called host-based, and various other names) are different. These low-cost printers depend on the operating system's graphics engine to convert the page into dots on the paper. With GDI the internal colour system is always RGB and adjustments are done by the OS. GDI can send either RGB or CMYK data to the printer. In the case of RGB, that implies that the printer will do the conversion. Many GDI printers do not have any built-in colour adjustments, so that has to be done in the OS.

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Windows (and moreover MS Word) does not know anything about your cartridges. Generally, application use simple GDI (generally RGB color space) to communicate with printer spooler, spooler in turn communicates with printer driver (not sure, imho on this step driver received commands in some universal language, like PCL). At last, driver (which know everything about printer hardware, cartriges, inks and so on) decides what actions the printer must perform to achieve desired effect.

imho, alternatively, the application can "draw" on printer canvas using common printer languages (like PCL for example). However, they limited to standard color spaces (RGB, CMYK,...). They don't know anything about cartriges - they may be 6-color, 4-color, 3-color, even 1-color (black/white).

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