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On display themes on computers there can be seen million colors, 20 million colors etc. There are also terms like true color ,high color , 32 bit, 64 bit etc. 256 color scheme is also there. Actually how many colors can a normal computer screen can produce?
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The total number of colors that the computer can display to the users is 256. According to the theory, there exist 16.777 millions of colors combination produced by the computer to display on the screen.  The Computer display is control within 8 bits of number. 

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As said in the previous answer, a computer monitor that claim to produce millions of colors can actually produce those colors but not at the same time.
Theoretically, a monitor can produce RGB combinations in Red, Green, and Blue which results in a number 16.7 million. ie: 256 colors of red, green and blue make the number like this: 256 x 256 x 256 = 16.7 million. But a normal monitor can only produce a maximum of one or two million pixels. So only about thousands of colors are produced on a monitor at a time.
So as a one-word answer we can tell a PC screen can produce 16.7 million colors!
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256 colors in each Red, Blue, Green.  Total 16.7 million . But I don't think a computer monitor can display all these millions of colors. Its may vary or depend upon the different types and make of monitors.
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It's not clear just what you are trying to ask. Most computers now use 24 bit color, capable of defining about 16.7 million colors. Some graphic cards use other methods to get very different definitions. The number of colors that a monitor can produce might be much less than the number that the machinery can define, and a printer is much worse than a monitor.

https://en.wikipedia.org/wiki/Glossary_of_computer_graphics#Color_resolution
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