Computer monitors are based on cathode ray tubes (CRTs). CRTs comprise an electron "gun" which beams electrons on to a surface coated with phosphorescent material (the screen). When the electrons hit the the screen the phosphors glow, if no electron strikes the screen the phosphors remain dark. The beam zigzags across the screen while it also moves from top to bottom. The combination of these movements and the alternation of light and dark dots produce the image. Modern colour monitors work on the same principal but use three electron guns to produce the illusion of full-colour. Because they use light to produce an image their colours fall into the additive colour gamut.
Computer monitors project beams of red, green and blue light through a mesh to form tiny pixels (or picture elements) on the screen. To control the colour of each pixel on the screen the computer's operating system must dedicate a small amount of memory to each pixel. The simplest computer display will dedicate a single bit of information to each pixel. A memory bit can only be positive or negative (0 or 1) thus such a system can only produce two colours (black or white) for each pixel.
The simplest computer display will dedicate a single bit of information to each pixel. A memory bit can only be positive or negative (0 or 1) thus such a system can only produce two colours (black or white) for each pixel.
When eight bits of information are dedicated to each pixel a computer monitor can display 256 colours. 256 is the maximum number of unique combinations of 0's and 1's achievable with eight bits of information. These colours are referenced to a "palette" or "index" and are sometimes called indexed colours. These colours are those used by HTML and GIF-format graphics so are particularly important in web design.

A computer can obtain nearly photographic colour by dedicating 24 bits of information to each pixel; eight each for the red, green and blue components. Such displays are called "True-colour" or "24-bit colour" and can show millions of colours simultaneously.

There are limitations when using computers to design for print. These come about because RGB colours and CMYK colours are created differently, and have their own characteristics. Each is incapable of producing certain colours that exist in the other spectrum. The colours that exist in each spectrum are known as the "colour space" or "gamut", and may be refered to as the RGB gamut or CMYK space.

References:
An Introduction to Digital Colour Prepress -Agfa Educational Publishing, USA, 1997

Yale Style Manual: Colour display guide

Text and graphics: John Bleaney and Shiralee Saul 2001
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