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Highcolour (or Hicolour, Highcolor, Hicolor, Thousands on a Macintosh) graphics is a method of storing image information in a computer's memory such that each pixel is represented by two bytes. Usually the colour is represented by all 16 bits, but some video chipsets also support 15 bit highcolour.
In 15 bit highcolour, one of the bits of the two bytes is ignored, and the remaining 15 bits are split between the red, green, and blue components of the final colour, like this:
Each of the RGB components has 5 bits associated, giving 32 intensities of each hue. This allows 32768 possible colours for each pixel.
When all 16 bits are used, one of the hues (usually green, more on next paragraph) gets an extra bit, allowing a 64 levels of intensity for that hue, and a total of 65536 available colours.
The reason why green is chosen for the extra bit in 16 bits is because human eye has its highest sensitivity for green shades. You can convince yourself of that by looking at the following picture (warning: this will work only if your display is truecolour, e.g. 24 or 32 bits) where we show off dark shades of red, green, blue using 128 levels of intensities for each hue (7 bits); if you're not visually impaired, bring your eyes closer to the screen for a moment: you can easily see the lines of green, while you have difficulties to see the lines of red, and you almost can't distinguish the lines of blue.
Unlike Planar or Chunky graphics, there is no need for a colour look-up table (CLUT, or palette) when in Highcolour mode, because there are enough available colours per pixel to represent graphics and photos reasonably satisfactorily.
See also: Planar, Chunky, Truecolour