A Single Byte Color Palette is a color palette that can be defined using eight or fewer bits rather than a lookup table. Single byte color palettes were popular in the early days of computing when memory was at a premium and palette lookup tables were memory intensive. There are many different algorithms used to encode an entire color palette into a single byte and quickly get the results.
In the early days of color graphics, RGB was actually pretty rare, but as computers pushed RGB on their monitors, they quickly became the predominant color system in computers and, because of their popularity, most other forms of color display. Here is an image using 24-bit RGB color (16,777,216 possible colors) as a reference for the one-byte palettes below.
R1-G1-B1, 3-bit, 8 Colors
RGB 3-bit uses one bit for each red, green, and blue value which allows for two intensities per value yielding eight colors total. To get each RGB value simply multiply its bit by 255. This is the smallest possible palette that can include red, green, and blue simultaneously. Graphic displays which use binary LEDs use a system similar to this where a series of red, green, and blue LED are placed next to each other in tandem, and are turned on or off to simulate other colors when viewed at a distance, though they do not have separate values for composites like cyan, yellow, magenta, and white. Such a limited color palette produces especially grainy results with real-life photos.
R4-G4-B4, 6-bit, 64 Colors
RGB 6-bit uses two bits for each red, green, and blue value which allows for four intensities per value yielding 64 colors total. In computer systems with 8-bit bytes, this color system isn't very compact because it leaves two unused bits per byte, although, the unused bits could be used to store additional information. On a computer which uses 12-bit bytes, two colors can be stored in a single byte. With 8-times the number of colors compared to 3-bit color, the output photo is much nicer looking.
R6-G6-B6, 8-bit, 216 Colors
Because RGB color has three unique values, it can't be stored into single 8-bit byte evenly while also using all the indexes. This has led to various algorithms being devised to get an optimal palette. The 6-6-6 method yields the largest number of colors possible while still having an equal number of intensities for each value. This layout uses all 8-bits, but the red, green, and blue values are determined with the following algorithm: (36×R)+(6×G)+B. This allows for six intensities per value yielding 216 colors total. The remaining 40 indexes are left unused and could be filled from a color table. While this makes it slightly more CPU intensive to extract a color from the palette, it does have the advantage of being perfectly uniform across each value. Naturally, the added colors make the end result more attractive.
R6-G7-B6, 8-bit, 252 Colors
Because the human eye is better at resolving green that red or blue, one of the more optimal palette generation algorithms is add emphasis to green. This 6-7-6 algorithm also uses all eight bits, but adds an extra intensity level for green with the algorithm (42×R)+(6×G)+B. This allows for seven intensities of green and two of red and blue yielding 252 colors total. Like 6-6-6, this is more CPU intensive, but by adding an additional 36 colors, it results in a better output.
R6-G8-B5, 8-bit, 240 Colors
This configuration is made because the human eye is actually a lot better at resolving green than blue, but it's also better at resolving red. So, this 6-8-5 give one intensity level of blue to green. The algorithm uses all eight bits and can be represented at (40×R)+(5×G)+B. This allows for six intensities of red, eight of green and only five of blue yielding 240 colors total. Like 6-6-6, it's also more CPU intensive, but by putting more emphasis on green at the cost of blue, it can actually yield better results for a human viewer, despite the lost colors.
R8-G8-B4, 8-bit, 256 Colors
This 8-bit configuration uses three bits for each red and green value, but only two bits for blue. This allows for eight intensities for red and green, and four for blue, yielding 256 colors. This layout is good for human viewing and yields the maximum amount of colors. While the palette might not be as versatile as a 6-7-6 or 6-8-5, it is far less CPU intensive because each value is stored in its own bit space.
R8-G4-B8, 8-bit, 256 Colors
To give you an idea of why green is the focus in all of the non-homogeneous palettes above, here is an algorithm similar to 8-8-4, but with the least emphasis on green. This system uses three bits for red and blue, and only two for green. This results in eight levels of intensity for red and blue, but only four for green, yielding 256 colors. Despite having four times the colors, the output isn't much better than the 64-color 3-3-3 output from above. Green is extremely important.
R4-G8-B8, 8-bit, 256 Colors
This is like the 8-8-4, but with emphasis added to blue and green over red. This system uses two bits for red, and three for green and blue. This results in four levels of intensity for red, but eight for green and blue, yielding 256 colors. Notice how the output paradoxically looks more red despite having less red intensity. The warmer tone comes from the loss of nuance in red.