This article is from the comp.sys.ibm.pc.hardware.video Frequently Asked Questions, by Michael Scott with numerous contributions by others. (v1.0).
[From: Michael Scott (scott@bme.ri.ccf.org)]
To understand this (and it isn't that difficult) you have to know what the binary (or base 2) number system is. Instead of each digit in a number varying between 0 and 9, the values can only be 0 or 1. This means that for a given digit, there are only two possible options. So, for say a 4 digit binary value, there are 4^2 (or 2x2x2x2) or 16 unique values. Now it becomes easy to translate between the number of bit planes (that's number of binary digits) and number of colours.
number of colours = 2^(# of bit planes) resulting in: 1 bit = 2 colours, 2 bit = 4 colours, 4 bit = 16 colours 8 bit = 256 colours, 15 bit = 32k, 16 bit = 64k, 24 bit = 16.7M
Note that the maximum colour depth at a given pixel addressability is limited by the video controller, not the monitor, since almost all modern monitors are analog.
 
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