RGB to HSB Conversion: An Introduction

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internet user
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I came across HSB for the first time when I was reading a guide on Java. What is the difference between the two, and how do you convert from RGB to HSB (and vice versa)?
 
Q: How do I do this thing?
A: Like this: public class DoThisThing extends Applet{

Hmmm...

It occurs to me that such conversions can't be exact. in HSB, if S=0, then H becomes irrelevant. No matter what value is in H, the exact same shade of grey is defined. Because there is no RGB equivalent to this, there are more RGB values then HSB values for any given bit depth.