in reply to
Converting hex colors to color safe hex
Do you perhaps mean "web safe" instead of "color safe"? If so, it's a pretty easy approach.
Each element of the color is 1 byte (0-255 unsigned), and expressed in hex. All you have to do is round the values of each byte to the nearest in the "web safe" color chart. (with some bounds-checking, of course).
Show us some code on what you've tried, perhaps trying to implement that kind of solution, and you'll get better help. Check out How (Not) To Ask A Question for tips on getting the best help here.
Ramblings and references
The Code that can be seen is not the true Code
I haven't found a problem yet that can't be solved by a well-placed trebuchet