Well, there are a couple reasons a programmer needs to know. I am only a hobby programmer, didn't finish my schooling, but....
Knowing binary can help with bit shifting operations to make faster computations and simpler code.
Base 16, because just about everything is in Base 16. 1 byte = 8 bits = 00-FF = 0-255.
When dealing with color codes, bit shifting, and other conversions, it could be useful. So essentially computers use Binary only, but a lot of binary (bits) gets grouped together into Hex (Base 16/bytes). Only people use base 10, because we have 10 fingers.




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