> WHY BASE 16 EXISTS AT ALL

A byte is 8 bits, and 8 bits happens to split evenly into two 4-bit chunks - and 4 bits covers exactly 16 possible values (0000 through 1111). That's the entire reason hex exists: it's a compact, human-typeable shorthand for binary that lines up perfectly with how computers actually chunk data, instead of an arbitrary choice. Octal (base 8, three bits per digit) served the same purpose on older systems that grouped bits in threes rather than fours, which is why it still shows up in file permission notation (like chmod 755) long after most other uses faded.

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