if the digit is a name for a base number 10, what would be the name for a base number 16? Hexgit?
Digit. Just hexadecimal.
Are you looking for an analog bit for a binary digit? Hexgit would not be my choice; it really does not go off the tongue. As for the storage unit, the hexadecimal digit represents the value (or nybble).
This is a "nibble" (i.e. half a byte).
http://en.wikipedia.org/wiki/Nibble
define: digit
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"Hexdigit" "hex digit" .
"Hexgit" would be a bad choice, since "hex" formally offers a basic six, not 16.
"Hexdecit" will retain the 6 + 10 representation, but I will stick to the "number".