A byte is always 8 bits. The word you're looking for is `word-size` which, in this case would be 4 bits.
This is why network RFCs talk of "octets", to avoid the ambiguity. Octets are always 8 bits.
(* technically, a 'foot' is not a standard unit of measure but that's due to the long history of 'foot' not being standardized until relatively recently)