The title of the question says it all. I have been researching SHA-1 and most places I see it being 40 Hex Characters long which to me is 640bit. Could it not be represented
There are two hex characters per 8-bit-byte, not two bytes per hex character.
If you are working with 8-bit bytes (as in the SHA-1 definition), then a hex character encodes a single high or low 4-bit nibble within a byte. So it takes two such characters for a full byte.