typically the hashes are represented as a sequence of hexadecimal digits, just as an example md5 and sha265

Hash value is just a value picked out of some domain. For most hashes this domain is Z_{2^n} with n usually divisible by 8. It is then convenient to represent that as hexadecimal number, but there is nothing special about that particular encoding. For purpose of generating secure password you can even use said hash as seed for CSPRNG and then use it for FIPS 181 random password generator algorith or something similar.