I. Overview.
In the (public key) section, we discussed the mechanism of public key generation, and based on the format of the private key, different forms of public keys can be generated: 'uncompressed public key' and 'compressed public key'. The public key is inherently public; can't it be used directly as an address? Why go through the trouble of converting it into an address?
There are three main reasons.
First: The public key has two forms, compressed and uncompressed, with different lengths—one is 65 bytes (1-byte prefix + 32-byte x value + 32-byte y value) and the other is 33 bytes (1-byte prefix + 32-byte x value). There may be a third or fourth format in the future, making the number of public key formats presented to the user too many, which could be confusing.