base58 bitcoin address encoding
Base58 was designed by Satoshi Nakamoto specifically for Bitcoin addresses: the goal was an alphabet humans could copy, read out over the phone and check visually without mixing up similar-looking characters, so it cuts exactly the symbols most likely to be swapped by mistake from the common alphanumeric alphabet.
The leading 1 comes from version byte 0x00, it is not part of the public key hash; the version defines the output character, not the content.
Swapping only the version byte from 0x00 to 0x05 changes the first character of the whole address, even with a 20-byte hash identical in size to a P2PKH.
The extra 0x01 byte at the end, 33 payload bytes against 32 without it, is what marks the key as compressed and shifts the leading character from 5 to K or L.
Base58 drops 0 (zero), O (uppercase o), l (lowercase L) and I (uppercase i) because they look alike in common fonts and are hard to tell apart when read aloud. That reduces transcription errors, which is critical for wallet addresses, where one swapped character can mean permanently lost funds.
It is SHA-256 applied twice over the version plus the payload, of which only the first 4 bytes become part of the encoded address. Any wrongly typed character changes those 4 checking bytes, so the wallet rejects the address before attempting to send anything, instead of sending funds to a destination that does not exist.
Because a compressed WIF payload is 33 bytes, one more than the 32 of an uncompressed WIF, and that extra byte (0x01) pushes the numeric value of the whole payload upward before the Base58 encoding, which shifts the leading character from 5 to K or L.
No, and that is exactly why the version bytes differ between the two networks: 0x00 and 0x05 on mainnet against 0x6f and 0xc4 on testnet. The version byte is the first thing Base58Check checks when decoding, so a wallet catches the wrong network before even checking the rest of the payload.
123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyzEverything is computed in your browser, including the SHA-256 behind the checksum. No key or address leaves this device.