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Note: The following is an excerpt from the official Ethereum site. It is provided here as a convenience and is not authoritative. Refer to the original document as the authoritative reference.

In English, convert the address to hex, but if the ith digit is a letter (ie. it’s one of abcdef) print it in uppercase if the 4*ith bit of the hash of the lowercase hexadecimal address is 1 otherwise print it in lowercase.

Benefit

• Backwards compatible with many hex parsers that accept mixed case, allowing it to be easily introduced over time
• Keeps the length at 40 characters
• On average there will be 15 check bits per address, and the net probability that a randomly generated address if mistyped will accidentally pass a check is 0.0247%. This is a ~50x improvement over ICAP, but not as good as a 4-byte check code.