Calculating the Hash: The Endianness Challenge

Calculating a Bitcoin block hash is mathematically simple but technically tricky due to Endianness. Bitcoin internally processes data in Little-Endian, but humans and block explorers display data in Big-Endian.

1. Internal Representation (Little-Endian)

Inside the 80-byte header, every field (except the Merkle Root and Prev Hash, which are already hashes) is stored in little-endian byte order.

• When a node hashes the header, it treats it as a raw blob of 80 bytes.

• The output of the double-SHA256 is also a 32-byte blob.

2. Display Representation (Big-Endian)

When you see a block hash like 000000000000000000052d31... on a website, it has been reversed.

• In the raw computer memory, those leading zeroes are actually at the end of the 32-byte string.

• The first non-zero bytes you see in the explorer are actually the last bytes in the raw data.

3. The 32-Byte Swap

To convert a raw internal block hash to a human-readable "Block ID":

1. Take the 32-byte output of the double-SHA256.

2. Reverse the order of the bytes (Byte 31 becomes Byte 0, etc.).

3. Convert the reversed bytes to a hexadecimal string.

4. Why the Confusion?

This discrepancy exists because SHA-256 is a "big-endian" algorithm by design (as defined in FIPS 180-4). However, the x86 processors that Bitcoin was originally developed on are "little-endian." Satoshi Nakamoto's original implementation handled these conversions in a way that resulted in the reversed display format we use today.

Format	Example Start	Used By
Internal (Raw)	6a 64 04 d6...	CPU, Hashing, Mining
Display (Hex)	00000000...	Block Explorers, Users

[!TIP] If you are writing a script to verify block hashes, always remember to reverse the byte order before comparing your result to a value from a block explorer.

Next, we will look at the Leading Zeroes Requirement and the probability of mining.