CS120: Bitcoin for Developers I

In Using the command line to retrieve block 277,316, we saw that the block contains the target, in a notation called "target bits" or just "bits," which in block 277,316 has the value of 0x1903a30c. This notation expresses the Proof-of-Work target as a coefficient/exponent format, with the first two hexadecimal digits for the exponent and the next six hex digits as the coefficient. In this block, therefore, the exponent is 0x19 and the coefficient is 0x03a30c.

The formula to calculate the difficulty target from this representation is:

• target = coefficient * 2^{(8*(exponent–3))}

Using that formula, and the difficulty bits value 0x1903a30c, we get:

• target = 0x03a30c * 2^{0x08*(0x19-0x03)}
• => target = 0x03a30c * 2^(0x08*0x16)
• => target = 0x03a30c * 2^0xB0

which in decimal is:

• => target = 238,348 * 2¹⁷⁶
• => target =
  22,829,202,948,393,929,850,749,706,076,701,368,331,072,452,018,388,575,715,328

switching back to hexadecimal:

• => target =
  0x0000000000000003A30C00000000000000000000000000000000000000000000

This means that a valid block for height 277,316 is one that has a block header hash that is less than this target. In binary that number must have more than 60 leading bits set to zero. With this level of difficulty, a single miner processing 1 trillion hashes per second (1 terahash per second or 1 TH/sec) would only find a solution once every 8,496 blocks or once every 59 days, on average.