guilospanck/btc-target-bits-difficulty

nBits, Target and Difficulty of BTC protocol.

Target, nBits, Difficulty, Time to mine

This project shows how to calculate those three values that are used in the Bitcoin protocol.

nBits

This is the compressed value that is used in the block header. It's a 4 byte (32 bits) value defined by:

• exponent: the first byte. It tells how "far to the left" is the value;
• coefficient: the last 3 bytes. It is the value itself (with some precision, but not full).

Example:

From https://learnmeabitcoin.com/technical/block/bits/

Note that the nBits is a value that is not 100% accurate, but nevertheless it is used by the miners.

Target

This is the uncompressed value that miners use to validate the block found, i.e., if the block hash is below it. It's a 32-byte (256 bits) value.

It is defined by:

$$target = coefficient * 2^{8(exponent-3)}$$

Difficulty

This value actually does not exist in the protocol, it is more to provide a human-readable information to how difficult it is to mine a block. It has the inverse meaning of the target, i.e., higher the target, lower the difficulty (easier it is to mine a block); lower it is the target, higher the difficulty (harder to mine a block).

It is defined by:

$$difficulty = \frac{max_{-}target}{current_{-}target}$$

where:

• max_target: hardcoded value defined in the protocol that has the value of 0x00000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff (but because of how the protocol is implemented, it is truncated to 0x00000000ffff0000000000000000000000000000000000000000000000000000;
• current_target: the current (uncompressed) value.

Time to mine a valid block

The time to mine a valid block is an equation that brings into consideration the current hashrate. The formula is given by:

$$time = \frac{difficulty * 2^{32}}{hashrate}$$

If the hashrate is given in hashes/seconds, then the result will be in seconds.

With this information, you can check in how many blocks (estatistically) the miner will find a valid block by knowing that each block is mined roughly every 10 minutes:

$$\frac{time}{60 * 10}$$