Had been reading a post written by Adam Back a couple years back (no pun intended) with regards to calculating bitcoin difficulty in bits (so we could arrive to the number of hashes roughly needed before a solution to a block is found).
The equation being log2(difficulty)+32.
From his post I also understood we could also find the difficulty in bits via the block hash in hex, i.e. each leading zero * 4, then check the next hex char with the following rule: >7=+0bits, >3=+1bit, >1=+2bits, 1=+3bits.
What is the intuition to Adam's elaboration of >7=+0bits, >3=+1bit, >1=+2bits, 1=+3bits? Maybe there is something with regards to hex conversion that I need to catch up on?
With log2(difficulty)+32, we could arrive to a fractional bit (e.g. 54.8713). Would it be possible to derive the same fractional bit given the leading block hash values, or are we at best left with an approximation?
Thanks in advance!