How to get numeric value of a hash?

Question

On the Proof of work blockchain wiki, one can find that the hash

0000c3af42fc31103f1fdc0151fa747ff87349a4714df7cc52ea464e12dcd4e9 

corresponds to the value 2^239.61238653. My question is, how can one calculate this numeric value of a hash?

Answer 1

First note that the block hash is usually represented as a hexadecimal, little endian value, when you try to convert to decimal. If your system is little-endian:

To convert to decimal in bash/perl:

$ hex=0000c3af42fc31103f1fdc0151fa747ff87349a4714df7cc52ea464e12dcd4e9
$ $ perl -le 'use bignum qw/hex/; print hex("0x".$ARGV[0])' --"$hex"
532607621168989936896605052113495566299419916018780134558135832581308350315356027254565114944

or, to get base2 log:

perl -le 'use bignum qw/hex/; print log(hex($ARGV[0]))/log(2)' -- "$hex" 
239.6123865298365295145460775449928303015

Which represents 2^239.61238653