Excerpt from page 6 of the yellow white paper:
I can understand the first three definitions, the fourth one is problematic. How does the m function actually work? Maybe I'm not too familiar with formal specification, but I'm specifically confused on the [i,i+1] part. Does it take the bits at position i and i+1 of the hash, sum them up and then apply modulo 2048?
Consider the following input
ethereum yellow paper
Consider it's Keccak-256 hash according to this website:
7f110dc4c0a897ea5187a67e2c3a7db3a43410df8d1754fbdf28351c7e58400f
The first three pairs of bytes of Keccak-256 of an input string-
{7,f},{f,1},{1,0}
1) {7,f}
low order 11 bits of each of the first three pairs of bytes calculated using this website
00110111011
Its decimal equivalent calculated using this website is 443. 443%2048 = 443
Bloom filter will set a 443'th bit of 2048 bit sequence.
2) {f,1}
low order 11 bits of each of the first three pairs of bytes calculated using this website
01100110001
Its decimal equivalent calculated using this website is 817. 817%2048 = 817
Bloom filter will set a 817'th bit of 2048 bit sequence.
3) {1,0}
00110001001
low order 11 bits of each of the first three pairs of bytes calculated using this website
Its decimal equivalent calculated using this website is 393. 393%2048 = 393
Bloom filter will set a 393'th bit of 2048 bit sequence.
[i,i+1] denotes bytes at position i and i+1
Hope it helps!
