I am trying to understand the distributed 6-color algorithm for vertex coloring (on page 10).
Here is a short description
Idea of the algorithm: We start with color labels that have $\log n$ bits. In each synchronous round we compute a new label with exponentially smaller size than the previous label, still guaranteed to have a valid vertex coloring.
Let $i$ be the smallest index where $c_v$ and $c_p$ differ; the new label is $i$ (as a bitstring) followed by the bit $c_v(i)$ itself
Grand-parent 0010110000 -> 10010 -> … Parent 1010010000 -> 01010 -> 111 Child 0110010000 -> 10001 -> 001
The problem I cannot understand this example. Let's take Grand-parent($c_p$ = 0010110000) and parent($c_v$ = 1010010000), on the round when $c_v$ receives $c_p$, so we need to change $c_v$. They differ in 5th bit, counting from 0 (5 in binary is 101), so according to definition, $c_p$ is "$101$"+$c_p=1010$, but in example it's 01010, what I get wrong?