Parity problem with a cellular automaton solution

The parity of a bit string of length N is a global quantity that can be efficiently computed using a global counter in $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ time. But is it possible to find the parity using cellular automata with a set of local rule tables without using any global counter? Here, we report a way to solve this problem using a number of $r=1\mathrm{}$ binary, uniform, parallel, and deterministic cellular automata applied in succession for a total of $\mathrm{O}{(N}^2)$ time.