Let $\Sigma = \{0,1\}$, with $w \in \Sigma^* $ and $value(w)$ the not negative integer value of $w$. $w$ is seen as binary string, with its first index being the least significant bit:
$$value(w_1 w_2 ... w_n) = \Sigma_{i=i}^n 2^{i-1} w_i$$
The languages is defined as: $$L = \{a_1b_1a_2b_2 ... a_nb_n \ \in \ \Sigma^* \ \vert \ value(a_1a_2 ... a_n) = 3 \ \cdot \ value(b_1b_2 ... b_n)\}$$
The task is to draw the accepting DFA. I frankly have no idea on how to approach this question. Can someone give me a hint, not the full answer please?