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Sketch of a deterministic finite automaton (DFA) for the following regular language (type 3):$$ L ~=~ \{ w \in \{0,1\}^* ~:~ w \text{ is the binary representation of } n \in \mathbb{N} \text{ which is divisible by 2 (possibly with leading 0s)} \} $$
This is an infinite language, with, for example, the following words:$$ L ~=~ \{ \varepsilon, 0, 011, 0110011, ~... \} $$