Confusing Language for a Deterministic Finite State Machine

Question

I am supposed to show a DFSM to accept the following language for my theory of computation class, but that isn't what I am having trouble with. I'm not even sure what the language means. Can someone explain what this means in English? If I understand what it means, I'm sure I can create the DFSM. Thanks for any help. Here is the language:

{w E {O, 1}* : w corresponds to the binary encoding, without leading O's, of natural numbers that are evenly divisible by 4}.

Answer 1

In base 10: 4, 8, 12, 16,...

In the requested encoding: 100, 1000, 1100, 10000, ...