Question: How can I get a list of all possible linear combinations?

So, I have a list of vectors v1,...v8 - and I want to consider all {0,1}v1 + {0,1}v2+ ... + {0,1}v8 (I need a list of all 2^8 possible combinations). 

 

I can run 8 simple for loops and use the mod command, but that's inconvenient. Is there a nice way to do what I'm trying to get done? 

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