Go away! No-1's Here!
Husk, 21 14 13 bytes
-7 bytes, thanks to @Neil's JS answer
-1 byte inspired by betaveros's Parradoc answer
Uses 0-indexing
mḋTmMo±&gt;ḋ2B3½

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Explanation
            ½    Half the input
          B3     Convert to Base 3
   m             Map over the list
    Mo±&gt;ḋ2       Function such that: 0 -&gt; [0,0], 1 -&gt; [0,1], 2 -&gt; [1,1]
        ḋ2       Binary 2, [1,0]
    M            For each in that list
     o±&gt;         check if the argument is greater than it
  T              Transpose
mḋ               Convert each from binary

Previous 21 byte Solution
First time I've seen a use for ».
mḋT»o%2+ȯ?´eḋε%3`-0B3

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Longer, as I was dealing with carries