Decompose binary into alternating subsequences
Pyth, 17 16 bytes

1 byte thanks to Jakube

iR2cJ.BQx1qVJ+dJ


Demonstration

A nice, clever solution. Uses some lesser known features of Pyth, like x&lt;int&gt;&lt;list&gt; and c&lt;str&gt;&lt;list&gt;.

iR2cJ.BQx1qVJ+dJ
                    Q = eval(input())
    J.BQ            Store in J the input in binary.
          qV        Vectorize equality function over
            J+dJ    J and J with a leading dummy char, to get the offset right.
                    This calculates whether each element matches its successor.
        x1          Find all of the indexes of 1 (True) in this list.
   cJ                Chop J at those locations.
iR2                  Convert from binary back to base ten and output.