## CJam, <s>10</s> 8 bytes

    l2/{)-}%

[Test it here.][1]


### Explanation

This is a very simple solution: in each pair, remove all instances of the last character. Repeated digits and unpaired trailing digits will be removed, as will be the second digit in any pair of unequal digits:

    "0"  --> ""
    "1"  --> ""
    "00" --> ""
    "01" --> "0"
    "10" --> "1"
    "11" --> ""

This leaves only the digits we're looking for. Here's how the code computes this:

    l     e# Read input.
    2/    e# Split into pairs. Odd inputs will yield a single-character string at the end.
    {     e# Map this block over the pairs...
      )   e#   Pull the last character off the string.
      -   e#   Remove all occurrences of that character from the remainder (which is either
          e#   an empty string to begin with or a single-digit string).
    }%

When the list is auto-printed at the end of the program, the empty strings are simply omitted.


 [1]: http://cjam.aditsu.net/#code=l2%2F%7B)-%7D%25&input=1011101010