$ perl -wle 'm[^(?{undef $var})(?:([01])(?{$var //= $^N}))+$] 
      and print "$_: '"'"'$var'"'"'" for qw[ 0 1 00 11 10 01 012]'
    0: '0'
    1: '1'
    00: '0'
    11: '1'
    10: '1'
    01: '0'