Another sequence

This representation looks utterly useless, but amusing anyway. You can easily see some patterns; there's a reason for them. (I have to do something when walking laps--mulling over crazy stuff works.) (And yes, you can represent all the integers this way.)

0
1
110
111
100
101
11010
11011
11000
11001
11110
  ....

hint below

You can go backwards too:

  ...
  1010
  1011
  1000
  1001
  1110
  1111
  1100
  1101
  10
  11
  0