# [Jelly], 13 bytes

    Dd4d2FṙJ$ḄṢIS

[Try it online!][TIO-ja2mp4fy]

### How it works

    Dd4d2FṙJ$ḄṢIS  Main link. Argument: n

    D              Decimal; convert n to base 10 (digit array).
     d4            Divmod 4; map each digit d to [d/4, d%4].
       d2          Divmod 2; map each [d/4, d%4] to [[d/8, d/4%2], [d%4/2, d%2]].
         F         Flatten the resulting 3D binary array.
          ṙJ$      Take all possible rotations.
             Ḅ     Convert each rotation from binary to integer.
              Ṣ    Sort the resulting integer array.
               I   Take the forward differences.
                S  Take the sum.

[Jelly]: https://github.com/DennisMitchell/jelly
[TIO-ja2mp4fy]: https://tio.run/##y0rNyan8/98lxSTFyO3hzpleKg93tDzcucgz@P/RPYfbHzWtcf//38jYREfBEErqKFiam1oYG@oomBhbGpibQASAkhYGZoYA "Jelly – Try It Online"