digits  binary 2^n  fibinary F(n+2)   ratio
     1           2                2   1.000
     2           4                3   0.750
     3           8                5   0.625
     4          16                8   0.500
     5          32               13   0.406
     6          64               21   0.328
     8         256               55   0.215
    10        1024              144   0.141
    13        8192              610   0.074

levels  binary digits  fibinary digits  extra
     2              1                1      0
     8              3                4      1
    16              4                6      2
    55              6                8      2
   144              8               10      2
   256              8               12      4
  1024             10               15      5
  8192             13               19      6