Starting with 0 0

     0 
    1 1 
   1 1 1 
  1 1 1 1 
 1 1 1 1 1 

     1 
    0 1 
   0 1 1 
  1 1 1 1 
 1 1 1 1 1 

     1 
    0 1 
   1 1 1 
  1 0 1 1 
 1 1 0 1 1 

     1 
    0 1 
   1 1 1 
  1 1 0 0 
 1 1 0 1 1 

     1 
    0 1 
   1 1 1 
  0 0 1 0 
 1 1 0 1 1 

     1 
    0 1 
   1 1 0 
  0 0 0 0 
 1 1 1 1 1 

     0 
    0 0 
   1 1 1 
  0 0 0 0 
 1 1 1 1 1 

========================
     0 
    1 1 
   1 1 1 
  1 1 1 1 
 1 1 1 1 1 

     1 
    1 0 
   1 1 0 
  1 1 1 1 
 1 1 1 1 1 

     1 
    1 0 
   1 1 1 
  1 1 0 1 
 1 1 0 1 1 

     1 
    1 0 
   1 1 1 
  0 0 1 1 
 1 1 0 1 1 

     1 
    1 0 
   1 1 1 
  0 1 0 0 
 1 1 0 1 1 

     1 
    1 0 
   0 1 1 
  0 0 0 0 
 1 1 1 1 1 

     0 
    0 0 
   1 1 1 
  0 0 0 0 
 1 1 1 1 1 

========================
Starting with 1 0
     1 
    0 1 
   1 1 1 
  1 1 1 1 
 1 1 1 1 1 

     1 
    1 1 
   0 1 1 
  0 1 1 1 
 1 1 1 1 1 

     1 
    1 1 
   1 0 0 
  0 1 1 1 
 1 1 1 1 1 

     1 
    1 1 
   1 1 0 
  0 1 0 1 
 1 1 1 0 1 

     1 
    0 1 
   1 0 0 
  0 1 1 1 
 1 1 1 0 1 

     1 
    0 1 
   1 0 1 
  0 1 0 1 
 1 1 0 0 1 

     1 
    0 1 
   1 0 1 
  0 1 0 1 
 0 0 1 0 1