// $%$ is the remainder operation, e.g.
// 15 divided by 2 is 7 with remainder 1, so 15 % 2 = 1, and
//  1 divided by 2 is 0 with remainder 1, so  1 % 2 = 1, and
// 16 divided by 2 is 8 with remainder 0, so 16 % 2 = 0.

   int n = 19; int x = 0; int y = 1;
   while (n != 0)
       if (n % 2 == 0)
           n = n/2;
       else {
           n = n-1;
           x = 10*x + 3;
           y = y*10;
       }
   y = (y-1) / 3;

here's the trace: notice the "heavy line" drawn each time the loop condition
is tested, including the final test that evaluates to $false$.

         #            #   #              #   #   #   #                #      
         #            #   #              #   #   #   #                #      
  +--+-+-#----+---+---#---#---+----+-----#---#---#---#---+-----+------#-----+
n |19| | # 18 |   |   # 9 # 8 |    |     # 4 # 2 # 1 # 0 |     |      #     |
  +--+-+-#----+---+---#---#---+----+-----#---#---#---#---+-----+------#-----+
x |  |0| #    | 3 |   #   #   | 33 |     #   #   #   #   | 333 |      #     |
  +--+-+-#----+---+---#---#---+----+-----#---#---#---#---+-----+------#-----+
y |  | |1#    |   | 10#   #   |    | 100 #   #   #   #   |     | 1000 # 333 |
  +--+-+-#----+---+---#---#---+----+-----#---#---#---#---+-----+------#-----+
         #            #   #              #   #   #   #                #      
         #            #   #              #   #   #   #                #