A manufacturer of mechanical encoders discovers the 2-bit Gray code and manufactures encoders with the decimal sequence 0, 1, 3, 2. Generalizing to n-bit encoders, they decide all they need to do is to reverse every other pair of values in the decimal sequence, resulting in a sequence of 0, 1, 3, 2, 4, 5, 7, 6, 8, 9, etc. But this proves to be less than perfect. As a function of n, how many "bad" boundaries are there? How much better is their code than an n-bit binary code?