in the b=2 case, you get:

  1 / 1 = 1 = b - 1
  1 % 1 = 0 = b - 2

they are the other way around, see for example the b=3 case:

  21 (base 3) = 7
  12 (base 3) = 5
  7 / 5 = 1 = b - 2
  7 % 5 = 2 = b - 1