Finite Cantor's Diagonal
CJam (15 14 bytes)

qN/ee{:=i2%)}%


Online demo

Thanks to Adnan for a one-byte saving.

Dissection

qN/    e# Split input on newlines
ee{    e# Label each line with its index and map:
  :=i  e#   Get the character at the same index (i.e. diagonalise)
  2%)  e#   Compute (ASCII value mod 2) + 1
       e#   Maps 0 1 2 3 4 5 6 7 8 9
       e#     to 1 2 1 2 1 2 1 2 1 2
}%