BMW internal codes:
Cooper engine: W10B16
Cooper S: R53
Cooper S engine: W11B16
The engine code is decoded with W10 and W11 being the engine family, B denotes a gas and not diesel engine (it escapes me at the moment what the letter is short for) and 16 is the displacement.
This code is consistent with BMW engines, for example the current 3.2L M3 engine is the S54B32.
"I feel that the dreams of the future are better than the history of the past."
FLAT OUT until you see God, then brake.