Consider an $m$ output, $n$ state Mealy machine. How many states does the equivalent Moore machine contain?
The answer is $mn$ but my argument is that the total number of output produced while reading a string of length $n$ ($n$ states) Mealy will produce $m$ outputs ($m$ transitions) but a Moore machine produces a output even in the initial state without any transitions. So to accommodate the first transition of the Mealy machine (the first output of the Mealy) we need another state in the Moore machine. So the answer should be $mn + 1$.
Can anyone tell where am I going wrong?