Why is the dynamic programming algorithm of the knapsack problem not polynomial? [duplicate]

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• The running time of the knapsack problem is $O(n\cdot \min(B,V))$ and is not polynomial, why? 1 answer

The dynamic programming algorithm for the knapsack problem has a time complexity of $O(nW)$ where $n$ is the number of items and $W$ is the capacity of the knapsack.

Why is this not a polynomial-time algorithm?

I have read that one needs $\lg W$ bits to represent $W$, so it is exponential time. But, I don't understand, one also needs $\lg n$ bits to represent $n$, doesn't one? So, for example, merge sort is not polynomial time, because its complexity is $O(n\lg n)$ and one needs $\lg n$ to represent $n$?

What am I missing here?