Explain what is meant by saying that a binary code $\mathcal{C}$ is a decodable code with words $C_{j}$ of length $l_{j}$ for $1 \leqslant j \leqslant n$. Prove the MacMillan inequality which states that, for such a code,

$$\sum_{j=1}^{n} 2^{-l_{j}} \leqslant 1$$