Each codeword has a length of $\ceil(-\log(p_i))$.

Don’t forget to change base!

We can then draw the tree, and then fill in the code words.
(Trees are drawn with the leafs being added as quickly as possible.)

Average Code Length

Average codeword length: Sum of (probability * code length * number of repetitions)

$ceil(-log(p_i)) * p_i * n$

Entropy / Limit

$-log(p_i) * p_i * n$