Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 31 / 1 / f

For the uniform 27-symbol model, $s=\lceil {\log }_{2}27\rceil =5$. The uniform-source Huffman length distribution givesThus five symbols receive four-bit codewords and the other 22 receive five-bit codewords. To realize these lengths, start with all 32 binary words of length five and collapse any five disjoint sibling pairs into their four-bit parents. This leaves exactly five leaves at depth four and 22 at depth five. All source letters have the same probability, so which five letters receive the shorter codewords is arbitrary.

The expected codeword length isThe 27 symbols may represent 26 letters and a space, but this idealization keeps them equiprobable; it is not an empirical frequency model of English.