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--- tanszek:oktatas:techcomm:shanon-fano_method [2024/08/27 16:34] – knehez
+++ tanszek:oktatas:techcomm:shanon-fano_method [2024/10/08 08:45] (current) – knehez
@@ Line 26: / Line 26: @@
 $$ H = -\left(\frac{2}{4} \log \frac{1}{4} + \frac{2}{8} \log \frac{1}{8} + \frac{4}{16} \log \frac{1}{16}\right) = 2.75 \, \text{[bit].} $$
+What is the average word length?
+We can calculate the average word length with the use of this function: \(  L = \sum_{i=1}^n x_i \mu_i \)
+After substituting:
+$$ L = \frac{2}{4} \cdot 2 + \frac{2}{8} \cdot 3  + \frac{4}{16} \cdot 4 = 2.75 \,\text{ [bit]}$$
+The original 8 symbols (X1-X8) can be stored with 4 bits. The average length is 2.75 bits, thus the compressed messages will be  \(\frac{2.75}{4} \approx 68.75\% \) shorter.