ExampleThe example shows the construction of the Shannon code for a small alphabet. The five symbols which can be coded have the following frequency:
Symbol
 A
 B
 C
 D
 E
 Count





 Probabilities
 0.38461538
 0.17948718
 0.15384615
 0.15384615
 0.12820513
 All symbols are sorted by frequency, from left to right (shown in Figure a). Putting the dividing line between symbols B and C results in a total of 22 in the left group and a total of 17 in the right group. This minimizes the difference in totals between the two groups.
With this division, A and B will each have a code that starts with a 0 bit, and the C, D, and E codes will all start with a 1, as shown in Figure b. Subsequently, the left half of the tree gets a new division between A and B, which puts A on a leaf with code 00 and B on a leaf with code 01.
After four division procedures, a tree of codes results. In the final tree, the three symbols with the highest frequencies have all been assigned 2bit codes, and two symbols with lower counts have 3bit codes as shown table below:
Results in 2 bits for A, B and C and per 3 bits for D and E an average bit number of
Shannon–Fano Algorithm
Date: 20141228; view: 941
