21.9. Finding Optimal Encoding

Try these first

1. 1.

   What is the purpose of Huffman encoding?

   Hint

   Think about how we can use fewer bits.

2. 2.

   Define the prefix property in encoding.

   Hint

   Consider how Morse code can create ambiguity.

3. 3.

   What does Huffman coding primarily optimize in data transmission?

   • Maximizes frequency of symbols
   • Minimizes average bits per letter
   • Increases binary code length

   Hint

   Think about the purpose of compressing a message.

4. 4.

   True or False: In typically fixed-length encoding, all letters are represented by the same number of bits.

   • True
   • False

   Hint

   Remember how each letter's length is consistent.

5. 5.

   Create a Huffman tree for the characters: A, B, C, D, E with frequencies: A=0.5, B=0.25, C=0.15, D=0.05, and E=0.05. Explain the encoding process.

   Hint

   Start with the smallest frequencies and merge.

6. 6.

   Explain how combining nodes in a Huffman tree reduces average encoding lengths.

   Hint

   Consider how many symbols are represented with fewer bits.