Compare and Honesty - Huffman Codes Use Shorter Names

The toy code saves one bit here, with clear limits on what that means.

highlighted = computed this step

Fixed names spend the same width

With four symbols, a fixed code would spend 2 bits on every symbol.

\text{fixed width}=2

The message has 6 symbols, so fixed names use 12 bits.

6\cdot2=12

The Huffman message uses 11 bits: one bit shorter for this tiny message.

12\text{ minus }11=1

NOTE: toy static prefix code only. This is not adaptive compression, not a file format, not an entropy optimality proof, and not encryption.

\text{toy static prefix code only}

Huffman coding gives common symbols shorter names. In this pinned example, ABACAD uses 11 Huffman bits instead of 12 fixed bits.

11<12