An advanced form of the Chappe semaphore consists of three wooden arms on top of a tower. Each arm can take one of five positions: Full Down’,Half Down’, Level’,Half Up’ and `Full Up’. An observer watches the semaphore through a telescope and notes down three consecutive positions of the three arms. What is the maximum possible information content of what he’s recorded?
I am not sure how to do this since I'm new to information theory, and I couldn't find any notes online nor has my professor supplied any. Any help would be appreciated!
I tried doing logbase(2)(4/12) since there are 12 possible outcomes and there are 4 choices, but I got it wrong the answer is slightly less than 21.
Each arm yields $\log_2(5)$ bits of information. The observer has seen 9 arms, with total information content $9 \log_2(5) \approx 20.90$ bits.