Question

Binary messages may be sent in Hexadecimal (4 bit ; 0−F ). For the message below estimate the probability of a "1" (p). What is the entropy of this message in bits?

Answer 1

The probability of '1' in the binary message is 0.25. The entropy of the message is 0.811 bits.

Step-by-step explanation:

To estimate the probability of a '1' in the given binary message, we can count the number of times '1' appears in the message and divide it by the total number of bits in the message. From the message provided, we can see that there are 16 instances of '1' out of a total of 64 bits, so the probability of '1' (p) is 16/64 = 0.25.

To calculate the entropy of the message, we can use the formula H = -Σ(p_i * log2(p_i)), where p_i is the probability of each symbol. In this case, we have two symbols ('0' and '1') and their respective probabilities are p=0.25 and q=0.75. Using these probabilities, we can calculate the entropy as H = -(0.25 * log2(0.25) + 0.75 * log2(0.75)) = 0.811 bits.