Computing the entropy of an integer variable

Question

Assignment:

Let X be an integer variable represented with 64 bits. The probability is ½ that Xis in the range (0, 216 - 1), the probability is I that X is in the range (2¹⁶, 2³² - 1), and the probability is that X is in the range (2³², 2⁶⁴ - 1). Within each range the values are equally likely. Compute the entropy of X.

Provide complete and step by step solution for the question and show calculations and use formulas.