e outcomes). While computers can routinely solve the issue in the general case, we can observe that the information measure provides a hunch of the minimum computing operations, and eventually boils down to greater speed and time savings. Exercises 3.1 (B): Picking a single card out a 32-card deck, what is the information on the outcome? 3.2 (B): Summing up the spots of a two-dice roll, how many message bits are required to provide the information on any possible outcome? 3.3 (B): A strand of DNA has four possible nucleotides, named A, T, C, and G. Assume that for a given insect species, the probabilities of having each nucleotide in a sequence of eight nucleotides are: p(A) = 1/4, p(T) = 1/16, p(C) = 5/16, and p(G) = 3/8. What is the information associated with each nucleotide within the sequence (according to the information-theory definition)? 3.4 (M): Two cards are simultaneously picked up from a 32-card deck and placed face down on a table. What is the information related to any of the events: (a) One of the two cards is the Queen of Hearts? (b) One of the two cards is the King of Hearts? (c) The two cards are the King and Queen of Hearts? (d) Knowing that one of the cards is the Queen of Hearts, the second is the King of Hearts? Conclusions? 3.5 (T): You must guess an integer number between 1 and 64, by asking as many questions as you want, which are answered by YES or NO. What is the minimal number of questions required to guess the number with 100% certainty? Provide an example of such a minimal list of questions. Entropy The concept of entropy is central to information theory (IT). The name, of Greek origin (entropia, tropos), means turning point or transformation. It was first coined in 1864 by the physicist R. Clausius, who postulated the second law of thermodynamics. 1 Among other implications, this law establishes the impossibility of perpetual motion, and also that the entropy of a thermally isolated system (such as our Universe) can only increase. 2 Because of its universal implications and its con