INFORMATION THEORY Part I: Use logarithms to measure information in the following problems, 1. If someone asks you to guess a number between 1 and a million and you use the "cut in half' strategy, what will your first question be? How many guesses will it take you? (Hint: The number of guesses required may remind you of another famous guessing game.] 2. Computer storage and memory is measured in 8-bit chunks called bytes. Each computer bit is a switch that is either on or off. When you see a memory dump from a computer, the bits are represented by Os and ls. You can think of each bit as being the answer to a yeso question, with O standing for no and 1 for yes. How many bits does it take to code one character from a standard computer keyboard which has 47 alphanumeric keys, each of which can be either unshifted (like lowercase u or the number 4) or shifted (like U or the dollar sign $)? Is this more or less than one byte? 3. How many bits does it take to identify uniquely every person in the United States (the current population is about 300 million)