Problem
A newly discovered archive of music recorded by DJ Marie is to be cataloged. Each recording falls into one of four unique categories: Solo (99 items), with the Data Representers (229 items), with Boole Al-Jabr (79 items), and with the Memory Managers (92 items).
1. Suppose you must code each item in the archive without considering categories. How many bits are required to represent each item in the entire archive with a unique binary code using the least number of bits?
2. Suppose you are required to code the category of each item explicitly, as well as a number, to identify that item within the category. How many bits are needed to represent each item with a unique binary code using the least number of bits? How could one tell an item's category by looking at the code?
3. Explain brie?y Why the results of parts (1) and (2) are different, as well as the advantages/ disadvantages of both representations.