Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• The Library of Congress, which is the United States’ official repository of all printed documents, contains approximately 120 million books. (a) Estimate the number of characters (letters, numbers, and spaces) in all the books in the Library of Congress. (b) Estimate the number of bits (1s and 0s) of information required to store the library in uncompressed format. (c) If these bits were stored on the surface of a copper-tin alloy as individual atoms (with a Cu atom meaning 1, and an Sn atom meaning 0, say), what would be the area required to store the whole library? (d) Using Shannon’s information theory, it can be shown that ordinary English text can be stored in a compressed format that contains only about two bits per letter. What surface area would be required to store the entire library in this compressed format? (e) If this compressed information was stored in the interior of a cube of metal alloy, how large would the cube be?
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