Question

A commonly-used estimate for the number of bytes needed to store one

page of a book is 2K (2,000). Harry Potter books have 800 pages. Each
book is 3 inches in height. How tall would the stack of Harry Potter books
be, in miles, that could be stored in a 32-bit memory space? Now, repeat
the question for a 64-bit memory space.

Answer 1

0.127 miles ; 5.458 *10^8 miles

Step-by-step explanation:

Number of bytes needed to store a page = 2000

Number of pages (Harry Potter's book) = 800

Total memory required to store entire book = (2000 * 800) = 1600000 = 16 * 10^5 bytes

Hence,

1 byte of memory will store : (height of each book / memory size of each book)

= 3 ÷ 16 * 10^5

= 1.875 * 10^-6

For 32 bit memory space :

(1.875 * 10^-6 * 2^32) = 8053.06368 inches

1 inch = 1.578 * 10^-5 mile

8053.06368 inches = 8053.06368 * (1.578 * 10^-5) = 0.1270773448704 miles

= 0.127 miles

For 64 bit memory size :

(1.875 * 10^-6 * (2^64)) = 3.45876 * 10^13 inches

(3.45876 * 10^13) * (1.578 * 10^-5)

= 5.458 *10^8 miles