15-110 PS1 Sample Solutions - Spring 2018

1. 
(a) NAME 2 INVENTIONS FROM THE 1800S THAT USED PUNCHED CARDS
(b) Jacquard's Loom and Hollerith's Tabulating Machine

2. 
(a) delta_f(x) = f(x+1) - f(x) = 2x + 8
    delta2_f(x) = delta_f(x+1) - delta_f(x) = 2
    delta2_f(0) = 2, delta_f(0) = 8, f(0) = 6
(b) delta3 column: 5,5,5,5
    delta2 column: 7,12,17,22
    delta column: 8,15,27,44
    f column: 16,24,39,66
    f(4) = 66

3.
(a) 64 is 2**6, so 64 times more powerful is 6 doublings.
    Since each doubling takes 2 years, the total time is 2*6=12 years.
(b) 4GB  = 2**2 * 2**30 = 2**32 bytes
    16MB = 2**4 * 2**20 = 2**24 bytes
    The number of modules needed is 2**32 / 2**24 = 2**8 = 256

4.
(a) Cameras shifted from film to digital memory which was initially 
    slow but then gained very quickly so they lost sales with 
    no time to adjust.
(b) Music copies in the 70s and 80s were imperfect (analog) 
    recordings which ended up being of lesser quality 
    but digital copies today are exactly the same as the original.
(c) No, because cyberspace still connects computers in countries 
    with political boundaries so freedom of speech protections vary.