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SOLUTIONS TO PROBLEMS 555
SOLUTIONS TO PROBLEMS
SOLUTIONS TO CHAPTER 1 PROBLEMS 1.1
Computing power increases by a factor of 2 every 18 months, which generalizes to a factor of 2 x every 18x months. If we want to ?gure the time at which computing power increases by a factor of 100, we need to sove 2x = 100, which reduces to x = 6.644. We thus have 18x = 18¡¿(6.644 months) = 120 months, which is 10 years.
SOLUTIONS TO CHAPTER 2 PROBLEMS 2.1
(a) [+999.999, ?999.999] (b) .001 (Note that error is 1/2 the precision, which would be .001/2 = .0005 for this problem.)
2.2
(a) 101111 (b) 111011 (c) 531 (d) 22.625 (e) 202.22
2.3
(a) 27 (b) 000101 (c) 1B (d) 110111.111 (e) 1E.8
2.4
2¡¿3-1 + 0¡¿3-2 + 1¡¿3-3 = 2/3 + 0 + 1/27 = 19/27
556 SOLUTIONS TO PROBLEMS
2.5 2.6 2.7 2.8 2.9 2.10 2.11
37.3 (17.5)10 ? (122.11)3 = (17.4)10 ?8 0 0011 0000 0101 0110 1001 0101
One¡¯s complement has two represent¡¦(»ý·«)