For the following ideal systems, calculate the hit ratio h required to achieve the stated speedup ratio S.

a. tm = 60 ns, tc = 3 ns, S = 1.1
b. tm = 60 ns, tc = 3 ns, S = 2.0
c. tm = 60 ns, tc = 3 ns, S = 5.0
d. tm = 60 ns, tc = 3 ns, S = 15.0


S = 1/(h?k + 1 ? h) or h = (S ? 1)/(S ? S?k) = (S ? 1)/(S?(1 ? k))
a. tm = 60 ns, tc = 3 ns, S = 1.1 k = 0.05 h = 0.1/(1.1 x 0.95) = 0.096
b. tm = 60 ns, tc = 3 ns, S = 2.0 k = 0.05 h = 1.0/(2.0 x 0.95) = 0.526
c. tm = 60 ns, tc = 3 ns, S = 5.0 k = 0.05 h = 4.0/(5.0 x 0.95) = 0.842
d. tm = 60 ns, tc = 3 ns, S = 15.0 k = 0.05 h = 14.0/(15.0 x 0.95) = 0.98

Computer Science & Information Technology

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