ITPEC FE Morning April 2022 Question 13

Topic: Computer Component

Which of the following is the list that contains A through D sorted starting with the shortest effective access time of the main memory?

 Cache memoryMain memory
Does the system have cache memory? (yes/no)Access time (nanoseconds)Hit rate (%)Access time (nanoseconds)
ANo--15
BNo--30
CYes206070
DYes109080

Explanation

A, D, B, C — compute each system's effective access time; a cache helps only if its hit rate and speed outweigh a slow main memory.

With a cache, effective time = hit rate × cache time + miss rate × main memory time:

  • •A (no cache): 15 ns
  • •B (no cache): 30 ns
  • •C: 0.6 × 20 + 0.4 × 70 = 12 + 28 = 40 ns
  • •D: 0.9 × 10 + 0.1 × 80 = 9 + 8 = 17 ns

Shortest first: A 15, D 17, B 30, C 40.

Answer (b)

Why not others:

  • •(a) — ranks by main memory access time alone (15, 30, 70, 80), ignoring the caches of C and D
  • •(c) — puts the cached systems first, and C ahead of D, but C is the slowest at 40 ns
  • •(d) — assumes any cache beats no cache; D at 17 ns is slower than A at 15 ns, and C at 40 ns is slower than both

Key rule: A low hit rate in front of a slow main memory can make a cached system slower than one with fast memory and no cache; always compute.

Computer Component · AI-written, may contain errors

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