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The efficiency (E) and speed up (sp) for Multiprocessor with p processors satisfies :

  • A.\(E \le p\) and \(s_p \le p\)
  • B.\(E \le 1\) and \(s_p \le p\)
  • C.\(E \le p\) and \(s_p \le 1\)
  • D.\(E \le 1\) and \(s_p \le 1\)

Answer: B

For a multiprocessor with p processors, the speed up cannot exceed the number of processors, so \(s_p \le p\), and the efficiency is the speed up divided by the number of processors, \(E = s_p / p\), so \(E \le 1\). The first option allows an efficiency up to p, which is impossible, the third allows a speed up of at most 1, which would mean no gain from more processors, and the fourth has both bounds too low. Only the second pair, \(E \le 1\) and \(s_p \le p\), is true for every system.

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