Andrew S. Tanenbaum (OS) Edition 4 Exercise 5 Question 53 (Page No. 434)

Question

If a CPU’s maximum voltage, $V,$ is cut to $V/n,$ its power consumption drops to $1/n^{2}$ of its original value and its clock speed drops to $1/n$ of its original value. Suppose that a user is typing at $1\: char/sec,$ but the CPU time required to process each character is $100\: msec.$ What is the optimal value of $n$ and what is the corresponding energy saving in percent compared to not cutting the voltage? Assume that an idle CPU consumes no energy at all.

Answer 1

CPU can can process one character $=100\;\text{msec}$

User's typing speed$=1\;\frac{\text{char}}{\text{sec}}$

CPU clock speed $= \frac{1\;\text{sec}}{100\;\text{msec}} = \frac{1}{10}^{\mathrm {th}}$ original value.

$\Rightarrow$ Optimal Value $\mathrm n = 100$

E  is the energy consumed in $1$ sec.

$\therefore$ It will run at full speed for $100\;\text{msec}$ and does idle for $900\;\text{msec}$ and use $\frac{\mathbf E}{10} $

Running for $\frac{1}{10}^{\mathrm th}$ for full second, it will use $\frac{\mathbf E}{100}$

Saving $= \frac{9\mathbf E}{100}$

$\therefore$ Percentage saving $=90\%$