Question

Consider three different processors, P1 P2 and P3, executing the same instruction set. P1 has a 3 GHz clock rate and a CPI of 1.5. P2 has a 2.5 GHz clock rate and a CPI of 1.0. P3 has a 4.0 GHz clock rate and a CPI of 2.2.
a) Which processor has the highest performance expressed in instructions per second? ​

Answer 1

$First,\ we\ must\ find\ Instruction\ Per\ Second\ (IPS) \ to\ compare\ the\ CPUs,$

             $So\ by\ the\ formula,$

                                        $\[CPU\ time=\ \frac{instructions\ \times CPI}{Clock\ rate}$                                      

                          $Therefore,$

                                              $\[\frac{instructions}{CPU\ time}=\frac{clock\ rate}{CPI}\]$

                                    $And,$

                                                $\[IPS=\frac{instructions}{CPU\ time}\]$

                                      $So,$

                                                 $\[IPS=\ \frac{clock\ rate}{CPI}\]$

           $Since,$ $1\ GHz =\ {10}^9Hz,$

                                 $\[{IPS}_1=\ \frac{{clock\ rate}_1}{{CPI}_1}=\frac{3\ Ghz}{1.5}=2\times {10}^9\]$

                               $\[{IPS}_2=\ \frac{{clock\ rate}_2}{{CPI}_2}=\frac{2.5\ Ghz}{1}=2.5\times {10}^9\]$

                               $\[{IPS}_3=\ \frac{{clock\ rate}_3}{{CPI}_3}=\frac{4\ Ghz}{2.2} = 1.82\times {10}^9\]$

$Hence, \ processor\ 2\ (P2) \ has\ the\ highest\ performance\ of\ all.$