HW

$1-$ A given program runs in $10sec$ on computer $A,$ which has a $100MHz$ clock. We are trying to help a computer designer build a computer $B,$ that will run this program in $6sec.$ The designer has determined that a substantial increase in the clock rate is possible, but this increase will affect the rest of the CPU design, causing computer B to require $1\mathrm{.}2$ times as many clock cycles as computer A for this program. What clock rate should we tell the designer to target

$2-$ Suppose we have $2$ implementations of the same instruction set architecture. Computer A has a clock cycle time of $10nsec$ and a CPI of $2\mathrm{.}0$ for some program, and computer B has a clock cycle time of $20nsec$ and $\frac{C}{P}$I of $1\mathrm{.}2$ for the same program. Which machine is faster for this program

$3-$ Use Amdahl's Law states doubling the speed of floating$-$point operations sounds like a great idea. But if only $10\%$ of the program execution time $T$ involves floating$-$point code, then the overall performance improves by just $5\%.$

$4-$ Suppose a program runs in $200$ seconds on a machine, with multiply responsible for $80$ seconds of this time. How much do we have to improve the speed of multiplication if we want the program to run $4$ times faster?

How about making the program $10$ times faster?