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Program X has the following characteristics:

- 20% of the instructions are memory operations;
- 50% of the instructions are performing integer calculations;
- 30% of the instructions are performing floating-point calculations.

Program X is compiled and run on machine A with the following characteristics:

- CPI of memory operations = 2;
- CPI of integer operations = 1;
- CPI of floating-point operations = 4.

- Calculate the average CPI of the program X.
- Calculate the CPU time of program X if X has 150 million instructions and machine A has a 200 MHz processor.

Now assume that a floating-point co-processor has been added to the system, and the CPI of floating-point operations is reduced to 2. Next:

- Calculate the performance improvement (in percentages) of the floating-point operations.
- Calculate the performance improvement (in percentages) of program X.
- What is the clock rate required in order for the system to execute program X without the float-point co-processor and achieve the same performance?

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