Final answer:
The processor executes 45 × 109 cycles and 22.5 × 109 instructions during the program. After reducing the execution time by 20% and increasing CPI by 25%, the new execution time is 8 seconds and the new CPI is 2.5. To achieve the time reduction, the target clock rate should be 70.313 GHz.
Step-by-step explanation:
To calculate the number of cycles executed by a processor during the program, we use the formula:
Number of cycles = Execution Time (seconds) × Clock Rate (Hz). Given a clock rate of 4.5 GHz (which is 4.5 × 109 Hz) and an execution time of 10 seconds, the number of cycles is 4.5 × 109 cycles/second × 10 seconds = 45 × 109 cycles.
To calculate the number of instructions executed, we use the formula:
Number of Instructions = Number of Cycles / Average CPI (Cycles per Instruction). With an average CPI of 2, the number of instructions is 45 × 109 cycles / 2 CPI = 22.5 × 109 instructions.
Reducing the execution time by 20% results in a new execution time of 80% of the original,
which is 0.80 × 10 seconds = 8 seconds. If the CPI increases by 25%, the new CPI is 2 CPI × 1.25 = 2.5 CPI.
To maintain the reduced execution time with the increased CPI, the target clock rate can be computed using the formula: Target Clock Rate = (Number of Instructions × Average CPI) / New Execution Time.
Substituting the values, we get Target Clock Rate = (22.5 × 109 instructions × 2.5 CPI) / 8 seconds = 70.3125 GHz, which when rounded to three decimal places is 70.313 GHz.