Final answer:
The processor executes 20 billion cycles and 10 billion instructions during the program. Reducing the execution time by 40% results in a new execution time of 6 seconds and a new CPI of 3. The target clock rate to achieve this time reduction is approximately 1.11 GHz.
Step-by-step explanation:
To determine the number of cycles executed by the processor during the program, we can use the following calculation:
- Number of cycles = Execution Time (seconds) × Clock Rate (hz)
- Number of cycles = 10 seconds × 2 GHz (or 2 × 109 hertz)
- Number of cycles = 20 × 109 cycles = 20 billion cycles
The number of instructions executed by this processor during the program is calculated as follows:
- Number of instructions = Number of cycles / Average CPI
- Number of instructions = 20 × 109 cycles / 2
- Number of instructions = 10 × 109 instructions = 10 billion instructions
To find the new execution time after reducing it by 40%, we do the following:
- New execution time = Original execution time × (1 - Reduction percentage)
- New execution time = 10 seconds × (1 - 0.40)
- New execution time = 10 seconds × 0.60 = 6 seconds
The new CPI after a 50% increase is calculated thusly:
- New CPI = Original CPI × (1 + Increase percentage)
- New CPI = 2 × (1 + 0.50)
- New CPI = 2 × 1.50 = 3
The target clock rate to achieve a 40% reduction in execution time with the new CPI is found by rearranging the formula for execution time:
- Execution Time = (Number of cycles / Clock Rate) × CPI
- Therefore, Clock Rate = Number of cycles / (Execution Time × CPI)
- Target Clock Rate = 20 × 109 cycles / (6 seconds × 3)
- Target Clock Rate = 20 × 109 cycles / 18 seconds
- Target Clock Rate = 1.11... × 109 hertz or approximately 1.11 GHz