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Step 1: 1.1. Processor Performance The performance of a processor in terms of throughput (instructions per second) is given by: Throughput = Clock Rate CPI Throughput = CPI Clock Rate ​ Using the given data: For P1: Throughput = 1.5 GHz 1.5 = 1 G instructions/sec Throughput = 1.5 1.5 GHz ​ = 1 G instructions/sec For P2: Throughput = 2.5 GHz 1.25 = 2 G instructions/sec Throughput = 1.25 2.5 GHz ​ = 2 G instructions/sec For P3: Throughput = 3.0 GHz 5.0 = 0.6 G instructions/sec Throughput = 5.0 3.0 GHz ​ = 0.6 G instructions/sec Explanation: Processor P2 has the highest performance with a throughput of 2 G instructions/second. Step 2: 1.2. Total Number of Cycles and Instructions Given each processor executes program PR in 12 seconds, we need to find the total number of cycles and the total number of instructions for each processor. Total number of cycles ( Total Cycles Total Cycles ) can be calculated as: Total Cycles = Clock Rate × Execution Time Total Cycles = Clock Rate × Execution Time Total number of instructions ( Total Instructions Total Instructions ) can be calculated as: Total Instructions = Total Cycles CPI Total Instructions = CPI Total Cycles ​ For each processor: For P1: Total Cycles = 1.5 GHz × 12 s = 18 × 1 0 9 cycles Total Cycles = 1.5 GHz × 12 s = 18 × 1 0 9 cycles Total Instructions = 18 × 1 0 9 1.5 = 12 × 1 0 9 instructions Total Instructions = 1.5 18 × 1 0 9 ​ = 12 × 1 0 9 instructions For P2: Total Cycles = 2.5 GHz × 12 s = 30 × 1 0 9 cycles Total Cycles = 2.5 GHz × 12 s = 30 × 1 0 9 cycles Total Instructions = 30 × 1 0 9 1.25 = 24 × 1 0 9 instructions Total Instructions = 1.25 30 × 1 0 9 ​ = 24 × 1 0 9 instructions For P3: Total Cycles = 3.0 GHz × 12 s = 36 × 1 0 9 cycles Total Cycles = 3.0 GHz × 12 s = 36 × 1 0 9 cycles Total Instructions = 36 × 1 0 9 5.0 = 7.2 × 1 0 9 instructions Total Instructions = 5.0 36 × 1 0 9 ​ = 7.2 × 1 0 9 instructions Explanation: P1: Total Cycles = 18 billion, Total Instructions = 12 billion P2: Total Cycles = 30 billion, Total Instructions = 24 billion P3: Total Cycles = 36 billion, Total Instructions = 7.2 billion Step 3: 1.3. New Clock Rates If reducing program PR’s executing time by 40% leads to a 30% increase in the average CPI, we need to find the new clock rates for each processor. New execution time: New Execution Time = 12 s × ( 1 − 0.40 ) = 7.2 s New Execution Time = 12 s × ( 1 − 0.40 ) = 7.2 s New CPI for each processor (30% increase): New CPI = Original CPI × 1.30 New CPI = Original CPI × 1.30 For each processor: For P1: New CPI = 1.5 × 1.30 = 1.95 New CPI = 1.5 × 1.30 = 1.95 Total Instructions = 12 × 1 0 9 instructions (remains same) Total Instructions = 12 × 1 0 9 instructions (remains same) Total Cycles = Total Instructions × New CPI = 12 × 1 0 9 × 1.95 = 23.4 × 1 0 9 cycles Total Cycles = Total Instructions × New CPI = 12 × 1 0 9 × 1.95 = 23.4 × 1 0 9 cycles New Clock Rate = Total Cycles New Execution Time = 23.4 × 1 0 9 7.2 s = 3.25 GHz New Clock Rate = New Execution Time Total Cycles ​ = 7.2 s 23.4 × 1 0 9 ​ = 3.25 GHz For P2: New CPI = 1.25 × 1.30 = 1.625 New CPI = 1.25 × 1.30 = 1.625 Total Instructions = 24 × 1 0 9 instructions (remains same) Total Instructions = 24 × 1 0 9 instructions (remains same) Total Cycles = Total Instructions × New CPI = 24 × 1 0 9 × 1.625 = 39 × 1 0 9 cycles Total Cycles = Total Instructions × New CPI = 24 × 1 0 9 × 1.625 = 39 × 1 0 9 cycles New Clock Rate = Total Cycles New Execution Time = 39 × 1 0 9 7.2 s = 5.42 GHz New Clock Rate = New Execution Time Total Cycles ​ = 7.2 s 39 × 1 0 9 ​ = 5.42 GHz For P3: New CPI = 5.0 × 1.30 = 6.5 New CPI = 5.0 × 1.30 = 6.5 Total Instructions = 7.2 × 1 0 9 instructions (remains same) Total Instructions = 7.2 × 1 0 9 instructions (remains same) Total Cycles = Total Instructions × New CPI = 7.2 × 1 0 9 × 6.5 = 46.8 × 1 0 9 cycles Total Cycles = Total Instructions × New CPI = 7.2 × 1 0 9 × 6.5 = 46.8 × 1 0 9 cycles New Clock Rate = Total Cycles New Execution Time = 46.8 × 1 0 9 7.2 s = 6.5 GHz New Clock Rate = New Execution Time Total Cycles ​ = 7.2 s 46.8 × 1 0 9 ​ = 6.5 GHz Explanation: P1: New Clock Rate = 3.25 GHz P2: New Clock Rate = 5.42 GHz P3: New Clock Rate = 6.5 GHz

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