cash flow

Question

cash flow

Anu Bhardwaj · Accepted Answer

Clock Rates: Computer X: 2.5 GHz Computer Y: 3 GHz Calculations: a) Average CPI of both machines To find the average CPI, use the formula: Average CPI = ∑ ( CPI × Instruction Mix ) 	ext{Average CPI} = \sum (	ext{CPI} 	imes 	ext{Instruction Mix}) Average CPI = ∑ ( CPI × Instruction Mix ) For Computer X: Average CPI X = ( 2 × 0.15 ) + ( 5 × 0.25 ) + ( 1 × 0.20 ) + ( 24 × 0.40 ) 	ext{Average CPI}_X = (2 	imes 0.15) + (5 	imes 0.25) + (1 	imes 0.20) + (24 	imes 0.40) Average CPI X ​ = ( 2 × 0.15 ) + ( 5 × 0.25 ) + ( 1 × 0.20 ) + ( 24 × 0.40 ) For Computer Y: Average CPI Y = ( 5 × 0.20 ) + ( 1 × 0.30 ) + ( 3 × 0.15 ) + ( 1 × 0.35 ) 	ext{Average CPI}_Y = (5 	imes 0.20) + (1 	imes 0.30) + (3 	imes 0.15) + (1 	imes 0.35) Average CPI Y ​ = ( 5 × 0.20 ) + ( 1 × 0.30 ) + ( 3 × 0.15 ) + ( 1 × 0.35 ) b) Which machine is faster based on: i) Execution Time Execution Time = (Instruction Count) × (CPI) / (Clock Rate) To compare execution time, use the formula for both computers and then compare. ii) MIP rate MIP rate (Million Instructions Per Second) = Clock Rate / (Average CPI) Detailed Solutions: a) Average CPI Calculation: For Computer X: Average CPI X = ( 2 × 0.15 ) + ( 5 × 0.25 ) + ( 1 × 0.20 ) + ( 24 × 0.40 ) 	ext{Average CPI}_X = (2 	imes 0.15) + (5 	imes 0.25) + (1 	imes 0.20) + (24 	imes 0.40)   Average CPI X = 0.30 + 1.25 + 0.20 + 9.60 Average CPI X = 11.35 	ext{Average CPI}_X = 11.35 Average CPI X ​ = 11.35 For Computer Y: Average CPI Y = ( 5 × 0.20 ) + ( 1 × 0.30 ) + ( 3 × 0.15 ) + ( 1 × 0.35 ) Average CPI Y = 1.00 + 0.30 + 0.45 + 0.35 	ext{Average CPI}_Y = 1.00 + 0.30 + 0.45 + 0.35   Average CPI Y = 2.10 b) Execution Time and MIP rate: For Computer X: Clock Rate = 2.5 GHz = 2.5 × 10^9 cycles/second For Computer Y: Clock Rate = 3 GHz = 3 × 10^9 cycles/second Using the formula: Execution Time = Instruction Count × CPI Clock Rate 	ext{Execution Time} = \frac{	ext{Instruction Count} 	imes 	ext{CPI}}{	ext{Clock Rate}} Execution Time = Clock Rate Instruction Count × CPI ​ Calculate the execution time for both computers and compare. For MIP rate: MIP rate = Clock Rate Average CPI 	ext{MIP rate} = \frac{	ext{Clock Rate}}{	ext{Average CPI}} MIP rate = Average CPI Clock Rate ​ Compare the MIP rate for both computers. a) Average CPI Calculation: For Computer X: Average CPI X = ( 2 × 0.15 ) + ( 5 × 0.25 ) + ( 1 × 0.20 ) + ( 24 × 0.40 ) 	ext{Average CPI}_X = (2 	imes 0.15) + (5 	imes 0.25) + (1 	imes 0.20) + (24 	imes 0.40) Average CPI X ​ = ( 2 × 0.15 ) + ( 5 × 0.25 ) + ( 1 × 0.20 ) + ( 24 × 0.40 ) Average CPI X = 0.30 + 1.25 + 0.20 + 9.60 	ext{Average CPI}_X = 0.30 + 1.25 + 0.20 + 9.60 Average CPI X ​ = 0.30 + 1.25 + 0.20 + 9.60 Average CPI X = 11.35 	ext{Average CPI}_X = 11.35 Average CPI X ​ = 11.35 For Computer Y: Average CPI Y = ( 5 × 0.20 ) + ( 1 × 0.30 ) + ( 3 × 0.15 ) + ( 1 × 0.35 ) 	ext{Average CPI}_Y = (5 	imes 0.20) + (1 	imes 0.30) + (3 	imes 0.15) + (1 	imes 0.35) Average CPI Y ​ = ( 5 × 0.20 ) + ( 1 × 0.30 ) + ( 3 × 0.15 ) + ( 1 × 0.35 ) Average CPI Y = 1.00 + 0.30 + 0.45 + 0.35 	ext{Average CPI}_Y = 1.00 + 0.30 + 0.45 + 0.35 Average CPI Y ​ = 1.00 + 0.30 + 0.45 + 0.35 Average CPI Y = 2.10 	ext{Average CPI}_Y = 2.10 Average CPI Y ​ = 2.10 b) Which machine is faster based on: i) Execution Time Execution Time = (Instruction Count) × (CPI) / (Clock Rate) Calculate the execution time for both computers for each instruction type and sum them up to get the total execution time. For Computer X: Clock Rate X = 2.5 × 1 0 9  cycles/second 	ext{Clock Rate}_X = 2.5 	imes 10^9 	ext{ cycles/second} Clock Rate X ​ = 2.5 × 1 0 9  cycles/second Execution Time X = ( 9 × 1 0 9 × 2 2.5 × 1 0 9 ) + ( 15 × 1 0 9 × 5 2.5 × 1 0 9 ) + ( 12 × 1 0 9 × 1 2.5 × 1 0 9 ) + ( 24 × 1 0 9 × 24 2.5 × 1 0 9 ) 	ext{Execution Time}_X = \left(\frac{9 	imes 10^9 	imes 2}{2.5 	imes 10^9}ight) + \left(\frac{15 	imes 10^9 	imes 5}{2.5 	imes 10^9}ight) + \left(\frac{12 	imes 10^9 	imes 1}{2.5 	imes 10^9}ight) + \left(\frac{24 	imes 10^9 	imes 24}{2.5 	imes 10^9}ight) Execution Time X ​ = ( 2.5 × 1 0 9 9 × 1 0 9 × 2 ​ ) + ( 2.5 × 1 0 9 15 × 1 0 9 × 5 ​ ) + ( 2.5 × 1 0 9 12 × 1 0 9 × 1 ​ ) + ( 2.5 × 1 0 9 24 × 1 0 9 × 24 ​ ) Execution Time X = ( 18 × 1 0 9 2.5 × 1 0 9 ) + ( 75 × 1 0 9 2.5 × 1 0 9 ) + ( 12 × 1 0 9 2.5 × 1 0 9 ) + ( 576 × 1 0 9 2.5 × 1 0 9 ) 	ext{Execution Time}_X = \left(\frac{18 	imes 10^9}{2.5 	imes 10^9}ight) + \left(\frac{75 	imes 10^9}{2.5 	imes 10^9}ight) + \left(\frac{12 	imes 10^9}{2.5 	imes 10^9}ight) + \left(\frac{576 	imes 10^9}{2.5 	imes 10^9}ight) Execution Time X ​ = ( 2.5 × 1 0 9 18 × 1 0 9 ​ ) + ( 2.5 × 1 0 9 75 × 1 0 9 ​ ) + ( 2.5 × 1 0 9 12 × 1 0 9 ​ ) + ( 2.5 × 1 0 9 576 × 1 0 9 ​ ) Execution&nbsp

AI tools

Study help

Free tools

Earn & more

Accounting

Accounting

Anu Bhardwaj

Answer

Extracted Transcript from Images

AI

Study help

Earn & more

Company