Question

Suppose we have developed new versions of a processor with the following characteristics: Version Voltage 1.5 V 1.2V Clock rate 2.4 GHz 3GHZ a) How much has the capacitive load varied between versions if the dynamic power has been reduced by 15%? Assuming that the capacitive load of version 2 is 70% the capacitive load of version 1, find the new voltage value for version 2 if the dynamic power of version 2 is reduced by 35% from version 1. Assuming you run a certain benchmark program on version 1 and 30% of the execution time is consumed on ALU instructions, how much improvement can be achieved in the execution time if the ALU unit was enhanced by a factor of 2? b) c) d) Assuming you run a certain benchmark program on version 1 and 30% of the execution time is consumed on ALU instructions, Can the ALU unit by enhanced for an overall 1.5x improvement? Why?

Answer 1

A) Dynamic power = capacitance x voltage² x frequency

for version 1

let capacitance be C

Dynamic power0 = C x (1.5) ^ 2 x 2.4 = 5.4 C

FOr version 2

let capacitance be C1

Dynamic power1 = C1 x (1.2) ^ 2 x 3 = 4.32C1

We know that Dynamic power1 is 15 % less than Dynamic power0

so Dynamic power1 = 0.85 x Dynamic power0

    4.32C1 = 5.4 C

   C1 = 5.4 / 4.32 C = 1.25

B)

Let Capacitance of version 1 will be C1

let capacitance of version2 C2

we know C2 = 0.7 x C1

let Dynamic power of version 1 = Dp1

Dynamic power of version 2 = Dp2

Dp2 = 0.65xDp1

C2 x V2² x frequency = 0.65 x (C1 x V1² x frequency1)

0.7x C1 x V2² x 3 = 0.65 x C1 x 1.5 ^ 2 x 2.4

V2 = 1.29 volt

C)

According to amdahl's law

speedup achieved =

(1 - fraction enchanced)fraction enchanced speedup enhance

fraction enhanced = 30 %

speedup enhanced = 2

speed up achieved = = 1.33

(1-0.30)+00

D)

According to amdahl's law

speedup achieved =

(1 - fraction enchanced)fraction enchanced speedup enhance

fraction enhanced = 30 %

speedup required = 1.5

speedup enhanced = ?

1.5 .30 (1-0.30) + speedup enhanced

speed up enhanced = 4.5

so we need to improve the alu 4.5 times to get 1.5x system wide speedup