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Q31). Consider a pipeline "x" consist of $5$ stages names as $IF$,$ID$,$OF$,$EX$ and $WB$ with the respective stage delays of $2 \text{ns}$ ,$5 \text{ns}$, $6 \text{ns}$ and $1 \text{ns}$ .The alternative pipeline "y" contains  the same number of stages but $EX$ stage is divided into $4$ sub stages, $(EX1,EX2,EX3 \ and \ EX4)$ with equal delay i.e. $(8 ns/4)$ and $ID$ stage is divided into $2$ substages $(ID1 \ and \  ID2)$ with equal delays of $(5 ns/2)$. In the pipeline 'x' and 'y' memory reference instructions are not overlapped so the penalty of memory reference instructions in the pipeline'x' is $4 \ \text{cycles}$ and in the pipeline 'y' is $8 \ \text{cycles}$.If the program contains $30 \%$ of the instructions which are memory based instructions, the speedup ratio of 'x' is speedup ratio of 'y' is _______

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Speedup S1=Twp1/Tp

Twp1=22ns

Tp1=0.30 x 4 x 8 + 0.70 x 8 x 1

S1=22/15.2=1.45

Similarly for S2

S2=Twp2/Tp2

S2=22ns/0.3 x 8 x 8 + 0.70 x 8 x 1=0.88

ratio=1.45/0.88=1.65

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