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73 votes
73 votes
The stage delays in a $4$-stage pipeline are $800, 500, 400$ and $300$ picoseconds. The first stage (with delay $800$ picoseconds) is replaced with a functionality equivalent design involving two stages with respective delays $600$ and $350$ picoseconds. The throughput increase of the pipeline is ___________ percent.
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Best answer
140 votes
140 votes
In pipeline ideally  $CPI=1$
So in $1$ cycle $1$ instruction gets completed
Throughput is instructions in unit time
In pipeline $1,$ cycle time$=$ max stage delay $=800\  \text{psec}$
In $800\ \text{psec},$ we expect to finish $1$ instruction
So, in $1\;\text{ps},$   $\dfrac{1}{800}$  instructions are expected to be completed, which is also the throughput for pipeline $1.$

Similarly pipeline $2,$ throughput$=\dfrac{1}{600}$
Throughput increase in percentage

$=\dfrac{\text{new-old} }{\text{old}}\times100$

$= \dfrac{\dfrac{1}{600}-\dfrac{1}{800}}{\dfrac{1}{800} }\times 100$

$=\dfrac{200}{600}\times 100$

$=33.33 \%$
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48 votes
48 votes

Maximum throughput of a Pipeline i.e in best case without any stalls is equal to Clock Frequency of the pipeline

In first case Clock cycle time $=\text{Max Stage Delay = Max(800,500,400 and 300)} = 800.$

So clock Frequency $=\dfrac{1}{800}$ (Ignore the units as we have to calculate percentage only)

In Second Case Clock cycle time $= \text{Max(600,350,500,400 and 300)} = 600.$

So clock Frequency $=\dfrac{1}{600}.$

Percentage increase in throughput of pipeline $=\text{percentage in Clock Frequency}$

$=\dfrac{\left(\dfrac{1}{600}-\dfrac{1}{800}\right)}{\dfrac{1}{800}}\times 100 = 33.33\%$

9 votes
9 votes

33.33 % increase

initial through put is 1 instruction for 3200 pico seconds  

Reason : 4*800  ( here 800 is maximum stage delay of any stage in an instruction so its selected as syncronous clock cycle time )

in the next design 

through put will be 1 instruction for 2400 pico seconds 

reason : 4*600 ( here 600 is maximum stage delay of any stage in an instuction so its selected as syncronous clock cycle time) 

now increase in throughput is caluclated by ((1/2400)-(1/3200))/(1/3200)*100

now there is an assumption that the pipeline used is syncronous because if assyncronous is used the through put is droped but not increased

7 votes
7 votes
Speed up = 800/600 = 1.3333
For %, just multiply 100,   133.33
So increase in thoughput is 33.33% (Ans)
Answer:

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