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In general, the time delay d is equivalent to a clock pulse and T m size 12{T rSub { size 8{m} } } {} >>d. Suppose that n instruction are processed with no branched.

  • The total time required T k size 12{T rSub { size 8{k} } } {} to execute all n instruction is:

T k size 12{T rSub { size 8{k} } } {} = [k + (n-1)]

  • The speedup factor for the instruction pipeline compared to execution without the pipeline is defined as:

S K = T 1 T K = nk τ k + ( n 1 ) τ = nk k + ( n 1 ) size 12{ { size 24{S} } rSub { size 8{K} } = { { { size 24{T} } rSub { size 8{1} } } over { { size 24{T} } rSub { size 8{K} } } } = { { ital "nk"τ} over { left [k+ \( n - 1 \) right ]τ} } = { { ital "nk"} over {k+ \( n - 1 \) } } } {}

  • An ideal pipeline divides a task into k independent sequential subtasks

– Each subtask requires 1 time unit to complete

– The task itself then requires k time units tocomplete. For n iterations of the task, the execution times will be:

– With no pipelining: nk time units

– With pipelining: k + (n-1) time units

Speedup of a k-stage pipeline is thus

S = nk / [k+(n-1)] ==>k (for large n)

2.2 pipeline limitations

Several factors serve to limit the pipeline performance. If the six stage are not of equal duration, there will be some waiting involved at various pipeline stage. Another difficulty is the condition branch instruction or the unpredictable event is an interrupt. Other problem arise that the memory conflicts could occur. So the system must contain logic to account for the type of conflict.

  • Pipeline depth

- Data dependencies also factor into the effective length of pipelines

- Logic to handle memory and register use and to control the overall pipeline increases significantly with increasing pipeline depth

– If the speedup is based on the number of stages, why not build lots of stages?

– Each stage uses latches at its input (output) to buffer the next set of inputs

+ If the stage granularity is reduced too much, the latches and their control become a significant hardware overhead

+ Also suffer a time overhead in the propagation time through the latches

- Limits the rate at which data can be clocked through the pipeline

  • Data dependencies

– Pipelining must insure that computed results are the same as if computation was performed in strict sequential order

– With multiple stages, two instructions “in execution” in the pipeline may have data dependencies. So we must design the pipeline to prevent this.

– Data dependency examples:

A = B + C

D = E + A

C = G x H

A = D / H

Data dependencies limit when an instruction can be input to the pipeline.

  • Branching

One of the major problems in designing an instruction pipeline is assuring a steady flow of instructions to initial stages of the pipeline. However, 15-20% of instructions in an assembly-level stream are (conditional) branches. Of these, 60-70% take the branch to a target address. Until the instruction is actually executed, it is impossible to determin whether the branch will be taken or not.

- Impact of the branch is that pipeline never really operates at its full capacity.

– The average time to complete a pipelined instruction becomes

Tave =(1-pb)1 + pb[pt(1+b) + (1-pt)1]

– A number of techniques can be used to minimize the impact of the branch instruction (the branch penalty).

- A several approaches have been taken for dealing with conditional branches:

+ Multiple streams

+ Prefetch branch target

+ Loop buffer

Questions & Answers

what is motion?
Abdulaziz Reply
where the solving of questions of this topic?
Bonifasi Reply
According to Nernst's distribution law there are about two solvents in which solutes undergo equilibria. But i don't understand how can you know which of two solvents goes bottom and one top? I real want to understand b'coz some books do say why they prefer one to top/bottom.
Elia Reply
I need chapter 25 last topic
Hafsa Reply
What is physics?
physics is the study of matter and energy in space and time and how they related to each other
interaction of matter and eneegy....
thanks for correcting me bro
What is electrostatics bassically?
Ehtisham Reply
study of charge at rest
A branch in physics that deals with statics electricity
what is PN junction?
please I don't understand the solution of the first example as in d working
habila Reply
what's the question? Write it here.
a cold body of 100°C and a hot body is of 100°F . Transfer heat = ?
jagan Reply
you are given two metal spheres mounted on portable insulating support. Find a way to give them equal and opposite charges. you may use a glass rod rubbed with silk but may not touch it to the spheres. Do the spheres have to be of equal size for your method to work?
Rai Reply
what is emotion?
in the 2nd example, for chapter 8.2 on page 3/3, I don't understand where the value 48uC comes from, I just couldn't get that value in my calculator.
Anita Reply
are you talking about the capacitance combination problem
please write the problem or send a snap of th page....I don't have the book in my vicinity.
yes, the 2nd example called Network of Capacitors on page 3/3 of section 8.2.
12 V = (Q1/12uF)+(Q1/6uF). So, Q1 = 12x4 = 48 uC.
ohhhh OK thanks so much!!!!!!!
hello guys,, I'm asking to know something about, How can i know which solvent goes down and which does up in determination of partion coefficient(Nernst's distribution law). Please Need help because i have seen many contradictions via few of text books even some videos on youtube they don't say
what is electromagnetic force. do electric and magnetic force happen differently
Short Reply
when electric charge exert force on another electric charge then this force is known as electrostatic force and when a magnet exert force on another magnet then this force is known as magnetic force and when force exerted on magnet due to varying electric field then this electromagnetic force
derived the electric potential due to disk of charge
aron Reply
how can we derived potential electric due to the disk
how can you derived electric potential of a disk
how can you derived electric potential due to disk
where is response?
what is difference between heat and temperature?
Qasim Reply
temperature is the measure of degree of hotness or coldness. on the other hand, heat is the form of energy, which causes temperature. So we can safely say, heat is the reason and temperature is its consequence.
Heat is the reason and temperature is the consequences
how many liquid metals do we have
Jeffery Reply
do we have gasses as metals
who knows should please tell us
yes...gallium & cesium
Hg is liquid. No metal gasses at standard temp and pressure
I don't ever understand any of this formulae
isaac Reply
which formula
How to determine a temperature scale
Masia Reply
what is the formula for absolute error
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Source:  OpenStax, Computer architecture. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10761/1.1
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