# 2.7 Module 8: instruction pipelining  (Page 2/3)

 Page 2 / 3

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

• The total time required ${T}_{k}$ to execute all n instruction is:

${T}_{k}$ = [k + (n-1)]

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

${S}_{K}=\frac{{T}_{1}}{{T}_{K}}=\frac{\text{nk}\tau }{\left[k+\left(n-1\right)\right]\tau }=\frac{\text{nk}}{k+\left(n-1\right)}$

• 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

what is motion?
where the solving of questions of this topic?
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.
I need chapter 25 last topic
What is physics?
Abdulaziz
physics is the study of matter and energy in space and time and how they related to each other
Manzoor
interaction of matter and eneegy....
Abdullah
thanks for correcting me bro
Manzoor
What is electrostatics bassically?
study of charge at rest
wamis
A branch in physics that deals with statics electricity
Akona
what is PN junction?
Manzoor
please I don't understand the solution of the first example as in d working
what's the question? Write it here.
SABYASACHI
a cold body of 100°C and a hot body is of 100°F . Transfer heat = ?
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?
what is emotion?
Abdulaziz
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.
are you talking about the capacitance combination problem
sam
please write the problem or send a snap of th page....I don't have the book in my vicinity.
SABYASACHI
yes, the 2nd example called Network of Capacitors on page 3/3 of section 8.2.
Anita
12 V = (Q1/12uF)+(Q1/6uF). So, Q1 = 12x4 = 48 uC.
sam
ohhhh OK thanks so much!!!!!!!
Anita
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
Elia
what is electromagnetic force. do electric and magnetic force happen differently
yes
yes
Pranay
why
Godson
how?
Godson
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
Ilyas
Yes
Akona
derived the electric potential due to disk of charge
how can we derived potential electric due to the disk
aron
how can you derived electric potential of a disk
aron
how can you derived electric potential due to disk
aron
where is response?
aron
what is difference between heat and temperature?
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.
SABYASACHI
Heat is the reason and temperature is the consequences
Angela
how many liquid metals do we have
do we have gasses as metals
Jeffery
who knows should please tell us
yes...gallium & cesium
Idris
Hg is liquid. No metal gasses at standard temp and pressure
Shane
I don't ever understand any of this formulae
which formula
How to determine a temperature scale
what is the formula for absolute error
Nyro
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