EEL 4930 6

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EEL 4930 (6) 5930 (5), Spring 2006Physical
Limits of Computing
http//www.eng.fsu.edu/mpf

• Slides for a course taught byDr. Michael P.
  Frankin the Department of Electrical Computer
  Engineering

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Overview of First Lecture

• Course Introduction
• Moores Law vs. Known Physics
• Mechanics of the course
• Course website
• Books / readings
• Topics schedule
• Assignments grading policies
• misc. other administrivia

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Physical Limits of ComputingIntroductory Lecture

• Moores Law vs. Known Physics

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Moores Law vs. Known Physics

• Outline of mini-lecture
• Moores law and Related Trends
• Status of Known Physics in the Modern Era
• Energy Efficiency and Performance Limits
• New Paradigms for More Efficient Computing
• Future Computing Technologies

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Moores Law

• Moores Law proper
• Trend of doubling of number of transistors per
  integrated circuit every 18 (later 24) months
• First observed by Gordon Moore in 1965 (see
  readings)
• Generalized Moores Law
• Various trends of exponential improvement in many
  aspects of information processing technology
  (both computing communication)
• Storage capacity/cost, clock frequency,
  performance/cost, size/bit, cost/bit,
  energy/operation, bandwidth/cost

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Moores Law (Devices/IC)
Intel µpus
Early Fairchild ICs
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Microprocessor Performance Trends
SourceHennessy Patterson,ComputerArchitectur
eA QuantitativeApproach,3rd
edition.AddedPerformanceanalysis based on
datafrom theITRS 1999roadmap.
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Super-Exponential Long-Term Trend
Ops/second/1,000
Source Kurzweil 99
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Known Physics

• The history of physics has been a story of
• Ever-increasing precision, unity, explanatory
  power
• Modern physics is veryclose to perfection!
• All accessible phenomena are exactly modeled, as
  far as we know, to the limits of experimental
  precision, which is 11 decimal places today.
• However, the story is not quite complete yet
• There is no experimentally verified theory
  unifying GR QM (so far)

String theory? M-theory?Loop quantum gravity?
Other?
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Fundamental Physical Limits of Computing
ImpliedUniversal Facts
Affected Quantities in Information Processing
Thoroughly ConfirmedPhysical Theories
Speed-of-LightLimit
Communications Latency
Theory ofRelativity
Information Capacity
UncertaintyPrinciple
Information Bandwidth
Definitionof Energy
Memory Access Times
QuantumTheory
Reversibility
2nd Law ofThermodynamics
Processing Rate
Adiabatic Theorem
Energy Loss per Operation
Gravity
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Device Size Scaling Trends
Based on ITRS 97-03 roadmaps
(1 µm)
Virus
Protein molecule
Naïve linear extrapolations
Effective gate oxide thickness
DNA/CNT radius
Silicon atom
Hydrogen atom
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Trend of Min. Transistor Switching Energy
Based on ITRS 97-03 roadmaps
fJ
Node numbers(nm DRAM hp)
Practical limit for CMOS?
aJ
Naïve linear extrapolation
zJ
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Implications of Energy Limits

• If the limits on energy dissipation of
  irreversible operations cant possibly be
  circumvented, this implies
• The number of low-level digital operations we can
  perform per unit of energy dissipation is
  limited.
• Digital system performance per unit of power
  consumption is limited.
• This could have deleterious long-term effects,
  including
• Braking of growth in the electronics industry
• Stagnation of the worlds information economy
• Perhaps even an eventual end to all life in the
  universe!
• Therefore, we have some very strong motivations
  for finding ways to circumvent these limits!
• How to accomplish this is a big part of what this
  course is about.

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What is entropy?

• First was characterized by Rudolph Clausius in
  1850.
• Originally was just defined as marginal heat
  temperature.
• Noted to never decrease in thermodynamic
  processes.
• Significance and physical meaning were
  mysterious.
• In 1880s, Ludwig Boltzmann proposed that
  entropy S is the logarithm of a systems number N
  of states, S k ln N
• What we would now call the information capacity
  of a system
• Holds for systems at equilibrium, in
  maximum-entropy state
• The modern understanding that emerged from
  20th-century physics is that entropy is indeed
  the amount of unknown or incompressible
  information in a physical system.
• Important contributions to this understanding
  were made by von Neumann, Shannon, Jaynes, and
  Zurek.

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Von Neumann / Landauer (VNL) bound for bit
erasure

• The von Neumann-Landauer (VNL) lower bound for
  energy dissipation from bit erasure
• First alluded to by John von Neumann in a 1949
  lecture
• Developed more explicitly by Rolf Landauer (IBM)
  in 1961.
• Oblivious erasure/overwriting/forgetting of a
  known logical bit really just moves the
  information that the bit previously contained to
  the environment
• We lose track of that information and so it
  becomes entropy.
• Leads to fundamental limit of kT ln 2 for
  oblivious erasure.
• This particular limit could only possibly be
  avoidable through reversible computing.
• Reversible computing de-computes unwanted bits,
  rather than obliviously erasing them!
• This can avoid entropy generation, enabling the
  signal energy to be preserved for later re-use,
  rather than being dissipated.

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Illustration of VNL Principle

• Either of 2 digital states is initially encoded
  by any of N possible physical microstates
• Illustrated as 4 in this simple example (the real
  number would usually be much larger)
• Initial entropy (given the digital state) S
  Logmicrostates Log 4 2 bits.
• Now, suppose some mechanism resets the digital
  state to 0 regardless of what it was before.
• Reversibility of physics ensures this bit
  erasure operation cant possibly merge two
  microstates, so it must double the number of
  possible microstates in the digital state!
• Entropy S Logmicrostates increases by Log 2
  1 bit (Log e)(ln 2) kB ln 2.
• To prevent entropy from accumulating locally, it
  must be expelled into the environment.

Microstates representinglogical 0
Microstates representinglogical 1
Entropy S log 4 2 bits
Entropy S' log 8 3 bits
Entropy S log 4 2 bits
?S S' - S 3 bits - 2 bits 1 bit
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Reversible Computing

• A reversible digital logic operation is
• Any operation that performs an invertible
  (one-to-one) transformation of the devices local
  digital state space.
• Or at least, of that subset of states that are
  actually used in a design.
• Landauers principle only limits the energy
  dissipation of ordinary irreversible
  (many-to-one) logic operations.
• Reversible logic operations could dissipate much
  less energy,
• Since they can be implemented in a
  thermodynamically reversible way.
• In 1973, Charles Bennett (IBM Research) showed
  how any desired computation can in fact be
  performed using only reversible logic operations
  (with essentially no bit erasure).
• This opened up the possibility of a vastly more
  energy-efficient alternative paradigm for digital
  computation.
• After 30 years of (sporadic) research, this idea
  is finally approaching the realm of practical
  implementability
• Making it happen is the goal of the RevComp
  project.

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How Reversible Logic Avoids the von
Neumann-Landauer Bound

• We arrange our logical manipulations to never
  attempt to merge two distinct digital states,
• but only to reversiblytransform them fromone
  state to another!
• E.g., illustrated is a reversible
  operationcCLR (controlled clear)
• Non-oblivious erasure
• It and its inverse (cSET)enable arbitrary logic!

a blogic 00
logic 01
a0a1
logic 10
logic 11
b0 b1
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Potential Cost-Efficiency Benefits
Scenario 1,000/3-years, 100-Watt conventional
computer, vs. reversible computers w. same
capacity.
100,000
1,000
Best-case reversible computing
Bit-operations per US dollar
Worst-case reversible computing
Conventional irreversible computing
All curves would ?0 if leakage not reduced.