INTRODUCTION INTRODUCTION Reza M. Rad Reza M. Rad UMBC UMBC Based on pages 321- Based on pages 321 -356 of 356 of “ “Nanoelectronics Nanoelectronics and and Information Technology” ”, Rainer , Rainer Waser Waser Information Technology
Outline Outline � Fundamental requirements for logic Fundamental requirements for logic � devices devices � Physical limitations of computing Physical limitations of computing � � Physical implementation concepts Physical implementation concepts � � Major aspects of architectures Major aspects of architectures � � Estimations of the performance of Estimations of the performance of � information processing systems information processing systems � The ultimate computer The ultimate computer �
Fundamentals of logic devices Fundamentals of logic devices � Requirements for logic Requirements for logic � devices devices � Logical states must be Logical states must be � mapped to physical mapped to physical properties like voltage properties like voltage amplitude or time of amplitude or time of pulses of a physical pulses of a physical property (fig1) property (fig1)
Fundamentals of logic devices Fundamentals of logic devices � Requirement 1: Non Requirement 1: Non- -linear characteristics linear characteristics � • Required to maintain sufficient signal to noise ratio Required to maintain sufficient signal to noise ratio • even in unlimited chains of gates even in unlimited chains of gates • The output signal intervals are smaller than input The output signal intervals are smaller than input • signal intervals signal intervals • Non Non- -linearity of CMOS gates stems from linearity of CMOS gates stems from • characteristics of MOSFETs MOSFETs characteristics of • In case of neurons, one important non In case of neurons, one important non- -linearity is linearity is • obtained by the threshold function (fig 2), (fig 3- obtained by the threshold function (fig 2), (fig 3 -1) 1)
Fundamentals of logic devices Fundamentals of logic devices � Fig 2 : non Fig 2 : non- -linear linear � characteristic in a logic characteristic in a logic gate gate � Fig 3 : non Fig 3 : non- -linearity in linearity in � CMOS (left) and CMOS (left) and biological neurons biological neurons (right) (right)
Fundamentals of logic devices Fundamentals of logic devices � Requirements for logic devices (cont) Requirements for logic devices (cont) � � Requirement 2: Power amplification Requirement 2: Power amplification � • To maintain signal level in logic chains, power To maintain signal level in logic chains, power • amplification is necessary amplification is necessary • It is not sufficient to have only signal amplification It is not sufficient to have only signal amplification • • Gate output must be able to drive at least two Gate output must be able to drive at least two • inputs inputs
Fundamentals of logic devices Fundamentals of logic devices • CMOS gates not only amplify the voltage but also CMOS gates not only amplify the voltage but also • drive current to charge and discharge the line and drive current to charge and discharge the line and input capacitances input capacitances • In biological neurons power amplification is done In biological neurons power amplification is done • through voltage triggered ion channels through voltage triggered ion channels (electrochemical potential difference) (fig 3- -2) 2) (electrochemical potential difference) (fig 3
Fundamentals of logic devices Fundamentals of logic devices � Requirements for logic devices (cont) Requirements for logic devices (cont) � � Requirement 3: Requirement 3: Concatenability Concatenability � • Input and output signals must be compatible • Input and output signals must be compatible (based on the same physical property and range) (based on the same physical property and range) � Requirement 4: Feedback Prevention Requirement 4: Feedback Prevention � • A directed flow of information is required A directed flow of information is required • • In CMOS feedback prevention is done by In CMOS feedback prevention is done by • MOSFET MOSFET • In biological neurons backward propagation is In biological neurons backward propagation is • prevented due to refractory period of voltage gated prevented due to refractory period of voltage gated Na+ channel Na+ channel
Fundamentals of logic devices Fundamentals of logic devices � Requirement 5: Complete set of Requirement 5: Complete set of boolean boolean � operators operators • A basic set of A basic set of boolean boolean operators is needed to operators is needed to • realize a complete boolean boolean algebra algebra realize a complete • A generic set consists of A generic set consists of “ “OR and NOT OR and NOT” ” or or “ “AND AND • and NOT” ” or NOR or NAND gates or NOR or NAND gates and NOT
Fundamentals of logic devices Fundamentals of logic devices � Dynamic properties of Dynamic properties of � logic gates logic gates � Fall time, rise time, Fall time, rise time, � propagation delay for propagation delay for high and low (fig 4) high and low (fig 4)
Fundamentals of logic devices Fundamentals of logic devices � Threshold gates Threshold gates � � Si Si- -based CMOS gates and biological neurons based CMOS gates and biological neurons � can be linked based on the operation of can be linked based on the operation of threshold gates threshold gates � Threshold gates are the basis of Threshold gates are the basis of � neuromorphic logic logic neuromorphic � Definition: a linear threshold gate is a logic Definition: a linear threshold gate is a logic � device that has n two- -valued inputs x1,x2 , .. , valued inputs x1,x2 , .. , device that has n two xn and a single two and a single two- -valued output y= valued output y= ƒ ƒ(x1,x2, (x1,x2, xn ..,xn xn) ) ..,
Fundamentals of logic devices Fundamentals of logic devices � Threshold gates (cont) Threshold gates (cont) � � ƒ ƒ is determined by weights is determined by weights � w1,w2, .., wn wn and the and the w1,w2, .., threshold value Θ Θ , (fig 5) , (fig 5) threshold value � Every Every boolean boolean function can be function can be � realized by threshold gates realized by threshold gates � AND gate is made by AND gate is made by � w1=w2=..=wn wn=1 and n =1 and n- -1< 1< Θ Θ <n <n w1=w2=..= = Χ − Θ = Χ > Θ Χ < Θ y sign ( ) { 1 if , 0 if } n ∑ Χ = = . , { 0 , 1 } w x x k k k = 1 k
Fundamentals of logic devices Fundamentals of logic devices � Basic advantage of Basic advantage of � threshold logic compared to threshold logic compared to conventional logic: inherent conventional logic: inherent parallel processing due to parallel processing due to internal multiple valued internal multiple valued computation of weighted computation of weighted sum sum � A full A full- -adder is shown in the adder is shown in the � figure (fig 6) figure (fig 6)
Physical limits to computation Physical limits to computation � Three fundamental limits to performance of logic Three fundamental limits to performance of logic � functions: functions: � Thermodynamics Thermodynamics � � Quantum mechanics Quantum mechanics � � Electromagnetism Electromagnetism � � Also a hierarchy of limits given by Also a hierarchy of limits given by materails materails, , � device type, circuit concept .. device type, circuit concept .. � Major limiting parameters: time and energy Major limiting parameters: time and energy �
Physical limits to computation Physical limits to computation � Typically performance limits of a device Typically performance limits of a device � are illustrated in a average power are illustrated in a average power dissipation (Pd) versus average delay (Td) dissipation (Pd) versus average delay (Td) diagram diagram � Average energy during logic operation is Average energy during logic operation is � Wd = Pd.Td Pd.Td Wd =
Physical limits to computation Physical limits to computation � Fundamental limit imposed by thermodynamics is the Fundamental limit imposed by thermodynamics is the � minimum energy required for a binary transition at a given minimum energy required for a binary transition at a given operating temperature: operating temperature: − = ≈ ∗ 21 W k T ln 2 3 10 j / bOP , min TD B (minimum energy dissipated for each bit) (minimum energy dissipated for each bit) The Heisenberg uncertainty principle of quantum The Heisenberg uncertainty principle of quantum � � mechanics imposes a second fundamental limit. Energy of mechanics imposes a second fundamental limit. Energy of a state with life time ∆ ∆ t can only be determined with a t can only be determined with a a state with life time precision of ∆ ∆ W given by : W given by : precision of = ∆ ≥ ∆ W QM W h / t , min
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