csv881: low-power design gate-level power optimization

Copyright Agrawal, 2011Copyright Agrawal, 2011 Lectures 10, 11, 12: Gate-level optimizationLectures 10, 11, 12: Gate-level optimization 11

CSV881: Low-Power DesignCSV881: Low-Power Design

Gate-Level Power Optimization Gate-Level Power Optimization

Vishwani D. AgrawalVishwani D. AgrawalJames J. Danaher ProfessorJames J. Danaher Professor

Dept. of Electrical and Computer EngineeringDept. of Electrical and Computer EngineeringAuburn University, Auburn, AL 36849Auburn University, Auburn, AL 36849

[email protected]://www.eng.auburn.edu/~vagrawal


Components of PowerComponents of PowerDynamicDynamic

Signal transitionsSignal transitionsLogic activityGlitches

Short-circuit (often neglected)Short-circuit (often neglected)StaticStatic

LeakageLeakage


Power of a TransitionPower of a Transition

VVDDDD

GroundGround

CL

R

R

Dynamic Power

= CLVDD2/2 + Psc

Vi

Vo

isc


Dynamic PowerDynamic PowerEach transition of a gate consumes Each transition of a gate consumes CV CV 22/2./2.Methods of power saving:Methods of power saving:

Minimize load capacitancesMinimize load capacitancesTransistor sizingLibrary-based gate selection

Reduce transitionsReduce transitionsLogic designGlitch reduction


Glitch Power ReductionGlitch Power Reduction Design a digital circuit for minimum transient Design a digital circuit for minimum transient

energy consumption by eliminating hazardsenergy consumption by eliminating hazards


Theorem 1Theorem 1 For correct operation with minimum energy For correct operation with minimum energy

consumption, a Boolean gate must produce consumption, a Boolean gate must produce no more than no more than oneone event per transition. event per transition.

Output logic state changesOne transition is necessary

Output logic state unchangedNo transition is necessary


Event PropagationEvent Propagation

2 4 61

1 3

5

3

10

0

0

2

2

Path P1

P2

Path P3

Single lumped inertial delay modeled for each gatePI transitions assumed to occur without time skew


Inertial Delay of an InverterInertial Delay of an Inverter

dHL dLH

dHL+dLH

d = ──── 2

Vin

Vout

time


Multi-Input GateMulti-Input Gate

Delay d < DPD

A

B

C

A

B

C d d Hazard or glitch

DPD

DPD: Differential path delay


Balanced Path DelaysBalanced Path Delays

Delayd < DPD

A

B

C

A

B

C d No glitch

DPD

Delay buffer


Glitch Filtering by InertiaGlitch Filtering by Inertia

Delay d > DPD

A

B

C

A

B

C

d > DPD

Filtered glitch

DPD


Given that events occur at the input of a gate, Given that events occur at the input of a gate, whose inertial delay is whose inertial delay is dd, at times, , at times, tt11 ≤ . . . ≤ ≤ . . . ≤ ttnn , the , the number of events at the gate output cannot exceednumber of events at the gate output cannot exceed

TheoremTheorem

min ( min ( n n , 1 + ), 1 + )ttnn – t – t11

────────dd

ttnn - t - t11

tt11 t t22 t t33 t tnn timetime


Minimum Transient DesignMinimum Transient Design

Minimum transient energy condition for a Minimum transient energy condition for a Boolean gate:Boolean gate:

| t| tii – t – tjj | < d | < d

Where tWhere tii and t and tjj are arrival times of input are arrival times of input

events and d is the inertial delay of gateevents and d is the inertial delay of gate


Balanced Delay MethodBalanced Delay Method

All input events arrive simultaneouslyAll input events arrive simultaneously Overall circuit delay not increasedOverall circuit delay not increased Delay buffers may have to be insertedDelay buffers may have to be inserted

11 111111 11

111111

33

11 11

No increase in critical path delay


Hazard Filter MethodHazard Filter Method Gate delay is made greater than maximum input Gate delay is made greater than maximum input

path delay differencepath delay difference No delay buffers needed No delay buffers needed (least transient energy)(least transient energy) Overall circuit delay may increaseOverall circuit delay may increase

11 111111 11

33111111 11


Designing a Glitch-Free CircuitDesigning a Glitch-Free Circuit Maintain specified critical path delay.Maintain specified critical path delay. Glitch suppressed at all gates byGlitch suppressed at all gates by

Path delay balancingPath delay balancing Glitch filtering by increasing inertial delay of gates or by inserting delay Glitch filtering by increasing inertial delay of gates or by inserting delay

buffers when necessary.buffers when necessary. A linear program optimally combines all objectives.A linear program optimally combines all objectives.

DelayD

Path delay = d1

Path delay = d2

|d1 – d2| < D


Problem ComplexityProblem Complexity

Number of paths in a circuit can be Number of paths in a circuit can be

exponential in circuit size.exponential in circuit size.

Considering all paths through enumeration Considering all paths through enumeration

is infeasible for large circuits.is infeasible for large circuits.

Example: c880 has 6.96M path constraints.Example: c880 has 6.96M path constraints.


Define Arrival Time VariablesDefine Arrival Time Variables ddi Gate delay.Gate delay.

Define two Define two timing window variables per gate output: per gate output: ttii Earliest time of signal transition at gate Earliest time of signal transition at gate ii..

TTii Latest time of signal transition at gate Latest time of signal transition at gate ii..

Glitch suppression constraint: Glitch suppression constraint: TTi – t – ti < d < di

t1, T1

tn, Tn

.

.

.

ti, Ti

Reference: T. Raja, Master’s Thesis, Rutgers Univ., 2002.

di


Linear ProgramLinear Program

Variables: gate and buffer delays, Variables: gate and buffer delays, arrival time variables.arrival time variables.

Objective: minimize number of buffers.Objective: minimize number of buffers.Subject to: overall circuit delay Subject to: overall circuit delay

constraint for all input-output paths.constraint for all input-output paths.Subject to: minimum transient energy Subject to: minimum transient energy

condition for all multi-input gates.condition for all multi-input gates.


An Example: Full Adder add1bAn Example: Full Adder add1b

11

11

Critical path delay = 6

11

11

1111

11

11

11


Linear ProgramLinear Program

Gate variables: dGate variables: d4 4 . . . d. . . d1212 Buffer delay variables: dBuffer delay variables: d15 15 . . . d. . . d2929 Window variables: tWindow variables: t4 4 . . . t. . . t2929 and T and T4 4 . . . . T. . . . T2929

For Gate 7:For Gate 7:

TT77 ≥ ≥ TT55 + d + d77 tt77 ≤≤ t t55 + d + d77 dd77 > T > T77 – t – t77

TT77 ≥≥ T T66 + d + d77 tt77 ≤≤ t t66 + d + d77 Glitch suppressionGlitch suppression


Multiple-Input Gate ConstraintsMultiple-Input Gate Constraints


Single-Input Gate ConstraintsSingle-Input Gate Constraints

T16 + d19 = T19

t16 + d19 = t19

Buffer 19:


Critical Path Delay ConstraintsCritical Path Delay Constraints

TT1111 ≤≤ maxdelaymaxdelay

TT1212 ≤≤ maxdelaymaxdelay

maxdelay is specifiedmaxdelay is specified

Objective FunctionObjective FunctionNeed to minimize the number of buffers.Need to minimize the number of buffers.Because that leads to a nonlinear Because that leads to a nonlinear

objective function, we use an approximate objective function, we use an approximate criterion:criterion:

minimize minimize ∑ (buffer delay)∑ (buffer delay)

all buffersall buffers

i.e.,i.e., minimize minimize dd1515 + d + d1616 + ∙ ∙ ∙ + d + ∙ ∙ ∙ + d2929

This gives a near optimum result.This gives a near optimum result.



AMPL Solution: AMPL Solution: maxdelay maxdelay == 66

11

22


22

11

1111

11

22

11

22

11


AMPL Solution: AMPL Solution: maxdelay maxdelay == 77

11

11


33

22

1111

11

22

11

22


AMPL Solution: AMPL Solution: maxdelay maxdelay ≥≥ 1111

11

44


55

33

3311

11

22

11


ALU4: Four-Bit ALU 74181ALU4: Four-Bit ALU 74181

maxdelaymaxdelay Buffers insertedBuffers inserted

77 55

1010 22

1212 11

1515 00

Maximum Power Savings (zero-buffer design):

Peak = 33%, Average = 21%


ALU4: Original and Low-PowerALU4: Original and Low-Power


Benchmark CircuitsBenchmark Circuits

Circuit

ALU4

C880

C6288

c7552

Max-delay(gates)

715

2448

4794

4386

No. ofBuffers

5 0

6234

294120

366111

Average

0.800.79

0.680.68

0.400.36

0.44 0.42

Peak

0.680.67

0.540.52

0.360.34

0.34 0.32

Normalized Power


C7552 Circuit: Spice SimulationC7552 Circuit: Spice Simulation

Power Saving: Average 58%, Peak 68%Power Saving: Average 58%, Peak 68%


ReferencesReferences R. Fourer, D. M. Gay and B. W. Kernighan, R. Fourer, D. M. Gay and B. W. Kernighan, AMPL: A Modeling Language for AMPL: A Modeling Language for

Mathematical ProgrammingMathematical Programming, South San Francisco: The Scientific Press, 1993., South San Francisco: The Scientific Press, 1993. M. Berkelaar and E. Jacobs, “Using Gate Sizing to Reduce Glitch Power,” M. Berkelaar and E. Jacobs, “Using Gate Sizing to Reduce Glitch Power,” Proc. Proc.

ProRISC WorkshopProRISC Workshop, Mierlo, The Netherlands, Nov. 1996, pp. 183-188., Mierlo, The Netherlands, Nov. 1996, pp. 183-188. V. D. Agrawal, “Low Power Design by Hazard Filtering,” V. D. Agrawal, “Low Power Design by Hazard Filtering,” Proc. Proc. 1010thth Int’l Conf. Int’l Conf.

VLSI DesignVLSI Design, Jan. 1997, pp. 193-197., Jan. 1997, pp. 193-197. V. D. Agrawal, M. L. Bushnell, G. Parthasarathy and R. Ramadoss, “Digital V. D. Agrawal, M. L. Bushnell, G. Parthasarathy and R. Ramadoss, “Digital

Circuit Design for Minimum Transient Energy and Linear Programming Method,” Circuit Design for Minimum Transient Energy and Linear Programming Method,” Proc. Proc. 1212thth Int’l Conf. VLSI Design Int’l Conf. VLSI Design, Jan. 1999, pp. 434-439., Jan. 1999, pp. 434-439.

T. Raja, V. D. Agrawal and M. L. Bushnell, “Minimum DynamicT. Raja, V. D. Agrawal and M. L. Bushnell, “Minimum Dynamic Power CMOS Power CMOS Circuit Design by a Reduced Constraint Set Linear Program,” Circuit Design by a Reduced Constraint Set Linear Program,” Proc.Proc. 16 16thth Int’l Int’l Conf. VLSI DesignConf. VLSI Design, Jan. 2003, pp. 527-532., Jan. 2003, pp. 527-532.

T. Raja, V. D. Agrawal, and M. L. Bushnell, “Transistor sizing of logicgates to T. Raja, V. D. Agrawal, and M. L. Bushnell, “Transistor sizing of logicgates to maximize input delay variability,” maximize input delay variability,” J. Low Power Electron., vol.J. Low Power Electron., vol.2, no. 1, pp. 121–2, no. 1, pp. 121–128, Apr. 2006.128, Apr. 2006.

T. Raja, V. D. Agrawal, and M. L. Bushnell, “Variable Input Delay CMOS Logic T. Raja, V. D. Agrawal, and M. L. Bushnell, “Variable Input Delay CMOS Logic for Low Power Design,” IEEE Trans. VLSI Design, vol. 17, mo. 10, pp. 1534-for Low Power Design,” IEEE Trans. VLSI Design, vol. 17, mo. 10, pp. 1534-1545. October 2009.1545. October 2009.

Exercise: Dynamic PowerExercise: Dynamic PowerAn average gateAn average gate

VDD, V = 1 voltVDD, V = 1 voltOutput capacitance, C = 1pFOutput capacitance, C = 1pFActivity factor, Activity factor, αα = 10% = 10%Clock frequency, f = 1GHzClock frequency, f = 1GHz

What is the dynamic power What is the dynamic power consumption of a 1 million gate VLSI consumption of a 1 million gate VLSI chip?chip?


AnswerAnswer

Dynamic energy per transition = 0.5CVDynamic energy per transition = 0.5CV22

Dynamic power per gateDynamic power per gate

= Energy per second= Energy per second

= 0.5 CV= 0.5 CV2 2 αα f f

= 0.5 ✕ 10 = 0.5 ✕ 10 – 12– 12 ✕ 1 ✕ 122 ✕ 0.1 ✕ ✕ 0.1 ✕ 101099

= 0.5 ✕ 10 = 0.5 ✕ 10 – 4– 4 = 50 = 50μμWWPower for 1 million gate chip = 50WPower for 1 million gate chip = 50WCopyright Agrawal, 2011Copyright Agrawal, 2011 Lectures 10, 11, 12: Gate-level optimizationLectures 10, 11, 12: Gate-level optimization 3535


Components of PowerComponents of PowerDynamicDynamic

Signal transitionsSignal transitionsLogic activityLogic activityGlitchesGlitches

Short-circuitShort-circuitStaticStatic

Leakage


Subthreshold ConductionSubthreshold ConductionVgs – Vth –Vds

Ids = I0 exp( ───── ) × (1– exp ─── ) nVT VT

Subthreshold slope

0 0.3 0.6 0.9 1.2 1.5 1.8 V Vgs

Ids

1mA100μA10μA1μA

100nA10nA1nA

100pA10pA

Vth

Sub

thre

shol

dre

gion

Saturation region

d

s

g


Thermal Voltage, Thermal Voltage, vvTT

VT = kT/q = 26 mV, at room temperature.

When Vds is several times greater than VT

Vgs – Vth

Ids = I0 exp( ───── ) nVT


Leakage CurrentLeakage Current

Leakage current equals Leakage current equals IIdsds when when VVgs gs = 0= 0

Leakage current, Leakage current, IIdsds = = II00 exp( exp( – V– Vthth/nV/nVTT))

At cutoff, At cutoff, VVgsgs = = VVth th , and , and IIdsds = = II00

Lowering leakage to 10Lowering leakage to 10--b b ✕ ✕ II00

VVthth = = bnVbnVT T ln 10 = 1.5ln 10 = 1.5b b × 26 ln 10 = 90× 26 ln 10 = 90bb mV mV

Example: To lower leakage to Example: To lower leakage to II00/1,000/1,000

VVthth = 270 mV = 270 mV


Threshold VoltageThreshold Voltage VVthth = = VVt0t0 + + γγ[([(ΦΦss++VVsbsb))½ ½ – – ΦΦss

½½]]

VVt0t0 is threshold voltage when source is at is threshold voltage when source is at

body potential (body potential (0.4 V for 180nm process)) ΦΦs s = = 22VVTT ln(ln(NNA A /n/ni i )) is surface potentialis surface potential

γγ = (2 = (2qqεεsi si NNAA))½½ttox ox //εεoxox is body effect is body effect

coefficient (0.4 to 1.0)coefficient (0.4 to 1.0) NNAA is doping level = is doping level = 8×1017 cm–3

ni = 1.45×1010 cm–3


Threshold Voltage, Threshold Voltage, VVsb sb = 1.1V= 1.1V

Thermal voltage, Thermal voltage, VVTT = = kT/qkT/q = 26 mV = 26 mV

ΦΦss = 0.93 V = 0.93 V

εεoxox = 3.9×8.85×10 = 3.9×8.85×10-14-14 F/cm F/cm

εεsisi = 11.7×8.85×10 = 11.7×8.85×10-14-14 F/cm F/cm

ttoxox = 40 A = 40 Aoo

γγ = 0.6 V = 0.6 V½½

VVthth = = VVt0t0 + + γγ[([(ΦΦss++VVsbsb))½½- - ΦΦss½½] = 0.68 V] = 0.68 V


A Sample CalculationA Sample Calculation

VVDDDD = 1.2V, 100nm CMOS process = 1.2V, 100nm CMOS processTransistor width, W = 0.5Transistor width, W = 0.5μμmmOFF device (OFF device (VVgsgs = = VVthth) leakage) leakage

II00 = 20nA/ = 20nA/μμm, for low threshold transistorm, for low threshold transistorII00 = 3nA/ = 3nA/μμm, for high threshold transistorm, for high threshold transistor

100M transistor chip100M transistor chipPower = (100×10Power = (100×1066/2)(0.5×20×10/2)(0.5×20×10-9-9A)(1.2V) = 600mW A)(1.2V) = 600mW for for

all low-threshold transistorsall low-threshold transistorsPower = (100×10Power = (100×1066/2)(0.5×3×10/2)(0.5×3×10-9-9A)(1.2V) = 90mW A)(1.2V) = 90mW for for

all high-threshold transistorsall high-threshold transistors


Dual-Threshold ChipDual-Threshold Chip

Low-threshold only for 20% transistors on Low-threshold only for 20% transistors on critical path.critical path.

Leakage power Leakage power = 600×0.2 + 90×0.8= 600×0.2 + 90×0.8

= 120 + 72= 120 + 72

= 192 mW= 192 mW


Dual-Threshold CMOS CircuitDual-Threshold CMOS Circuit


Dual-Threshold DesignDual-Threshold Design To maintain performance, all gates on To maintain performance, all gates on

critical paths are assigned low critical paths are assigned low VVth th ..

Most other gates are assigned high Most other gates are assigned high VVth th .. But, some gates on non-critical paths But, some gates on non-critical paths

may also be assigned low may also be assigned low VVthth to prevent to prevent

those paths from becoming critical.those paths from becoming critical.


Integer Linear Programming (ILP) to Integer Linear Programming (ILP) to Minimize Leakage PowerMinimize Leakage Power

Use dual-threshold CMOS processUse dual-threshold CMOS process First, assign all gates low First, assign all gates low VVthth

Use an ILP model to find the delay (Use an ILP model to find the delay (TTcc) of the ) of the

critical pathcritical path Use another ILP model to find the optimal Use another ILP model to find the optimal VVthth

assignment as well as the reduced leakage power assignment as well as the reduced leakage power for all gates without increasing for all gates without increasing TTcc

Further reduction of leakage power possible by Further reduction of leakage power possible by letting letting TTcc increase increase


ILP -ILP -VariablesVariables For each gate For each gate ii define two variables. define two variables. TTi i :: the longest time at which the output of the longest time at which the output of

gate gate ii can produce an event after the can produce an event after the occurrence of an input event at a primary occurrence of an input event at a primary input of the circuit. input of the circuit.

XXi i :: a variable specifyinga variable specifying low or high low or high VVthth for for gate gate i i ;; X Xii is an integer [0, 1], is an integer [0, 1],

1 1 gate gate ii is assigned low is assigned low VVth th ,,

0 0 gate gate ii is assigned high is assigned high VVth th ..


ILP - ILP - objective functionobjective function

minimize the sum of all gate leakage currents, given by minimize the sum of all gate leakage currents, given by

IILi Li is the leakage current of gate is the leakage current of gate ii with low with low VVthth IIHiHi is the leakage current of gate is the leakage current of gate ii with high with high VVthth Using SPICE simulation results, construct a leakage Using SPICE simulation results, construct a leakage

current look up table, which is indexed by the gate current look up table, which is indexed by the gate type and the input vectortype and the input vector. .

i

leakiddleak IVP

i

HiiLii IXIXMin 1

Leakage power:


ILP - ILP - ConstraintsConstraints

For each gateFor each gate (1)(1)

output of gate output of gate jj is fanin of gate is fanin of gate ii

(2) (2)

Max delay constraints for primary outputs (PO)Max delay constraints for primary outputs (PO)

(3) (3)

TTmaxmax is the maximum delay of the critical path is the maximum delay of the critical path

HiiLiiji DXDXTT 1

10 iX

maxTTi

Gate j

Gate i

Tj

Ti


ILP Constraint ExampleILP Constraint Example

Assume all primary input (PI) signals on the left arrive at the Assume all primary input (PI) signals on the left arrive at the same time. same time.

For gate 2, constraints areFor gate 2, constraints are

0

3

1

2

222202 1 HL DXDXTT

22222 10 HL DXDXT

HiiLiiji DXDXTT 1


ILP – Constraints (cont.)ILP – Constraints (cont.)

DDHi Hi is the delay of gateis the delay of gate i i with highwith high V Vthth

DDLi Li is the delay of gateis the delay of gate i i with lowwith low V Vthth

A second look-up table is constructed and A second look-up table is constructed and specifies the delay for given gate types specifies the delay for given gate types and fanout numbers. and fanout numbers.


ILP – Finding Critical DelayILP – Finding Critical Delay

TTmaxmax can be specified or be the delay of longest path (can be specified or be the delay of longest path (TTcc).).

To find To find TTc c , we first delete the above constraint and assign , we first delete the above constraint and assign

all gates low all gates low VVthth

Maximum Maximum TTii in the ILP solution is in the ILP solution is TTcc..

If we replace If we replace TTmaxmax with with TTc c , the objective function then , the objective function then

minimizes leakage power without sacrificing performance.minimizes leakage power without sacrificing performance.

10 iX

maxTTi

1iX


Power-Delay TradeoffPower-Delay Tradeoff

1 1.1 1.2 1.3 1.4 1.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized Critical Path Delay

Nor

mal

ized

Lea

kage

Pow

er

C432

C880

C1908


Power-Delay TradeoffPower-Delay Tradeoff

If we gradually increase If we gradually increase TTmaxmax from from TTc c , leakage , leakage

power is further reduced, because more gates power is further reduced, because more gates can be assigned high can be assigned high VVth th ..

But, the reduction trends to become slower.But, the reduction trends to become slower. When When TTmax max = = (130%)(130%) T Tcc , the reduction about , the reduction about

levels off because almost all gates are levels off because almost all gates are assigned high assigned high VVth th . .

Maximum leakage reduction can be 98%. Maximum leakage reduction can be 98%.


Leakage & Dynamic Power Optimization 70nm Leakage & Dynamic Power Optimization 70nm CMOS c7552 Benchmark Circuit @ 90CMOS c7552 Benchmark Circuit @ 90ooCC

0

100

200

300

400

500

600

700

800

900

Mic

row

att

s

Original circuit Optimizeddesign

Leakage powerDynamic powerTotal power

Leak

age

exce

eds

dyn

amic

pow

er Y. Lu and V. D. Agrawal, “CMOS Leakage and Glitch Minimization for Power-Performance Tradeoff,” Journal of Low Power Electronics (JOLPE), vol. 2, no. 3, pp. 378-387, December 2006.


SummarySummary

Leakage power is a significant fraction of the Leakage power is a significant fraction of the total power in nanometer CMOS devices.total power in nanometer CMOS devices.

Leakage power increases with temperature; can Leakage power increases with temperature; can be as much as dynamic power.be as much as dynamic power.

Dual threshold design can reduce leakage.Dual threshold design can reduce leakage. Reference: Y. Lu and V. D. Agrawal, “CMOS Leakage

and Glitch Minimization for Power-Performance Tradeoff,” J. Low Power Electronics, Vol. 2, No. 3, pp. 378-387, December 2006.

Access other paper at http://www.eng.auburn.edu/~vagrawal/TALKS/talks.html


Problem: Leakage ReductionProblem: Leakage ReductionFollowing circuit is designed in 65nm CMOS technology using low threshold transistors. Each gate has a delay of 5ps and a leakage current of 10nA. Given that a gate with high threshold transistors has a delay of 12ps and leakage of 1nA, optimally design the circuit with dual-threshold gates to minimize the leakage current without increasing the critical path delay. What is the percentage reduction in leakage power? What will the leakage power reduction be if a 30% increase in the critical path delay is allowed?


Solution 1: No Delay IncreaseSolution 1: No Delay IncreaseThree critical paths are from the first, second and third inputs to the last output, shown by a dashed line arrow. Each has five gates and a delay of 25ps. None of the five gates on the critical path (red arrow) can be assigned a high threshold. Also, the two inverters that are on four-gate long paths cannot be assigned high threshold because then the delay of those paths will become 27ps. The remaining three inverters and the NOR gate can be assigned high threshold. These gates are shaded blue in the circuit.The reduction in leakage power = 1 – (4×1+7×10)/(11×10) = 32.73%Critical path delay = 25ps

5ps

5ps

5ps

5ps

5ps

5ps5ps

12ps

12ps

12ps

12ps


Solution 2: 30% Delay IncreaseSolution 2: 30% Delay IncreaseSeveral solutions are possible. Notice that any 3-gate path can have 2 high threshold gates. Four and five gate paths can have only one high threshold gate. One solution is shown in the figure below where six high threshold gates are shown with shading and the critical path is shown by a dashed red line arrow.The reduction in leakage power = 1 – (6×1+5×10)/(11×10) = 49.09%Critical path delay = 29ps

12ps

12ps

12ps

12ps12ps

12ps5ps

5ps

5ps

5ps

5ps

csv881: low-power design gate-level power optimization

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