Upload File

karnaugh maps and other topic on combinatorial logic · k-map rules summary 1. groups can contain...

  • Home
  • Documents
  • Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal
40
Karnaugh Maps and Other Topic on Combinatorial Logic CS 64: Computer Organization and Design Logic Lecture #12 Fall 2018 Ziad Matni, Ph.D. Dept. of Computer Science, UCSB

Upload: lykien

Post on 30-Apr-2019

221 views

Category:

Documents


0 download

Report

TRANSCRIPT

Page 1: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

KarnaughMapsandOtherTopiconCombinatorialLogic

CS64:ComputerOrganizationandDesignLogicLecture#12Fall2018

ZiadMatni,Ph.D.

Dept.ofComputerScience,UCSB

Page 2: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Administrative

•  Lab#7onTuesday•  DuebySundayatmidnight– NotFriday…HappyThanksgiving!

•  NoclassthisWednesday!JJJ

11/18/18 Matni,CS64,Fa18 2

Page 3: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

LectureOutline

•  LogicFunctionsandtheirSimplifications:

TruthTableUsevs.KarnaughMaps

11/18/18 Matni,CS64,Fa18 3

Page 4: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

ScalingUpSimplification

•  Whenwegettomorethan3variables,itbecomeschallengingtousetruthtables

•  WecaninsteaduseKarnaughMapstomakeitimmediatelyapparentastowhatcanbesimplified

11/18/18 Matni,CS64,Fa18 4

Page 5: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

ExampleofaK-MapA B f(A,B)0 0 a0 1 b1 0 c1 1 d

11/18/18 Matni,CS64,Fa18 5

A B f(A,B)0 0 00 1 11 0 11 1 1

0123

Page 6: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

K-Mapswith3or4Variables

11/18/18 Matni,CS64,Fa18 6

Notetheadjacentplacementof:00011110

It’sNOT:

00011011

Page 7: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

RulesforUsingK-MapsforSimplification

1.  Grouptogetheradjacentcellscontaining“1”2.  Groupsshouldnotincludeanythingcontaining“0”

3.  Groupsmaybehorizontalorvertical,butnotdiagonal

11/18/18 Matni,CS64,Fa18 7

Page 8: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

RulesforUsingK-MapsforSimplification

4.   Groupsmustcontain1,2,4,8,oringeneral2ncells.

11/18/18 Matni,CS64,Fa18 8

Page 9: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

RulesforUsingK-MapsforSimplification

5.   Eachgroupmustbeaslargeaspossible(Otherwisewe’renotbeingasminimalaswecanbe, eventhoughwe’renotbreakinganyBooleanrules)

11/18/18 Matni,CS64,Fa18 9

Page 10: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

RulesforUsingK-MapsforSimplification

6.   Eachcellcontaininga“1”mustbeatleastinonegroup

11/18/18 Matni,CS64,Fa18 10

Page 11: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

RulesforUsingK-MapsforSimplification

7.   Groupsmayoverlapesp.tomaximizegroupsize

11/18/18 Matni,CS64,Fa18 11

Page 12: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

RulesforUsingK-MapsforSimplification

8.   Groupsmaywraparoundthetable.Theleftmostcellinarowmaybegroupedwiththerightmostcellandthetopcellinacolumnmaybegroupedwiththebottomcell.

11/18/18 Matni,CS64,Fa18 12

Page 13: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Example12vars

F(X,Y)=XY+Y=Y(X+1)=Y

11/18/18 Matni,CS64,Fa18 13

0 1

0

1

YX

1

1

F(X,Y)=Y

Y=1column

Verifyingresults!

Page 14: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Example23vars

F(X,Y,Z)=XZ+Z(X'+XY)=XZ+ZX’+ZXY=Z(X+X’+XY)=Z(1+XY)=Z

11/18/18 Matni,CS64,Fa18 14

00 01 11 10

0

1

XYZ

1111

F(X,Y,Z)=Z

Y=1 X=1

Verifyingresults!

Page 15: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Example33vars

!A!B!C+!A!BC+!ABC+!AB!C+A!B!C+AB!C

11/18/18 Matni,CS64,Fa18 15

00 01 11 10

0

1

ABC

1111

F(X,Y,Z)=!C+!A

1 1

Page 16: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Example44vars

F(A,X,Y,Z)=AX+Z(X+A’+Y)=AX+ZX+ZA’+ZY

11/18/18 Matni,CS64,Fa18 16

00 01 11 10

00

01

11

10

XYAZ

1 1F(A,X,Y,Z)=ZA’+AX+ZY

11

1 1Z=1

A=1

Y=1 X=1

11

1

Page 17: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Example44vars

F(A,B,C,D)=ABCD’+ABC’D+CD+A’B’+C’D

11/18/18 Matni,CS64,Fa18 17

00 01 11 10

00

01

11

10

ABCD

F(A,B,C,D)=A’B’+D+ABC

D=1

C=1

B=1 A=1

1

1

1 1 1 1

1

1

1

1 1

Page 18: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

K-MapRulesSummary1.  Groupscancontainonly1s2.  Only1sinadjacentgroupsareallowed3.  GroupsmayONLYbehorizontalorvertical(nodiagonals)4.  Thenumberof1sinagroupmustbeapoweroftwo(1,2,4,8...)5.  GroupsmustbeaslargeANDasfewinno.sas“legally”possible6.  All1smustbelongtoagroup,evenifit’sagroupofoneelement7.  Overlappinggroupsarepermitted8.  Wrappingaroundthemapispermitted

11/18/18 Matni,CS64,Fa18 18

Page 19: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Exploiting“Don’tCares”

•  Anoutputvariablethat’sdesignated“don’tcare”(symbol=X)meansthatitcouldbea0ora1(i.e.we“don’tcare”which)– Thatis,itisunspecified,

usuallybecauseofinvalidinputs

11/18/18 Matni,CS64,Fa18 19

Page 20: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

ExampleofaDon’tCareSituation

•  Considercodingalldecimaldigits(say,foradigitalclockapp):– 0thru9---requireshowmanybits?

•  4bits– But!4bitsconveymorenumbersthanthat!

•  Don’tforgetAthruF!

•  Notallbinaryvaluesmaptodecimal

11/18/18 Matni,CS64,Fa18 20

Page 21: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

ExampleContinued…

11/18/18 Matni,CS64,Fa18 21

Page 22: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Don’tCare:SoWhat?

•  RecallthatinaK-map,wecanonlygroup1s

•  Becausethevalueofadon’tcareisirrelevant,wecantreatitasa1ifitisconvenienttodoso(ora0ifthatwouldbemoreconvenient)

11/18/18 Matni,CS64,Fa18 22

Page 23: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Example

•  Acircuitthatcalculatesifthe4-bitbinarycodedsingledigitdecimalinput%2==0

•  So,although4-bitswillgivemenumbersfrom0to15,Idon’tcareabouttheonesthatyield10to15.

11/18/18 Matni,CS64,Fa18 23

I3 I2 I1 I0 R

0 0 0 0 1

0 0 0 1 0

0 0 1 0 1

0 0 1 1 0

0 1 0 0 1

0 1 0 1 0

0 1 1 0 1

0 1 1 1 0

1 0 0 0 1

1 0 0 1 0

1 0 1 0 X

1 0 1 1 X

1 1 0 0 X

1 1 0 1 X

1 1 1 0 X

1 1 1 1 X

Page 24: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

ExampleasaK-Map

11/18/18 Matni,CS64,Fa18 24

0 1 0 1

Page 25: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

IfWeDon’tExploit“Don’tCares”

11/19/18 Matni,CS64,Fa18 25

0 1 0 1

R=I1I0I3+I1I0I3+I0I1I2I3

Page 26: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

IfWeDOExploit“Don’tCares”

11/19/18 Matni,CS64,Fa18 26

0 1 0 1

R=I0

Page 27: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

CombinatorialLogicDesigns

•  Whenyoucombinemultiplelogicblockstogethertoformamorecomplexlogicfunction/circuit

11/18/18 Matni,CS64,Fa18 27

Whatistheoutput?A.B+C

Whatisitstruthtable?A B C F0 0 0 10 0 1 00 1 0 10 1 1 01 0 0 11 0 1 01 1 0 11 1 1 1

WhatisitsK-Map?00 01 11 10

01

ABC

1 1 111

Page 28: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Exercise1

•  Giventhefollowingtruthtable,drawtheresultinglogiccircuit

– STEP1:DrawtheK-Mapandsimplifythefunction

– STEP2:Constructthecircuitfromthenowsimplifiedfunction

11/18/18 Matni,CS64,Fa18 28

A B C D F0 0 0 0 00 0 0 1 00 0 1 0 00 0 1 1 00 1 0 0 10 1 0 1 00 1 1 0 00 1 1 1 01 0 0 0 01 0 0 1 01 0 1 0 11 0 1 1 11 1 0 0 11 1 0 1 01 1 1 0 11 1 1 1 1

Page 29: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Exercise1–Step1Getthesimplifiedfunction

11/18/18 Matni,CS64,Fa18 29

A B C D F0 0 0 0 00 0 0 1 00 0 1 0 00 0 1 1 00 1 0 0 10 1 0 1 00 1 1 0 00 1 1 1 01 0 0 0 01 0 0 1 01 0 1 0 11 0 1 1 11 1 0 0 11 1 0 1 01 1 1 0 11 1 1 1 1

00 01 11 10

00

01

11

10

ABCD

1 1

11

B=1 A=1

D=1

C=1

F(A,B,C)=B.C’.D’+A.C1 1

Page 30: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Exercise1–Step2Drawthelogiccircuitdiagram

11/18/18 Matni,CS64,Fa18 30

F(A,B,C)=B.C’.D’+A.C

AC

CBD

F

Page 31: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Exercise2

•  Giventhefollowingtruthtable,drawtheresultinglogiccircuit

11/18/18 Matni,CS64,Fa18 31

A B C F0 0 0 10 0 1 10 1 0 10 1 1 01 0 0 11 0 1 11 1 0 01 1 1 0

00 01 11 10

0

1

ABC

111

F(A,B,C)=B’+A’.C’

1 1

B

AC

F

Page 32: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Exercise3

•  Giventhefollowingschematicofacircuit,(a)writethefunctionand(b)filloutthetruthtable:

X=A.B+(A.C)’(notethatalsomeans:X=A.B+A’+C’)

11/18/18 Matni,CS64,Fa18 32

ABAC

X

A.B

(A.C)’

A B C X0 0 0 10 0 1 10 1 0 10 1 1 11 0 0 11 0 1 01 1 0 11 1 1 1

X

Page 33: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Exercise3

•  Giventhefollowingschematicofacircuit,(a)writethefunctionand(b)filloutthetruthtable:

X=A.B+(A.C)’(notethatalsomeans:X=A.B+A’+C’)

11/18/18 Matni,CS64,Fa18 33

ABAC

X

A.B

(A.C)’

A B C X0 0 0 10 0 1 10 1 0 10 1 1 11 0 0 11 0 1 01 1 0 11 1 1 1

Page 34: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Multiplexer•  Alogicalselector:–  SelecteitherinputAorinputBtobetheoutput

//ifs=0,outputisa//ifs=1,outputisbintmux(inta,intb,ints){if(!s)returna;elsereturnb;

}11/18/18 Matni,CS64,Fa18 34

Page 35: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

Multiplexer(Muxforshort)

•  Typicallyhas3groupsofinputsand1output–  IN:2data,1select–  OUT:1data

•  1oftheinputdatalinesgetsselectedtobecometheoutput,basedonthe3rd(select)input–  If“Sel”=0,thenI0getstobetheoutput–  If“Sel”=1,thenI1getstobetheoutput

•  TheoppositeofaMuxiscalledaDemulitplexer(orDemux)

11/18/18 Matni,CS64,Fa18 35

Page 36: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

MuxConfigurations

11/18/18 Matni,CS64,Fa18 36

MuxescanhaveI/Othataremultiplebits

Ortheycanhavemorethantwodatainputs

2:1

A0A1B0B1SEL

O0O1

Thisiscalleda2-bit,2-to-1mux

6:1

ABCDEFSEL

O

Thisiscalleda1-bit,6-to-1mux

Page 37: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

TheUseofMultiplexers

•  Makesitpossibleforseveralsignals(variables)toshareoneresource– Verycommonlyusedindatacommunicationlines

11/18/18 Matni,CS64,Fa18 37Mux De

mux

… …DataLines

DataLines

Select

Shareddataline(“trunk”)

Select

Page 38: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

MuxTruthTableandLogicCircuit1-bitMux

I0 I1 S O0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1

11/18/18 Matni,CS64,Fa18 38

00 01 11 10

0

1

I0I1S

1

11

1

O=S.I1+S’.I0

I0I1

S

O

=linesarephysicallyconnected

00011011

Page 39: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

YOURTO-DOs

•  Lab#7onTuesday–DuebySundayatmidnight

•  NoclassonWednesday!JJJ

11/18/18 Matni,CS64,Fa18 39

Page 40: Karnaugh Maps and Other Topic on Combinatorial Logic · K-Map Rules Summary 1. Groups can contain only 1s 2. Only 1s in adjacent groups are allowed 3. Groups may ONLY be horizontal

11/18/18 Matni,CS64,Fa18 40


Chapter 1catalogimages.johnwiley.com.au/Attachment/07314... · 22s1 19K: 1s 22s22p63s23p64s1 6C: 1s 22s22p2 17Cl: 1s 22s22p63s23p5 18Ar: 1s 22s22p63s23p6 7N: 1s 22s22p3 22. (a) 1s22s22p63s23p3

Models D12-1S, 2S, 1CC Owner D18-1S, 2S, 1CC, 2CC ......D48-1S, 2S, 1CC, 2CC, DHO48-1S, 2S D64-1S, 2S, DHO64-1S, 2S Extensive Product Information Available at: Ultraviolet.com BuyUltraviolet.com

Pennington County - South Dakota Department of Education · 2020. 1. 13. · 2n 3e 2n 1e 2s 4e 1n 3e 2n 4e 1n 1e 1n 2e 1n 4e 1n 6e 2n 2e 1s 6e 1s 1e 1s 2e 1s 3e 1s 4e 1s 5e 1s 7e

1S Sequence 01

METAL CUTTING BAND SAW MACHINE - · PDF file"this machine 1s for metal cutting only, it 1s not approved for cutting wood.the supplier accepts no responsibility for any machine when

CeC 1S«545296

Ingles 1s - Ya

CS64 Week 6 Lecture 2 - UCSBkyledewey/cs64f15/lectures/week6/lecture… · K-Map Rules in Summary (1) • Groups can contain only 1s • Only 1s in adjacent groups are allowed (no

TCEQ-Registrations for Air Standard Permit Form PI … · Web viewPI-1S Instructions PI-1S Instructions PI-1S Instructions TCEQ-10370 (APDG 5235v2 9, Revised 01/19) PI-1S This form

i Us/Electronic... · / s~anc~ 1s _deterrmn~d only w~en. apphcation 'ther~for_ is made to. a consular officer; eligibility for adm~s s1on or adjustment. 1s determined only when ~pphcatmn

Models D12-1S, 2S, 1CC Owner D18-1S, 2S, 1CC, 2CC, DHO18-1S, … · 2020-02-21 · D30-1S, 2S, DHO30-1S, 2S D36-1S, 2S, 1CC, 2CC, DHO36-1S, 2S D48-1S, 2S, 1CC, 2CC, DHO48-1S, 2S D64-1S,

Belknap · ConcW4 D14 1S 4137 845 8.3% ConcW1 D11 1S 4465 1173 15.6% ConcW2 D12 1S 4381 1089 13.7% ConcW3 D13 1S 4328 1036 12.6% ConcW5 4077 D10 3S 9666 -207 …

Unosider 1S catalogue

Final art 1s review

Ghost-S Spec Sheet - Bikers World Store · Ghost-S Spec Sheet PROFESSIONAL ACTION ... 1s, 2s. 5s) (10/s | 1s, 2s, 5s) (20/s | 1s) (30/s | 1s) Scene Mode Normal / Vivid / Low ... >>

1s · 7. Title: 1s Created Date: 10/15/2014 10:23:16 AM

Mean = 41.21Median = 42.5s = 7.59 x - 1s – x + 1s – Assignment #1

Electron Configurations H = 1s 1 1s1s He = 1s 2 1s1s Li = 1s 2 2s 1 1s1s 2s2s Be = 1s 2 2s 2 1s1s 2s2s C = 1s 2 2s 2 2p 2 1s1s 2s2s 2px2px 2py2py 2pz2pz

SKM 308e20052614290 · Title: SKM_308e20052614290 Author: 1s » ¬Â YýÆÎr V Subject: 1s » ¬Â YýÆÎr V Keywords: 1s » ¬Â YýÆÎr V

Honor Choir 1s

Shielding in Li 1s 2s and Li 1s 2p - Boston University

lMrlM 1S - Imprimis

HW-SM521ENG XERUN XR10 Pro 1S 160906 · 1S LiPo/3-4NiMH Only 6V@3A (Continuous) (Switch-mode) Input End: No Connectors; Output End: No Connectors 37.5x31x15.9mm / 35.6g PRG/FAN Port

2S 1S - j.b5z.net

XYZ X XYZ Y Z - Omron · Released in July, 2016 1S Servomotor R88M-1 NJ/NX/NY * Controller *4 3 *3. Industrial PC Platform NY-series IPC Machine Controller only. *4. 1S Servo Drive

Fashionshoot 1s

1S, 4 S, 5 S, 6 S Excited States of the Beryllium Atom3 1S, 4 1S, 5 1S, 6 1S, and 7 1S Excited States of the Beryllium Atom James S. Sims National Institute of Standards and Technology,

Filosofia Cp 1s Vol3reduzido

lMltlM 1S - Imprimis

DISTANCE AND DISPLACEMENT 1. Determine the … the distance and displacement of the following: 1s t 1s t 2nd 2nd 1s t 2nd 1s t 1s t 2nd 2. Determine the speed and velocity of the following:

synthese proteines 1S

CS64 Week 6 Lecture 2 · K-Map Rules in Summary (1) • Groups can contain only 1s • Only 1s in adjacent groups are allowed (no diagonals) • The number of 1s in a group must be

Paradigm of 1s

Multiplication 0s 1s

Derivados 1S 2012