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COMP541 COMP541 Digital Logic and Digital Logic and Computer DesignComputer Design

Montek SinghMontek Singh

Jan 9, 2012Jan 9, 2012

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TodayToday’’s Topicss Topics Course descriptionCourse description

WhatWhat’’s it abouts it aboutMechanics: grading, etc.Mechanics: grading, etc.

Material from Chapter 1 (self-study Material from Chapter 1 (self-study review)review)What is digital logic?What is digital logic?Binary signalingBinary signalingNumber systemsNumber systemsCodesCodes

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WhatWhat’’s Course About?s Course About? DigitalDigital logic,logic, focusing on the design focusing on the design of computersof computers

Stay mostly at a high level (i.e., Stay mostly at a high level (i.e., above transistors)above transistors)

Each person designs a MIPS CPUEach person designs a MIPS CPUand peripheral logic (VGA, joystick)and peripheral logic (VGA, joystick)Project like an Atari 2600 gameProject like an Atari 2600 game

High-level language High-level language Modern design practicesModern design practices

FocusFocus Stay above Stay above transistor leveltransistor levelAt most one class At most one class on transistors and on transistors and VLSIVLSI

Expect you to Expect you to know assembly know assembly language language programmingprogramming

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Physics

Devices

AnalogCircuits

DigitalCircuits

Logic

Micro-architecture

Architecture

OperatingSystems

ApplicationSoftware

electrons

transistorsdiodes

amplifiersfilters

AND gatesNOT gates

addersmemories

datapathscontrollers

instructionsregisters

device drivers

programs

focu

s of

this

cou

rse

More Than Just ArchitectureMore Than Just Architecture Designing and implementing a computer Designing and implementing a computer is also aboutis also aboutManaging complexity (hierarchy, modularity, Managing complexity (hierarchy, modularity, regularity).regularity).

DebuggingDebuggingTesting and verifyingTesting and verifying

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The Three -YThe Three -Y’’ss HierarchyHierarchy

A system divided into modules and submodulesA system divided into modules and submodules

ModularityModularityHaving well-defined functions and interfacesHaving well-defined functions and interfaces

RegularityRegularityEncouraging uniformity, so modules can be Encouraging uniformity, so modules can be easily reusedeasily reused

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How Can We Do This?How Can We Do This? Labs on FridaysLabs on Fridays

Use: Field Programmable Gate Arrays Use: Field Programmable Gate Arrays (FPGAs)(FPGAs)Chips with a lot of circuitsChips with a lot of circuits

Tens of thousands to millions of transistorsTens of thousands to millions of transistorsProgrammableProgrammable

We write descriptions of the designWe write descriptions of the design““programsprograms”” describing design describing design

Tools translate to gates/wiresTools translate to gates/wires Download pattern/interconnection to Download pattern/interconnection to chipchipSort of like burning music to a rewritable CDSort of like burning music to a rewritable CD

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We Will Use This BoardWe Will Use This Board

What’s on it?

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Schematic DiagramSchematic Diagram

• Old fashioned way to describe logic• Still useful for documentation

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VerilogVerilog/*/* * A 32-bit counter with only 4 bits of output. The idea is* A 32-bit counter with only 4 bits of output. The idea is * to select which of the counter stages you want to pass on.* to select which of the counter stages you want to pass on. ** * Anselmo Lastra, November 2002* Anselmo Lastra, November 2002 */*/ module cntr_32c(clk,res,out);module cntr_32c(clk,res,out); input clk;input clk; input res;input res; output [3:0] out;output [3:0] out;

reg [31:0] count;reg [31:0] count;

always @ (posedge res or posedge clk)always @ (posedge res or posedge clk) if(res)if(res)

count <= 0;count <= 0;elseelse

count <= count + 1;count <= count + 1; assign out[3] = count[28];assign out[3] = count[28]; assign out[2] = count[27];assign out[2] = count[27]; assign out[1] = count[26];assign out[1] = count[26]; assign out[0] = count[25];assign out[0] = count[25];

endmoduleendmodule

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Xilinx SoftwareXilinx Software Use design tools from chip makerUse design tools from chip maker Have full version on lab PCsHave full version on lab PCs Can install on your PCCan install on your PC

Download from webDownload from web

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Class Web PagesClass Web Pages Will be up by ThursdayWill be up by Thursday’’s classs class Linked from my home pageLinked from my home pagehttp://www.cs.unc.edu/~montek

All lecture slides posted thereAll lecture slides posted thereWill Will trytry to put them there before class to put them there before class

Schedule, homework, etc. posted thereSchedule, homework, etc. posted there Lab documents there alsoLab documents there also See Blackboard/Sakai for scores/gradesSee Blackboard/Sakai for scores/grades

TextbookTextbook Harris and HarrisHarris and Harris Digital Design and Computer Digital Design and Computer ArchitectureArchitecture

Morgan Kaufmann, 2007Morgan Kaufmann, 2007 Amazon has for $70Amazon has for $70 Extra material onExtra material onhttp://www.elsevierdirect.com/companion.jsp?ISBN=9780123704979

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Overview of TextbookOverview of Textbook Chapters 1-5: Digital logicChapters 1-5: Digital logic

Combinational, sequential, basic circuits, Combinational, sequential, basic circuits, HDLHDL

Chapter 6: ArchitectureChapter 6: ArchitectureFast – review for those who took COMP 411Fast – review for those who took COMP 411

Chapter 7: MicroarchitecturesChapter 7: Microarchitectures Chapters 8: MemoriesChapters 8: Memories Appendix A: ImplementationAppendix A: Implementation

FPGAs, etc.FPGAs, etc.

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Order of TopicsOrder of Topics Will change order from that in bookWill change order from that in book

To try to get you working on interesting labs To try to get you working on interesting labs soonersooner

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May Also NeedMay Also Need COMP411 textbook (Patterson/Hennessy)COMP411 textbook (Patterson/Hennessy)

For MIPS referenceFor MIPS referenceHow many have one?How many have one?I can copy the few necessary pagesI can copy the few necessary pages

Verilog referenceVerilog referenceBook optionalBook optionalWeb pages – see course home pageWeb pages – see course home page

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GradingGrading Labs – 35%Labs – 35%

Easier at first; later ones will count moreEasier at first; later ones will count more

Lab final project – 15%Lab final project – 15% Homework – 25%Homework – 25% Two tests spaced evenly – 12.5% eachTwo tests spaced evenly – 12.5% each

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LabsLabs Paced slowly at firstPaced slowly at first

Familiarization with tools, simple Familiarization with tools, simple combinational design, design a digital lock combinational design, design a digital lock or similaror similar

Peripheral – VGA, opt. keyboard Peripheral – VGA, opt. keyboard interface or joystickinterface or joystick

Build up computer componentsBuild up computer componentsRegisters, ALU, decoderRegisters, ALU, decoder

Assemble a simple MIPSAssemble a simple MIPS Add more features, enough for simple Add more features, enough for simple computercomputer

Final demo – game or similarFinal demo – game or similar

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Lab SectionsLab Sections No lab this FridayNo lab this Friday

You need a little more info to beginYou need a little more info to beginBegin next weekBegin next week

Lab is in FB007Lab is in FB007

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Late PolicyLate Policy Homework assignments and lab reports Homework assignments and lab reports due by classdue by classLabs due on Monday after the lab periodLabs due on Monday after the lab period

One class late, 10 points offOne class late, 10 points off Two classes late, 25 points offTwo classes late, 25 points off Not accepted laterNot accepted later

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WhatWhat’’s Your Background?s Your Background? Course experienceCourse experience Work, etc.Work, etc. Which COMP411?Which COMP411? WhatWhat’’s your intent in taking class?s your intent in taking class?

Questions?Questions?

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Office HoursOffice Hours Would like to wait a week to setWould like to wait a week to set

Send email if you want to meet in the Send email if you want to meet in the mean timemean time

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Now Shift to TechnologyNow Shift to Technology

Should be review for all of youShould be review for all of you

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Digital vs. AnalogDigital vs. Analog Analog – infinite resolutionAnalog – infinite resolution

Like (old fashioned) radio dialLike (old fashioned) radio dialWeWe’’ll do very little with analogll do very little with analog

VGA, maybe soundVGA, maybe sound

Digital – a finite set of valuesDigital – a finite set of valuesLike moneyLike moneyCanCan’’t get smaller than centst get smaller than centsTypically also has maximum valueTypically also has maximum value

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Binary SignalingBinary Signaling Zero voltsZero volts

FALSE or 0FALSE or 0

5 or 3.3 (or 1.8 or 1.5) volts5 or 3.3 (or 1.8 or 1.5) voltsTRUE or 1TRUE or 1

Modern chips down to 1VModern chips down to 1V

Why not multilevel signaling?Why not multilevel signaling?

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Discrete DataDiscrete Data Some data inherently discreteSome data inherently discrete

Names (sets of letters)Names (sets of letters)

Some quantizedSome quantizedMusic recorded from microphoneMusic recorded from microphoneNote that other examples like music from CD Note that other examples like music from CD or electronic keyboard already quantizedor electronic keyboard already quantized

Mouse movement is quantizedMouse movement is quantizedWell, some miceWell, some mice

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Numbers and ArithmeticNumbers and Arithmetic I have put most of these slides at endI have put most of these slides at end

Backup in case youBackup in case you’’ve forgottenve forgotten Review of binary numbers, Review of binary numbers, Hexadecimal,Hexadecimal,ArithmeticArithmetic

LetLet’’s covers coverOther codes, parityOther codes, parity

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BCDBCD Binary Coded DecimalBinary Coded Decimal Decimal digits stored in binaryDecimal digits stored in binary

Four bits/digitFour bits/digit Like hex, except stops at 9Like hex, except stops at 9 ExampleExample

931 is coded as 1001 0011 0001931 is coded as 1001 0011 0001

Remember: these are just Remember: these are just encodingsencodings. Meanings . Meanings are assigned by us.are assigned by us.

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Other Codes ExistOther Codes Exist Non positionalNon positional Example: Gray CodeExample: Gray Code

Only one bit changes at a timeOnly one bit changes at a time000,001,011,010,110,111,101,100000,001,011,010,110,111,101,100Why is this useful?Why is this useful?

Actually thereActually there’’s a family of Gray codess a family of Gray codes

Ref: http://lib-www.lanl.gov/numerical/bookcpdf/c20-2.pdf

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Shaft EncoderShaft Encoder

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Character CodesCharacter Codes From numbers to lettersFrom numbers to letters ASCIIASCII

Stands for American Standard Code for Stands for American Standard Code for Information InterchangeInformation Interchange

Only 7 bits definedOnly 7 bits defined

UnicodeUnicode You may make up your own code for the You may make up your own code for the MIPS VGAMIPS VGA

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ASCII tableASCII table

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Even ParityEven Parity Sometimes high-order bit of ASCII coded Sometimes high-order bit of ASCII coded to enable detection of errorsto enable detection of errors

Even parity – set bit to make number of Even parity – set bit to make number of 11’’s evens even

ExamplesExamplesA (01000001) with even parity is 01000001A (01000001) with even parity is 01000001

C (01000011) with even parity is 11000011C (01000011) with even parity is 11000011

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Odd ParityOdd Parity Similar except make the number of 1Similar except make the number of 1’’s s oddodd

ExamplesExamplesA (01000001) with odd parity is 11000001A (01000001) with odd parity is 11000001

C (01000011) with odd parity is 01000011C (01000011) with odd parity is 01000011

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Error DetectionError Detection Note that parity detects only simple Note that parity detects only simple errorserrorsOne, three, etc. bitsOne, three, etc. bits

More complex methods existMore complex methods exist Some that enable Some that enable recoveryrecovery of original of original infoinfoCost is more redundant bitsCost is more redundant bits

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TodayToday’’s Topicss Topics IntroductionIntroduction Digital logicDigital logic Number systemsNumber systems ArithmeticArithmetic CodesCodes ParityParity The encoding is keyThe encoding is key

Standards are used to agree on encodingsStandards are used to agree on encodings Special purpose codes for particular usesSpecial purpose codes for particular uses

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HomeworkHomework None, but…None, but… I expect you to know number systems well and I expect you to know number systems well and be able to do conversions and arithmeticbe able to do conversions and arithmetic Decimal – BinaryDecimal – Binary Binary – DecimalBinary – Decimal Decimal – HexDecimal – Hex Hex – DecimalHex – Decimal

Can do some of the problems – 1.7 to 1.27 are Can do some of the problems – 1.7 to 1.27 are all about conversion – if you think you need a all about conversion – if you think you need a refresher. Answers to odd numbered on book refresher. Answers to odd numbered on book website.website.

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ReadingReading Read Chapter 1Read Chapter 1

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Next ClassNext Class Combinational Logic BasicsCombinational Logic Basics

Next Week: Lab previewNext Week: Lab previewI will demo tools in class, probably I will demo tools in class, probably WednesdayWednesday

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Backup SlidesBackup Slides

Should be all review materialShould be all review material

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Binary NumbersBinary Numbers Strings of binary digits (Strings of binary digits (““bitsbits””))

One bit can store a number from 0 to 1One bit can store a number from 0 to 1nn bits can store numbers from 0 to 2 bits can store numbers from 0 to 2nn

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Binary – Powers of 2Binary – Powers of 2 Positional representation Positional representation Each digit represents a power of 2Each digit represents a power of 2

So 101 binary isSo 101 binary is

1 1 •• 2 222 + 0 + 0 • • 2211 + 1 + 1 •• 2 200

oror

1 1 • 4 + • 4 + 0 0 • 2 + • 2 + 1 1 • 1 = 5• 1 = 5

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Converting Binary to DecimalConverting Binary to Decimal Easy, just multiply digit by power of 2Easy, just multiply digit by power of 2 Just like a decimal number is Just like a decimal number is representedrepresented

Example follows Example follows

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Binary Binary Decimal Example Decimal Example

77 66 55 44 33 22 11 00

2277 2266 2255 2244 2233 2222 2211 2200

128128 6464 3232 1616 88 44 22 11

11 00 00 11 11 11 00 00

128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = 156 128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = 156

What is 10011100 in decimal?What is 10011100 in decimal?

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Decimal to BinaryDecimal to Binary A little more work than binary to A little more work than binary to decimaldecimal

Some examplesSome examples3 = 2 + 1 = 3 = 2 + 1 = 1111 (that (that’’s 1s 1••2211 + 1 + 1••2200))5 = 4 + 1 = 5 = 4 + 1 = 101101 (that (that’’s 1s 1••2222 + 0 + 0••2211 + 1 + 1••2200))

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Algorithm – Decimal to Algorithm – Decimal to BinaryBinary Find largest power-of-two smaller than Find largest power-of-two smaller than decimal numberdecimal number

Make the appropriate binary digit a Make the appropriate binary digit a ‘‘11’’ Subtract the power of 2 from decimalSubtract the power of 2 from decimal Do the same thing againDo the same thing again

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Decimal Decimal Binary Example Binary Example Convert 28 decimal to binaryConvert 28 decimal to binary

77 66 55 44 33 22 11 00

2277 2266 2255 2244 2233 2222 2211 2200

128128 6464 3232 1616 88 44 22 11

32 is too large, so use 16Binary 10000 Decimal 28 – 16 = 12

Binary 11000 Decimal 12 – 8 = 4Next is 8

Binary 11100 Decimal 4 – 4 = 0Next is 4

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HexadecimalHexadecimal Strings of 0s and 1s too hard to writeStrings of 0s and 1s too hard to write Use base-16 or Use base-16 or hexadecimalhexadecimal – 4 bits – 4 bits

DecDec BinBin HexHex

00 00000000 00

11 00010001 11

22 00100010 22

33 00110011 33

44 01000100 44

55 01010101 55

66 01100110 66

77 01110111 77

DecDec BinBin HexHex

88 10001000 88

99 10011001 99

1010 10101010 ??

1111 10111011 ??

1212 11001100 ??

1313 11011101 ??

1414 11101110 ??

1515 11111111 ??

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HexadecimalHexadecimal Letters to represent 10-15Letters to represent 10-15

DecDec BinBin HexHex

00 00000000 00

11 00010001 11

22 00100010 22

33 00110011 33

44 01000100 44

55 01010101 55

66 01100110 66

77 01110111 77

DecDec BinBin HexHex

88 10001000 88

99 10011001 99

1010 10101010 aa

1111 10111011 bb

1212 11001100 cc

1313 11011101 dd

1414 11101110 ee

1515 11111111 ff

•Power of 2Power of 2

•Size of byteSize of byte

Why useWhy usebase 16?base 16?

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Hex to BinaryHex to Binary

Convention – write 0x before numberConvention – write 0x before number Hex to Binary – just convert digitsHex to Binary – just convert digits

BinBin HexHex

00000000 00

00010001 11

00100010 22

00110011 33

01000100 44

01010101 55

01100110 66

01110111 77

10001000 88

10011001 99

10101010 aa

10111011 bb

11001100 cc

11011101 dd

11101110 ee

11111111 ff

0x2ac0x2ac

00100010 10101010 11001100

0x2ac = 0010101011000x2ac = 001010101100

No magic – remember hex digit = 4 bitsNo magic – remember hex digit = 4 bits

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Binary to HexBinary to Hex

Just convert groups of 4 bitsJust convert groups of 4 bits

BinBin HexHex

00000000 00

00010001 11

00100010 22

00110011 33

01000100 44

01010101 55

01100110 66

01110111 77

10001000 88

10011001 99

10101010 aa

10111011 bb

11001100 cc

11011101 dd

11101110 ee

11111111 ff

101001101111011101001101111011

10111011

55 33 77 bb

101001101111011 = 0x537b101001101111011 = 0x537b

0101 0101 0111 0111 0011 0011

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Hex to DecimalHex to Decimal Just multiply each hex digit by Just multiply each hex digit by decimal value, and add the results.decimal value, and add the results.

161633 161622 161611 161600

40964096 256256 1616 11

0x2ac0x2ac

2 2 • 256• 256 + 10 + 10 • 16• 16 + 12 + 12 • 1• 1 = 684= 684

DecDec HexHex

00 00

11 11

22 22

33 33

44 44

55 55

66 66

77 77

88 88

99 99

1010 aa

1111 bb

1212 cc

1313 dd

1414 ee

1515 ff

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Decimal to HexDecimal to HexAnalogous to decimal Analogous to decimal binary. binary.

1.1. Find largest power-of-16 smaller Find largest power-of-16 smaller than decimal numberthan decimal number

2.2. Divide by power-of-16. The integer Divide by power-of-16. The integer result is hex digit.result is hex digit.

3.3. The remainder is new decimal The remainder is new decimal number.number.

4.4. Do the same thing againDo the same thing again

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Decimal to HexDecimal to Hex

161633 161622 161611 161600

40964096 256256 1616 11

DecDec HexHex

00 00

11 11

22 22

33 33

44 44

55 55

66 66

77 77

88 88

99 99

1010 aa

1111 bb

1212 cc

1313 dd

1414 ee

1515 ff

684684

684/256 = 2684/256 = 2 0x2__

684%256 = 172684%256 = 172

172/16 = 10 = a172/16 = 10 = a 0x2a_172%16 = 12 = c172%16 = 12 = c 0x2ac

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OctalOctal Octal is base 8Octal is base 8 Similar to hexadecimalSimilar to hexadecimal

ConversionsConversions

Less convenient for use with 8-bit Less convenient for use with 8-bit bytesbytes

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Arithmetic -- additionArithmetic -- addition Binary similar to decimal arithmeticBinary similar to decimal arithmetic

00 11 11 00 00

++ 11 00 00 00 11

11 11 11 00 11

No carries 11 00 11 11 00 00

11 00 11 11 00

++ 11 00 11 11 11

11 00 11 11 00 11

Carries

1+1 is 2 (or 102), which results in a carry

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Arithmetic -- subtractionArithmetic -- subtraction

11 00 11 11 00

-- 11 00 00 11 00

00 00 11 00 00

No borrows 00 00 11 11 00

11 11 11 11 00

-- 11 00 00 11 11

00 11 00 11 11

Borrows

0 - 1 results in a borrow

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Arithmetic -- multiplicationArithmetic -- multiplication

11 00 11 11

00 00 00 00

11 00 11 11

11 11 00 11 11 11

Successive additions of multiplicand or zero,multiplied by 2 (102).

Note that multiplication by 102 just shifts bits left.

11 00 11 11

XX 11 00 11