l01 introduction

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Digital Design Chapter 1: Introduction Slides to accompany the textbook Digital Design, with RTL Design, VHDL, and Verilog, 2nd Edition, by Frank Vahid, John Wiley and Sons Publishers, 2010. http://www.ddvahid.com Copyright © 2010 Frank Vahid Instructors of courses requiring Vahid's Digital Design textbook (published by John Wiley and Sons) have permission to modify and use these slides for customary course-related activities, subject to keeping this copyright notice in place and unmodified. These slides may be posted as unanimated pdf versions on publicly-accessible course websites.. PowerPoint source (or pdf with animations) may not be posted to publicly-accessible websites, but may be posted for students on internal protected sites or distributed directly to students by other electronic means. Instructors may make printouts of the slides available to students for a reasonable photocopying charge, without incurring royalties. Any other use requires explicit permission. Instructors may obtain PowerPoint source or obtain special use permissions from Wiley – see http://www.ddvahid.com for information.

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  • Digital Design 2eCopyright 2010Frank Vahid

    1

    Digital DesignChapter 1: Introduction

    Slides to accompany the textbook Digital Design, with RTL Design, VHDL, and Verilog, 2nd Edition,

    by Frank Vahid, John Wiley and Sons Publishers, 2010. http://www.ddvahid.com

    Copyright 2010 Frank VahidInstructors of courses requiring Vahid's Digital Design textbook (published by John Wiley and Sons) have permission to modify and use these slides for customary course-related activities, subject to keeping this copyright notice in place and unmodified. These slides may be posted as unanimated pdf versions on publicly-accessible course websites.. PowerPoint source (or pdf with animations) may not be posted to publicly-accessible websites, but may be posted for students on internal protected sites or distributed directly to students by other electronic means. Instructors may make printouts of the slides available to students for a reasonable photocopying charge, without incurring royalties. Any other use requires explicit permission. Instructors may obtain PowerPoint source or obtain special use permissions from Wiley see http://www.ddvahid.com for information.

  • Some Useful Information Where can I get help

    www.cse.nd.edu/courses/cse20221/www/ TAs during lab time: M,T,W,T,F 3:00 5:20 email [email protected] 325 D Cushing Hall 108 Stinson-Remick on Tues. & Thurs. during lab

    What will make the lab easier If there is a video for the lab, view it before you come to lab Download the Xilinx software for lab on your personal computer Review the lab assignment before you come to lab Complete the design work before you come to lab

    2

  • Questions? Is there lab this week? No Are there copies of the lecture? Yes, on course web site. When are the lectures updated? 30 minutes before class. Do I have to come to my assigned lab time? Yes Can I demo my lab work at another lab time? Yes Can I get late homework or lab work graded? No Is digital logic design really all that important? Only if you

    want things like an iPhone, iPod, computer, CDs or CD players

    Is this course difficult. No Is this course fun? Absolutely!

    3

  • Digital Design 2eCopyright 2010Frank Vahid

    4

    Why Study Digital Design? Look under the hood of computers

    Solid understanding --> confidence, insight, even better programmer when aware of hardware resource issues

    Electronic devices becoming digital Enabled by shrinking and more capable chips Enables:

    Better devices: Sound recorders, cameras, cars, cell phones, medical devices,...

    New devices: Video games, PDAs, ... Known as embedded systems

    Thousands of new devices every year Designers needed: Potential career direction

    1995

    Portablemusic players

    1997

    Satellites

    1999

    Cell phones

    2001

    DVDplayers

    Videorecorders

    Musicalinstruments

    2003

    Cameras TVs ???

    2005 2007 Years shown above indicate when digital version began to dominate

    (Not the first year that a digital version appeared)

    1.1

  • Digital Design 2eCopyright 2010Frank Vahid

    5

    What Does Digital Mean? Analog signal

    Infinite possible values Ex: voltage on a wire

    created by microphone

    valu

    e

    timeva

    lue

    time

    microphone

    Sound waves

    which movesthe magnet,

    which createscurrent in the nearby wire

    move themembrane,

    analog signal

    3 421

    2 digital signal

    Digital signal Finite possible values

    Ex: button pressed on a keypad

    01234

    Possible values:1.00, 1.01, 2.0000009, ... infinite possibilities

    Possible values:0, 1, 2, 3, or 4.Thats it.

    1.2

    a

    a

  • Digital Design 2eCopyright 2010Frank Vahid

    6

    Digital Signals with Only Two Values: Binary Binary digital signal -- only two

    possible values Typically represented as 0 and 1 One binary digit is a bit Well only consider binary digital signals Binary is popular because

    Transistors, the basic digital electric component, operate using two voltages (more in Chpt. 2)

    Storing/transmitting one of two values is easier than three or more (e.g., loud beep or quiet beep, reflection or no reflection)

    valu

    e

    time

    10

  • Digital Design 2eCopyright 2010Frank Vahid

    7

    Example of Digitization Benefit

    Analog signal (e.g., audio, video) may lose quality

    Voltage levels not saved/copied/transmitted perfectly

    Digitized version enables near-perfect save/cpy/tran.

    Sample voltage at particular rate, save sample using bit encoding

    Voltage levels still not kept perfectly

    But we can distinguish 0s from 1s

    time

    Volts

    0123

    original signal

    leng

    thy

    trans

    mis

    sion

    (e.g

    , cel

    l pho

    ne)

    time0123

    received signal

    How fix -- higher, lower, ?

    leng

    thy

    trans

    mis

    sion

    (e.g

    , cel

    l pho

    ne)

    01 10 11 10 11

    01 10 11 10 11

    Volts

    digitized signal

    time01

    a2d

    Volts

    0123

    d2aLet bit encoding be: 1 V: 012 V: 103 V: 11

    timeCan fixdistinguish 0s/1s, restore

    01

    Higher sampling rate and more bits per encoding improves re-creation

    a

    Not a perfect re-creation due to a2d and d2a

  • Digital Design 2eCopyright 2010Frank Vahid

    8

    Digitization Benefit: Can Store on Digital Media

    10 100100 11 11 11 01 10 10 0001

    2

    3

    Volts

    analog signalon wire

    time

    0001101011111101101000

    analog-to-digitalconverter

    samples

    digitized signalmicrophone

    wire

    (a)

    0001101011111101101000 read from tape, CD, etc.

    digital-to-analogconverter

    wire

    speaker

    10 100100 11 11 11 01 10 10 0001

    3

    Volts

    analog signalreproduced fromdigitized signal

    time

    2

    (b)

    a

    Store on CD, USB drive, etc. No deterioration.

  • Digital Design 2eCopyright 2010Frank Vahid

    9

    Digitized Audio: Compression Benefit Digitized audio can be

    compressed e.g., MP3s A CD can hold about 20

    songs uncompressed, but about 200 compressed

    Compression also done on digitized pictures (jpeg), movies (mpeg), and more

    Digitization has many other benefits too

    0000000000 0000000000 0000001111 1111111111

    10000001111

    Example compression scheme:00 means 000000000001 means 11111111111X means X

    a00 00 01

  • Digital Design 2eCopyright 2010Frank Vahid

    10

    How Do We Encode Data as Binary for Our Digital System?

    Some inputs inherently binary Button: not pressed (0),

    pressed (1) Some inputs inherently

    digital Just need encoding in

    binary e.g., multi-button input:

    encode red=001, blue=010, ...

    Some inputs analog Need analog-to-digital

    conversion As done in earlier slide --

    sample and encode with bits

    0

    button

    1

    green blackbluered

    0 00

    red

    0 10

    green blackblue

    1 00

    green blackbluered

    temperaturesensor

    air

    0 0 1 10 0 0 0

    33 degrees

    a

    sensors andother inputs

    Digital System

    actuators andother outputs

    A2D

    D2A

    analogphenomena

    electricsignal

    digitaldata

    digitaldata

    electricsignal

    digitaldata

    digitaldata

  • Digital Design 2eCopyright 2010Frank Vahid

    11

    How to Encode Text: ASCII, Unicode ASCII: 7- (or 8-)

    bit encoding of each letter, number, or symbol

    Unicode: Increasingly popular 16-bit encoding Encodes

    characters from various world languages

    Question: What does this ASCII bit sequence represent?

    1010010 1000101 1010011 1010100

    R E S Ta

    Sample ASCII encodingsSymbolEncoding

    010 0000 010 0001 !010 0010 "010 0011 #010 0100 $010 0101 %010 0110 &010 0111 '010 1000 (010 1001 )010 1010 *010 1011 +010 1100 ,010 1101 -010 1110 .010 1111 /

    SymbolEncoding100 1110 N100 1111 O101 0000 P101 0001 Q101 0010 R101 0011 S101 0100 T101 0101 U101 0110 V101 0111 W101 1000 X101 1001 Y101 1010 Z

    100 0001 A100 0010 B100 0011 C100 0100 D100 0101 E100 0110 F100 0111 G100 1000 H100 1001 I100 1010 J100 1011 K100 1100 L100 1101 M

    SymbolEncoding

    SymbolEncoding

    011 0000 0011 0001 1011 0010 2011 0011 3011 0100 4011 0101 5011 0110 6011 0111 7011 1000 8011 1001 9

    110 0001 a110 0010 b ...111 1001 y111 1010 z

  • Digital Design 2eCopyright 2010Frank Vahid

    12

    How to Encode Numbers: Binary Numbers Each position represents a

    quantity; symbol in position means how many of that quantity Base ten (decimal)

    Ten symbols: 0, 1, 2, ..., 8, and 9 More than 9 -- next position

    So each position power of 10 Nothing special about base 10 --

    used because we have 10 fingers Base two (binary)

    Two symbols: 0 and 1 More than 1 -- next position

    So each position power of 2

    24 23 22

    1 0 1

    21 20

    104 103 102

    5 2 3

    101 100

    Q: How much?+ =

    4 1 5+ =

    a

  • Digital Design 2eCopyright 2010Frank Vahid

    13

    Using Digital Data in a Digital System

    temperature sensor

    0 0 1 10 0 0 0 "33"

    Digital System

    display N

    "N"1 0 00 1 1 1

    if (input = "11010100") // "212"

    output = "1000010" // "B"

    else

    output = "1001110" // "N"

    A temperature sensor outputs temperature in binary

    The system reads the temperature, outputs ASCII code: F for freezing (0-32) B for boiling (212 or more) N for normal

    A display converts its ASCII input to the corresponding letter

    a

  • Digital Design 2eCopyright 2010Frank Vahid

    14

    Converting from Binary to Decimal Just add weights

    12 is just 1*20, or 110. 1102 is 1*22 + 1*21 + 0*20, or 610. We might think of this using

    base ten weights: 1*4 + 1*2 + 0*1, or 6. 100002 is 1*16 + 0*8 + 0*4 + 0*2 + 0*1, or 1610. 100001112 is 1*128 + 1*4 + 1*2 + 1*1 = 13510. Notice this time

    that we didnt bother to write the weights having a 0 bit. 001102 is the same as 1102 above the leading 0s dont change

    the value.

    a

    24 23 22 21 2029 28 27 26 25

    16 8 4 2 1512 256 128 64 32

    16 8 4 2 1512 256 128 64 32Practice counting up by powers of 2:

    Useful to know powers of 2:a

  • Digital Design 2eCopyright 2010Frank Vahid

    15

    Converting from Decimal to Binary

    Put 1 in leftmost place without sum exceeding number

    Track sum

    16 18 4 20

    16 18 4 28

    1

    16 18 4 212 1 1

    16 18 4 2done 1 1 00

    016 > 12, too big;Put 0 in 16s place

    8

  • Digital Design 2eCopyright 2010Frank Vahid

    16

    Converting from Decimal to Binary

    Example using a more compact notation 16 18 4 20

    1

    Desired decimalnumber: 23

    Binarynumber

    (a)

    (d)(c)

    (b)

    sum:16

    0

    1620

    1 1

    2223

    1

    (e)

    a

  • Digital Design 2eCopyright 2010Frank Vahid

    17

    Example: DIP-Switch Controlled Channel Ceiling fan

    receiver should be set in factory to respond to channel 73

    Convert 73 to binary, set DIP switch accordingly

    channel receiver

    Ceiling fanmodule

    0

    if (InA = InB)Out = 1

    elseOut = 0

    0 1 0 10 1 0 0"73"

    DIP switch

    10

    0 0 1 00 0 0 1

    InA InB

    Out

    Desired value: 73

    4

    0 02

    1116

    08

    132

    064

    1128

    0

    64 72 73sum:

    "34"

    (b)(a)

    (c)

    a

    Q:

  • Digital Design 2eCopyright 2010Frank Vahid

    18

    Base Sixteen: Another Base Used by Designers

    Nice because each position represents four base-two positions Compact way to write binary numbers

    Known as hexadecimal, or just hex

    164 163 162

    8 A F

    8

    1000 1010 1111

    A F

    161 160

    00000001001000110100010101100111

    01234567

    hex binary

    10001001101010111100110111101111

    89ABCDEF

    hex binary

    Q: Write 11110000 in hex

    F 0 a

    Q: Convert hex A01 to binary

    1010 0000 0001

    a

  • Digital Design 2eCopyright 2010Frank Vahid

    19

    Decimal to Hex Easy method: convert to binary first, then binary to hex

    Convert 99 base 10 to hex

    First convert to binary: 0 1 10 0114 2 116 83264128

    0

    Then binary to hex:6 3

    (Quick check: 6*16 + 3*1 = 96+3 = 99)

    a

    a

    a

  • Digital Design 2eCopyright 2010Frank Vahid

    20

    Hex Example: RFID Tag Batteryless tag powered by radio field

    Transmits unique identification number Example: 32 bit id

    8-bit province number, 8-bit country number, 16-bit animal number Tag contents are in binary But programmers use hex when writing/reading

    RFIDtag

    Province # City # Animal #

    Province: 7 City: 160 Animal: 513

    1010000000000111 00000010 00000001A007 02 01

    Tag ID in hex: 07A00201

    (a)

    (b)

    (c)(d)

    (f)

    (e)

  • Digital Design 2eCopyright 2010Frank Vahid

    21

    Converting To/From Binary by Hand: Summary

    BinaryDecimal

    16 8 4

    0 1 0

    2 1

    1 1

    16 + 8 + 2

    To decimal

    To hex

    1 1010

    = 2610

    = 1A16

    To octal

    11 010= 328

    2610

    To binary

    4

    0 1

    2

    0

    116

    1

    8

    1

    1616+8= 24 24 --24+2

    = 26

  • Digital Design 2eCopyright 2010Frank Vahid

    22

    Divide-By-2 Method Common in Automatic Conversion Repeatedly divide decimal number by 2, place remainder

    in current binary digit (starting from 1s column)

    1. Divide decimal number by 2 Insert remainder into the binary number Continue since quotient (6) is greater than 0

    2. Divide quotient by 2 Insert remainder into the binary number Continue since quotient (3) is greater than 0

    01

    18

    14

    02

    01

    14

    02

    01

    01

    02

    Decimal Binary

    12212

    0

    6

    6260

    3

    3. Divide quotient by 2 Insert remainder into the binary number Continue since quotient (1) is greater than 0

    3221

    1

    4. Divide quotient by 2 Insert remainder into the binary number Quotient is 0, done

    1201

    0

    (current value: 12)

    (current value: 4)

    (current value: 0)

    (current value: 0)

    Note: Works for any base Njust divide by N instead

  • Dibble-Dabble Algorithm2|12 r = 0 least significant bit2|6 r = 0 2|3 r = 1 2|1 r = 1 most significant bit

    12 10 = 11002

    23

  • Digital Design 2eCopyright 2010Frank Vahid

    24

    Bytes, Kilobytes, Megabytes, and More Byte: 8 bits Common metric prefixes:

    kilo (thousand, or 103), mega (million, or 106), giga (billion, or 109), and tera (trillion, or 1012), e.g., kilobyte, or KByte

    BUT, metric prefixes also commonly used inaccurately 216 = 65536 commonly written as 64 Kbyte Typical when describing memory sizes

    Also watch out for KB for kilobyte vs. Kb for kilobit

  • Digital Design 2eCopyright 2010Frank Vahid

    25

    Implementing Digital Systems: Programming Microprocessors Vs. Designing Digital Circuits

    Microprocessors a common choice to implement a digital system

    Easy to program Cheap (as low as

    $1) Readily available

    I3I4I5I6I7

    I2I1I0

    P3P4P5P6P7

    P2P1P0 void main()

    {while (1) {

    P0 = I0 && !I1; // F = a and !b,

    }} 0

    F

    b

    a

    10101

    6:00 7:057:06 9:009:01 time

    Desired motion-at-night detectorProgrammed

    microprocessorCustom designed

    digital circuit

    1.3

  • Digital Design 2eCopyright 2010Frank Vahid

    26

    Digital Design: When Microprocessors Arent Good Enough

    With microprocessors so easy, cheap, and available, why design a digital circuit? Microprocessor may be too

    slow Or too big, power hungry, or

    costly

    Wing controller computation task:

    50 ms on microprocessor

    5 ms as custom digital circuit

    If must execute 100 times per second:

    100 * 50 ms = 5000 ms = 5 seconds

    100 * 5 ms = 500 ms = 0.5 seconds

    Microprocessor too slow, circuit OK.

  • Digital Design 2eCopyright 2010Frank Vahid

    27

    Digital Design: When Microprocessors Arent Good Enough

    Commonly, designers partition a system among a microprocessor and custom digital circuits (a)

    Micro-processor

    (Read,Compress,and Store)Memory

    Image Sensor

    (b)

    (c)

    Sample digital camera task execution times (in seconds) on a microprocessor versus a digital circuit:

    Q: How long for each implementation option?

    a

    5+8+1=14 sec

    .1+.5+.8=1.4 sec

    .1+.5+1=1.6 sec

    Good compromise

    Readcircuit

    Compresscircuit

    Memory Storecircuit

    Image Sensor

    Compresscircuit

    Microprocessor(Store)Memory

    Image Sensor Readcircuit

    Task Microprocessor Custom Digital Circuit

    Read 5 0.1

    Compress 8 0.5

    Store 1 0.8

  • 28

    Chapter 1 Summary Digital systems surround us

    Inside computers Inside many other electronic devices (embedded systems)

    Digital systems use 0s and 1s Encoding analog signals to digital can provide many benefits

    e.g., audiohigher-quality storage/transmission, compression, etc. Encoding integers as 0s and 1s: Binary numbers

    Microprocessors (themselves digital) can implement many digital systems easily and inexpensively But often not good enoughneed custom digital circuits

  • Digital Design 2eCopyright 2010Frank Vahid

    29

    Chapter 2 Introduction Lets learn to design digital circuits, starting with a

    simple form of circuit: Combinational circuit

    Outputs depend solely on the present combination of the circuit inputs values

    2.1

    Note: Slides with animation are denoted with a small red "a" near the animated items

    DigitalSystem

    b=0 F=0

    DigitalSystem

    if b=0, then F=0if b=1, then F=1

    b=1 F=1

    DigitalSystem

    b=0 F=0

    (a)

    DigitalSystem

    b=1 F=1

    Vs. sequential circuit: Has memory that impacts outputs too

    a

    Motionsensor Digital

    System

    Lightsensor

    Lamp

    a

    b

    F

    if a=0 and b=0, then F=0if a=0 and b=1, then F=0if a=1 and b=0, then F=1if a=1 and b=1, then F=0(b)

    a

    DigitalSystem

    b=0 F=1

    Cannot determine value ofF solely from presentinput value

    (c)a

  • Digital Design 2eCopyright 2010Frank Vahid

    30

    Switches Electronic switches are the basis of

    binary digital circuits Electrical terminology

    Voltage: Difference in electric potential between two points (volts, V)

    Analogous to water pressure Resistance: Tendency of wire to resist

    current flow (ohms, ) Analogous to water pipe diameter

    Current: Flow of charged particles (amps, A) Analogous to water flow

    V = I * R (Ohms Law) 9 V = I * 2 ohms I = 4.5 A

    4.5 A

    4.5

    A

    4.5 A

    2 ohms

    9 V

    0V 9V

    +

    2.2

    If a 9V potential difference is appliedacross a 2 ohm resistor, then 4.5 A of current will flow.

    a

  • Digital Design 2eCopyright 2010Frank Vahid

    31

    Switches A switch has three parts

    Source input, and output Current tries to flow from source

    input to output Control input

    Voltage that controls whether that current can flow

    The amazing shrinking switch 1930s: Relays 1940s: Vacuum tubes 1950s: Discrete transistor 1960s: Integrated circuits (ICs)

    Initially just a few transistors on IC Then tens, hundreds, thousands...

    off

    on

    outputsourceinput

    outputsourceinput

    controlinput

    controlinput

    (b)

    relay vacuum tube

    discrete transistor

    IC

    quarter(to see the relative size)

    a

  • Digital Design 2eCopyright 2010Frank Vahid

    32

    Moores Law IC capacity doubling about every 18 months

    for several decades Known as Moores Law after Gordon Moore,

    co-founder of Intel Predicted in 1965 predicted that components

    per IC would double roughly every year or so Book cover depicts related phenomena

    For a particular number of transistors, the IC area shrinks by half every 18 months

    Consider how much shrinking occurs in just 10 years (try drawing it)

    Enables incredibly powerful computation in incredibly tiny devices

    Todays ICs hold billions of transistors The first Pentium processor (early 1990s)

    needed only 3 million

    An Intel Pentium processor IChaving millions of transistors

  • Digital Design 2eCopyright 2010Frank Vahid

    33

    The CMOS Transistor CMOS transistor

    Basic switch in modern ICs

    does notconduct

    0

    conducts

    1gate

    nMOS

    does notconduct

    1gate

    pMOS

    conducts

    0

    Silicon -- not quite a conductor or insulator:Semiconductor

    2.3

    a

    gate

    source drainoxide

    A positive voltage here...

    (a)

    IC package

    IC

    ...attracts electrons here, turning the channel betweenthe source and drain intoa conductor

  • Digital Design 2eCopyright 2010Frank Vahid

    34

    CMOS Transistor Analogy

    gatesource

    draindrain

    sourcegate

  • Digital Design 2eCopyright 2010Frank Vahid

    35

    Boolean Logic GatesBuilding Blocks for Digital Circuits

    (Because Switches are Hard to Work With)

    Logic gates are better digital circuit building blocks than switches (transistors) Why?...

    2.4

  • Digital Design 2eCopyright 2010Frank Vahid

    36

    Boolean Algebra and its Relation to Digital Circuits To understand the benefits of logic gates vs. switches,

    we should first understand Boolean algebra Traditional algebra

    Variables represent real numbers (x, y) Operators operate on variables, return real numbers (2.5*x + y - 3)

    Boolean Algebra Variables represent 0 or 1 only Operators return 0 or 1 only Basic operators

    AND: a AND b returns 1 only when both a=1 and b=1 OR: a OR b returns 1 if either (or both) a=1 or b=1 NOT: NOT a returns the opposite of a (1 if a=0, 0 if a=1)

    a0011

    b0101

    AND0001 a

    0011

    b0101

    OR0111a

    01

    NOT10

    a

  • Digital Design 2eCopyright 2010Frank Vahid

    37

    Boolean Algebra and its Relation to Digital Circuits Developed mid-1800s by George Boole to formalize human thought

    Ex: Ill go to lunch if Mary goes OR John goes, AND Sally does not go. Let F represent my going to lunch (1 means I go, 0 I dont go) Likewise, m for Mary going, j for John, and s for Sally Then F = (m OR j) AND NOT(s)

    Nice features Formally evaluate

    m=1, j=0, s=1 --> F = (1 OR 0) AND NOT(1) = 1 AND 0 = 0 Formally transform

    F = (m and NOT(s)) OR (j and NOT(s)) Looks different, but same function Well show transformation techniques soon

    Formally prove Prove that if Sally goes to lunch (s=1), then I dont go (F=0) F = (m OR j) AND NOT(1) = (m OR j) AND 0 = 0

    a0011

    b0101

    AND0001

    a0011

    b0101

    OR0111

    a01

    NOT10

  • Digital Design 2eCopyright 2010Frank Vahid

    38

    Evaluating Boolean Equations Evaluate the Boolean equation F = (a AND b) OR (c

    AND d) for the given values of variables a, b, c, and d: Q1: a=1, b=1, c=1, d=0.

    Answer: F = (1 AND 1) OR (1 AND 0) = 1 OR 0 = 1. Q2: a=0, b=1, c=0, d=1.

    Answer: F = (0 AND 1) OR (0 AND 1) = 0 OR 0 = 0. Q3: a=1, b=1, c=1, d=1.

    Answer: F = (1 AND 1) OR (1 AND 1) = 1 OR 1 = 1.

    a

    a0011

    b0101

    AND0001

    a0011

    b0101

    OR0111

    a01

    NOT10

  • Digital Design 2eCopyright 2010Frank Vahid

    39

    Converting to Boolean Equations Convert the following English

    statements to a Boolean equation Q1. a is 1 and b is 1.

    Answer: F = a AND b Q2. either of a or b is 1.

    Answer: F = a OR b Q3. a is 1 and b is 0.

    Answer: F = a AND NOT(b) Q4. a is not 0.

    Answer: (a) Option 1: F = NOT(NOT(a)) (b) Option 2: F = a

    a

  • Homework Chapter 1: 2,10,16,18, 21 Due date: Thursday, January 27

    40

    Digital DesignSome Useful InformationQuestions?Why Study Digital Design?What Does Digital Mean?Digital Signals with Only Two Values: BinaryExample of Digitization BenefitDigitization Benefit: Can Store on Digital MediaDigitized Audio: Compression BenefitHow Do We Encode Data as Binary for Our Digital System?How to Encode Text: ASCII, UnicodeHow to Encode Numbers: Binary NumbersUsing Digital Data in a Digital SystemConverting from Binary to DecimalConverting from Decimal to BinaryConverting from Decimal to BinaryExample: DIP-Switch Controlled ChannelBase Sixteen: Another Base Used by DesignersDecimal to HexHex Example: RFID TagConverting To/From Binary by Hand: SummaryDivide-By-2 Method Common in Automatic ConversionDibble-Dabble AlgorithmBytes, Kilobytes, Megabytes, and MoreImplementing Digital Systems: Programming Microprocessors Vs. Designing Digital CircuitsDigital Design: When Microprocessors Arent Good EnoughDigital Design: When Microprocessors Arent Good EnoughChapter 1 SummaryChapter 2 IntroductionSwitchesSwitchesMoores LawThe CMOS TransistorCMOS Transistor AnalogyBoolean Logic GatesBuilding Blocks for Digital Circuits (Because Switches are Hard to Work With)Boolean Algebra and its Relation to Digital CircuitsBoolean Algebra and its Relation to Digital CircuitsEvaluating Boolean EquationsConverting to Boolean EquationsHomework