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Chapter 1Chapter 1

Introduction to Digital Systems DesignIntroduction to Digital Systems Design

ECEn 224ECEn 224

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Digital vs. AnalogDigital vs. Analog

Analog systems represent informationAnalog systems represent information

using physical quantitiesusing physical quantities

Voltage on a wire, magnetic field strengthVoltage on a wire, magnetic field strength Digital systems represent informationDigital systems represent information

using binary digits, orusing binary digits, orbitsbits

1 or 0, high or low, on or off1 or 0, high or low, on or off

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Positional Number SystemsPositional Number Systems

Two discrete values are insufficient forTwo discrete values are insufficient for

most applicationsmost applications

We combine bits to represent more valuesWe combine bits to represent more values We use a positional number system forWe use a positional number system for

binary just like we do in decimalbinary just like we do in decimal

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Positional Number SystemsPositional Number Systems

DecimalDecimal, base 10, base 10,, means we have 10 digits (0means we have 10 digits (0--9)9)

Decimal example:Decimal example:

103210321010 = 1= 1x10x1033 + 0+ 0x10x1022 +3+3x10x1011 + 2+ 2x10x1000

HexadecimalHexadecimal, base 16, means we have 16 digits (0, base 16, means we have 16 digits (0--9, A9, A--F)F)

Hexadecimal example:Hexadecimal example:

2A52A51616 = 2= 2x16x1622 + 10+ 10x16x1611 + 5+ 5x16x1600 = 512 + 160 + 5 = 677= 512 + 160 + 5 = 677

BinaryBinary, base 2, follows the same pattern, base 2, follows the same pattern

Binary example:Binary example:

1011101122 = 1= 1x2x233

+ 0+ 0x2x222 + 1+ 1x2x211 + 1+ 1x2x200 = 8 + 0 + 2 + 1 = 11= 8 + 0 + 2 + 1 = 11

Counting in any base is analogous to counting in decimalCounting in any base is analogous to counting in decimal

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Digital vs. AnalogDigital vs. Analog

Analog thermometerAnalog thermometer

0V to 10V, could be used to represent 00V to 10V, could be used to represent 0 toto

100100 FF

Each 1/10Each 1/10thth volt represents 1 degreevolt represents 1 degree

Digital thermometerDigital thermometer

77--bit binary number could be used tobit binary number could be used to

representrepresent 00 to 127to 127 FF

Seven bits can be used to represent theSeven bits can be used to represent the

numbers 0 to 127numbers 0 to 127

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Digital PrecisionDigital Precision

How would you represent 10.5How would you represent 10.5 F?F?

Analog example: 1.05VAnalog example: 1.05V

Digital example: ????Digital example: ???? 0001010000101022 = 10= 101010

0001011000101122 = 11= 111010

We must either add bits or decrease theWe must either add bits or decrease therangerange

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Digital PrecisionDigital Precision

99--bit thermometer, 0bit thermometer, 0 to 127.75to 127.75 FF Each discrete number increase represents 0.25Each discrete number increase represents 0.25 FF

10.510.5 FF 10.5/0.25 = 42 = 10101010.5/0.25 = 42 = 10101022

77--bit thermometer, 0bit thermometer, 0 to 12.7to 12.7 FF Each discrete number represents 12.7Each discrete number represents 12.7/127 = 0.1/127 = 0.1 FF

10.510.5 FF 10.5/0.1 = 105 = 110100110.5/0.1 = 105 = 110100122

It is not possible to representIt is not possible to represent allallvalues exactlyvalues exactly

using digital representationusing digital representation Example: 1/3 cant be represented in binary, just likeExample: 1/3 cant be represented in binary, just like

it cant be represented in decimalit cant be represented in decimal

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Example: Analog PhotographyExample: Analog Photography

An analog camera uses a chemicalAn analog camera uses a chemical

reaction in the film when exposed to lightreaction in the film when exposed to light

The amount of exposure is directly relatedThe amount of exposure is directly relatedto the amount of light that hits the filmto the amount of light that hits the film

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Example: Digital PhotographyExample: Digital Photography

A digital camera uses an array of lightA digital camera uses an array of light--

sensitive receptors that measure the lightsensitive receptors that measure the light

as a binary numberas a binary number

Image quality is determined mostly by twoImage quality is determined mostly by two

factors:factors:

The number of bits per pixelThe number of bits per pixel

The number of pixels per imageThe number of pixels per image

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Example: Digital PhotographyExample: Digital Photography

1284x897 pixels, 24-bit color




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Analog vs. Digital StorageAnalog vs. Digital Storage

Analog storage mediums fade over time due toAnalog storage mediums fade over time due to

gradual physical degradationgradual physical degradation

Photos turn yellow with timePhotos turn yellow with time

Cassette audio tapes lose their clarityCassette audio tapes lose their clarity

Digital storage mediums dont fade like analogDigital storage mediums dont fade like analog

If a 0 or 1 fades it will still be a 0 or 1If a 0 or 1 fades it will still be a 0 or 1

A .jpg image taken 10 years ago isA .jpg image taken 10 years ago is exactlyexactlythethesame todaysame today

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Analog vs. Digital StorageAnalog vs. Digital Storage

Making an analog copy implies measuring theMaking an analog copy implies measuring the

storage mediumstorage medium

Always introduces some errorsAlways introduces some errors

Copies of copies are even worseCopies of copies are even worse

Making digital copies implies distinguishing 0sMaking digital copies implies distinguishing 0s

from 1s so copies are exactfrom 1s so copies are exact

Copies can be made without any errorCopies can be made without any error Copies of copies are identicalCopies of copies are identical

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Analog vs. Digital ProcessingAnalog vs. Digital Processing

Modern computers and digital circuitsModern computers and digital circuits

make it easy to do extremely complexmake it easy to do extremely complex

processingprocessing

Digital processing allows precision andDigital processing allows precision and

error to be exactly predictederror to be exactly predicted

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Combinational vs. Sequential CircuitsCombinational vs. Sequential Circuits

Digital circuits consist of binary inputs andDigital circuits consist of binary inputs andoutputsoutputs

In combinational circuits, the output is a directIn combinational circuits, the output is a directfunction of its inputsfunction of its inputs

In sequential circuits the output depends on theIn sequential circuits the output depends on thecurrent input and previous inputscurrent input and previous inputs Sequential circuits contain memory that tracks stateSequential circuits contain memory that tracks state

A clock is used to signal when to change statesA clock is used to signal when to change states

AB

CD

XY

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Combinational vs. SequentialCombinational vs. Sequential

Combinational example: Clock chimeCombinational example: Clock chime

Inputs:Inputs: secondsseconds andand minutesminutes

Output:Output: chimechime

Behavior: OutputBehavior: Output chimechime is 1 if and only ifis 1 if and only ifsecondsseconds isis0 and0 and minutesminutes is 0, 15, 30, or45.is 0, 15, 30, or45.

Sequential example: CounterSequential example: Counter

Inputs:Inputs: incinc andand clkclk

Output:Output: countcount

Behavior: Increment count onBehavior: Increment count on clkclk edge if and only ifedge if and only if

incinc is 1is 1

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