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1

The Digital System Hierarchy

Systems(e.g., computers)

Functional Units(e.g., Registers, Memories, Arithmetic units, etc.)

Gates and Flip-Flops

Circuits

David Buchla modified by Weiqiang Sun. - Shanghai Jiao Tong University

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The Digital System Hierarchy

Systems(e.g., computers)

Functional Units(e.g., Registers, Memories, Arithmetic units, etc.)

Gates and Flip-Flops

Circuits

David Buchla modified by Weiqiang Sun. - Shanghai Jiao Tong University

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3

Digital Concepts

Digital Systems

Digital and analog signals (levels)

Digitization of Analog signals (values)

Digital representation of information, pulses Binary digits, logic levels and digital waveforms

Effect of noise on the digital signal

Integrated Chips (ICs) packages Basic logic operations

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Why This Course?

Isnt other courses greatenough?

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Just Digital is far from enough

Mechanical Transducers

(Car/Airplane Sensors,

MEMS, Nanopore)

Video

(Dig. Camera, LCD TV,

TFT Display)

Digital Storage

(DVD, Hard Disk, Flash)

Phone Lines, Cables

(DSL, Cable Modem)

E&M Waves

(Cellphone, Radio,

GPS)

Audio

(

MP3, Hearing Aid)

Digital World

(DT, DA)

Analog World(CT, CA)

Biochemical Sensors

(Hazard detection, Drug

Delivery, Lab-on-a-Chip)

Paul Grays eggshell diagram

From: Professor Y. Chiu - EECT 7327 Data Converters

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Advantages of Digital

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Advantages of Digital Noise immunity, robustness

Unlimited precision or accuracy

Flexibility, programmability, and scalability

Electronic design automation (EDA) tools widely available and successful

Benefiting from Moores lawThe number of transistors on a chip

doubles every 18 months, IEDM, 1975

Cost/function drops 29% every year

Thats 30X in 10 years

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Whats the temperature?

Ref: http://bit.ly/wrgSSF

Chapter 1 Digital Concepts

http://bit.ly/wrgSSFhttp://bit.ly/wrgSSF

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Graph of an analog quantity

analogquantity: has continuous values

most natural quantities that we experience are analog:

temperature, speed, force, sound intensity,

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Sampling and quantisation

Samplingtakes snapshots of signal (generally at regularly spaced time intervals)

Quantisationrounds the amplitude to the nearest predefined value

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Sampling and quantisation

Analog

Sampling

Quantisation

Digital

A digital signaltakes one of a finite number of values ateach sampling interval

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Analog-to-digital conversion

Ananalog-to-digital converter (ADC)converts an analog

signal to a series of 1s and 0s

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Analog-to-digital conversion

How many discrete quantization levels

for this 4-bit ADC? 16 levels (0,1,,15)

How many levels for an n-bit ADC? 2n

levels

How many discrete quantization levels

for this 4-bit ADC?

How many levels for an n-bit ADC?

4-bit ADC

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and from digital back to analog

Digital-to-analog converter (DAC)

Digital information stored on compact disc

Scale at bottom of figure shows 1m intervals

1 m = 10-6m = 0.000001m

Ref: M. G. Carasso et al., Compact disc: Digital audio, Philips

Tech. Rev., 40(6):151180, 1982

http://bit.ly/y8Ug2t

Digital audio (CD): 44.1 kHz sampling,

16-bits on each stereo channel

http://bit.ly/y8Ug2thttp://bit.ly/y8Ug2t

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The digital advantage

Immunity to noise

Can reconstruct a digital signal even if it is contaminated by noise, by

rounding to the nearest level

Works for small amounts of noise

Flexibility

Can treat data, audio, video, images etc in the same way as each other

Can process, compress, store, and transmit data more efficiently thananalog

Cost

Digital equipment is cheap, and getting cheaper

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Introductory concepts

Digital and analog quantities

Binary digits, logic levels and digital

waveforms

Basic logic operations

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Binary digits

time

digital signal value

High

Low

(only 2

values)

Binary Signal

Binary system has just two digits: 1 and 0

Each digit is called a bit= binary digit

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Logic levels

Digital electronics uses circuits

that have two states

These states are represented by

two different voltage levelscalled HIGHand LOW

The voltages represent numbers

in the binary number system

HIGH=1 and LOW=0

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Logic levels

Range of LOW and HIGH

voltages depends on the digital

circuit technology being used

One type of circuit technology isCMOS

CMOS = Complementary Metal-

Oxide Semiconductor

For CMOS:

LOW range: 0V to 0.8V

HIGH range: 2V to 3.3V

+3.3V

+0.8V

+2V

0V

Logic HIGH (1)

Undefined logic

Logic LOW (0)

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Positive-going pulse: LOW logic level to a HIGHlevel and then back again

Negative-going pulse: HIGH to LOW to HIGH

Digital waveforms

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Rise timetr andfall timetf Measured between 10% to 90% of pulse amplitude

Pulse widthtw Measured between 50% points on rising and falling edges

Non-ideal pulses

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Waveform characteristics

Periodicpulse waveforms

Composed of pulses that

repeat in a fixed interval called

the period (T)

measured in seconds (s)

The frequency (f)is the rate it

repeats

measured in hertz (Hz)

T

f 1

f

T 1

What is the period of a

repetitive wave if f = 1 GHz?

(1GHz = 109Hz)

Period = 1/109= 10-9s= 1ns

What is the period of a

repetitive wave if f = 1 GHz?

(1GHz = 109Hz)

Period =

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A digital waveform carries binary information

In digital systems, all waveforms are synchronised with a

basic periodic timing waveform called the clock

Example:the speed of a computer is measured by the clock

frequency of its microprocessor, e.g. 3.5 GHz

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Clock frequency= 1MHz

Time to transfer 8 bits in waveform A = 8sTime to transfer 8 bits in waveform A =

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A timing diagramis used to show the relationship between

two or more digital waveforms

A diagram like this can be observed

directly on a logic analyzer

Timing diagrams

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2009 Pearson Education, Upper Saddle River,Floyd, Digital

Summar

yProgrammable Logic

Programmable logic devices (PLDs) are an alternative

to fixed function devices. The logic can be

programmed for a specific purpose. In general, they

cost less and use less board space that fixed function

devices.

Fixed ORarray and

output logic

ProgrammableAND array

A PAL device is a form of PLD that uses a

combination of a programmable AND array and a

fixed OR array:

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Selected Key

Terms

Analog

Digital

Binary

Bit

Pulse

Being continuous or having continuous values.

Related to digits or discrete quantities; having a set

of discrete values.

Having two values or states; describes a numbersystem that has a base of two and utilizes 1 and 0

as its digits.

A binary digit, which can be a 1 or a 0.

A sudden change from one level to another,

followed after a time, called the pulse width, by a

sudden change back to the original level.

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Selected Key

Terms

Clock

Gate

NOT

AND

OR

A basic timing signal in a digital system; a periodic

waveform used to synchronize actions.

A logic circuit that performs a basic logic

operations such as AND or OR.

A basic logic function that performs inversion.

A basic logic operation in which a true (HIGH)

output occurs only when all input conditions are

true (HIGH).

Abasic logic operation in which a true (HIGH)

output occurs when when one or more of the

input conditions are true (HIGH).

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Selected Key

Terms

Fixed-function

logic

Programmable

logic

A category of digital integrated circuits having

functions that cannot be altered.

A category of digital integrated circuits capable

of being programmed to perform specified

functions.

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1. Compared to analog systems, digital systems

a. are less prone to noise

b. can represent an infinite number of values

c. can handle much higher power

d. all of the above

2008 Pearson

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2009 Pearson Education, Upper Saddle River,Floyd, Digital

Summar

yTest and Measurement Instruments

The logic analyzer can display multiple channels of

digital information or show data in tabular form.

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Introductory concepts

Digital and analog quantities

Binary digits, logic levels and digital

waveforms

Basic logic operations

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Logic

Propositions: statements which are true if certain

conditions are true

Example: The light is on is true if:

the bulb is not burned out AND the switch is on

Boolean algebra: formulate logic statements with symbols

named after Irish mathematician George Boole c1850

Three basic logic operations: AND, OR, NOT

Just the basics today lots more in Weeks 3 and beyond

Logisim: demo free software package for logic simulation

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NOT

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AND

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OR