Week 01A - Intro
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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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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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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