Transcript File

Digital
Fundamentals
Tenth Edition
Floyd
Chapter 1
© 2008 Pearson Education
What you will Learn in this Course?
• Towards the end of this course, you should be able to:
– Carry out arithmetic computation in various number systems
– Apply rules of Boolean algebra to simplify Boolean expressions
– Translate Boolean expressions into equivalent truth tables and
logic gate implementations and vice versa
– Design efficient combinational and sequential logic circuit
implementations from functional description of digital systems
– Carry out simple CAD simulations to verify the operation of logic
circuits
Is it Worth the Effort?
• Absolutely!
• Digital circuits are employed in the design of:
– Digital computers
– Data communication
– Digital phones
– Digital cameras
– Digital TVs, etc.
• This course presents the basic tools for the design of
digital circuits and provides the fundamental concepts
used in the design of digital systems
Which Book will be Used?
• “Digital Fundamentals”,
Thomas L. Floyd.
• Pearson Prentice Hall, Ninth
Edition.
• ISBN: 0-13-197255-3
• www.umartalha.weebly.com
Grading Policy
• Assignments & Quizzes
15%
• Project
10%
• Midterm Exam
25%
• Final Exam
50%
NO makeup exam will be given whatsoever
Introduction
• Digital is derived from the way computers
perform operations, by counting digits.
• In past digital electronics confined to
computer systems.
• Today, digital technology every where..
TV, radar, medicine, communication,
military, transportation..
Analog Quantities
Most natural quantities that we see are analog and vary
continuously. Analog systems can generally handle higher
power than digital systems.
Temperature
(°F)
100
95
90
85
80
75
70
Time of day
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
A .M .
P.M .
Digital systems can process, store, and transmit data more
efficiently but can only assign discrete values to each point.
Analog v/s Digital System
Are computers analog or digital systems?
Computer are digital systems
Which is easier to design an analog or a digital system?
Digital systems are easier to design, because they
deal with a limited set of values rather than an infinitely
large range of continuous values
The world around us is analog
It is common to convert analog parameters into digital form
This process is called digitization
Analog and Digital Systems
Many systems use a mix of analog and digital electronics to
take advantage of each technology. A typical CD player
accepts digital data from the CD drive and converts it to an
analog signal for amplification.
CD drive
10110011101
Digital data
Digital-to-analog
converter
Linear amplifier
Analog
reproduction
of music audio
signal
Speaker
Sound
waves
Analog and Digital Systems
Many systems use a mix of analog and digital electronics to
take advantage of each technology. A typical CD player
accepts digital data from the CD drive and converts it to an
analog signal for amplification.
CD drive
10110011101
Digital data
Digital-to-analog
converter
Linear amplifier
Analog
reproduction
of music audio
signal
Speaker
Sound
waves
ADC and DAC Converters
Analog-to-Digital Converter (ADC)
input analog
signals
Analog-to-Digital
Converter (ADC)
Produces digitized version of analog signals
Analog input => Digital output
Digital-to-Analog Converter (DAC)
input digital
signals
Digital System
Regenerate analog signal from digital form
Digital input => Analog output
Our focus is on digital systems only
Both input and output to a digital system are digital
signals
output digital
signals
Digital-to-Analog
Converter (DAC)
output analog
signals
Digital Advantages:
•Processed more efficiently and reliably
•Compact storage
•Greater accuracy
•Does not affected by noise as well as
analog values
Binary Digits and Logic Levels
Digital electronics uses circuits that have two states, which
are represented by two different voltage levels called HIGH
and LOW. The voltages represent numbers in the binary
system.
HIGH = 1 =True
LOW = 0 = False
Binary Digits and Logic Levels
Digital electronics uses circuits that have two states, which
are represented by two different voltage levels called HIGH
and LOW. The voltages represent numbers in the binary
system.
VH(max)
In binary, a single number is
called a bit (for binary digit).
The value of a bit is either 0 or
1, corresponding to signal
voltage LOW or HIGH,
respectively (example).
HIGH
VH(min)
Invalid
VL(max)
LOW
VL(min)
Digital Waveforms
Digital waveforms change between the LOW and HIGH
levels. A positive going pulse is one that goes from a
normally LOW logic level to a HIGH level and then back
again. Digital waveforms are made up of a series of pulses.
HIGH
HIGH
Rising or
leading edge
LOW
Falling or
trailing edge
t0
(a) Positive–going pulse
t1
Falling or
leading edge
LOW
Rising or
trailing edge
t0
(b) Negative–going pulse
t1
`
Pulse Definitions
Actual pulses are not ideal but are described by the rise time,
fall time, amplitude, and other characteristics.
Overshoot
Ringing
Droop
90%
Amplitude
tW
50%
Pulse width
10%
Ringing
Base line
Undershoot
tr
tf
Rise time
Fall time
Periodic Pulse Waveforms
Periodic pulse waveforms are composed of pulses that repeat
at fixed intervals (period). The frequency is the rate at which
the pulses repeat; measured in Hertz.
1
f 
T
1
T
f
Periodic Pulse Waveforms
Periodic pulse waveforms are composed of pulses that repeat
at fixed intervals (period). The frequency is the rate at which
the pulses repeat; measured in Hertz.
1
f 
T
1
T
f
The clock is a basic timing signal that is an example of a
periodic wave.
What is the period of a repetitive wave if f = 3.2 GHz?
T
1
1

 313 ps
f 3.2 GHz
Pulse Definitions
In addition to frequency and period, repetitive pulse waveforms
are described by the amplitude (A), pulse width (tW) and duty
cycle. Duty cycle is the ratio of tW to T.
Volts
Amplitude (A)
Pulse
width
(tW)
Time
Period, T
Pulse Definitions
In addition to frequency and period, repetitive pulse waveforms
are described by the amplitude (A), pulse width (tW) and duty
cycle. Duty cycle is the ratio of tW to T.
Duty Cycle = (tW / T)*100%
= (1ms / 10ms)*100%=
10%
Timing Diagrams
A timing diagram is used to show the relationship between
two or more digital waveforms,
Clock
A
B
C
A diagram like this can be observed
directly on a logic analyzer.
Serial and Parallel Data
Data can be transmitted by either serial transfer or parallel
transfer.
1
t0
0
t1
1
t2
1
t3
0
0
t 4 t 5 t6
1
0
t7
Computer
Modem
1
Computer
Printer
0
1
1
0
0
1
0
t0
t1
Basic Logic Functions
True only if all input conditions
are true.
True only if one or more input
conditions are true.
Indicates the opposite condition.
n-input Gates
Because + and * are binary operations, they can be
cascaded together to OR or AND multiple inputs.
A
B
C
A
B
A+B+C
ABC
C
A
B
C
A
B
C
A+B+C
ABC
n-input Gates
For convenience, it is sometimes useful to think of the
logic gates processing n-bits at a time. This really refers to
n instances of the logic gate, not a single logic date with ninputs.
1101100101
1101110111
0100110111
10001111
00111100
110001
00001100
001110
Basic System Functions
And, or, and not elements can be combined to form
various logic functions. A few examples are:
The comparison function
A
Comparator
A> B
Two
binary
numbers
A= B
B
Basic arithmetic functions
Outputs
A< B
Adder
A
Two
binary
numbers
B
Carry in
Cin
Σ
Cout
Sum
Carry out
Basic System Functions
HIGH
The encoding function
7
4
8
5
9
6
1
2
3
0
.
+/–
9
8
7
6
5
4
3
2
1
0
Encoder
Binary code
for 9 used for
storage and/or
computation
Calculator keypad
The decoding function
Decoder
Binary input
7-segment display
Basic System Functions
The data selection function
Multiplexer
A
∆t1
B
Demultiplexer
Data from
A to D
Data from
B to E
Data from
C to F
Data from
A to D
∆ t1
∆ t2
∆ t3
∆t 1
D
∆t1
E
∆t2
C
∆t2
∆t3
∆t3
Switching
sequence
control input
Switching
sequence
control input
F
Basic System Functions
The counting function
Counter
1
2
3
4
Input pulses
5
Parallel
output lines
Binary
code
for 1
Binary
code
for 2
Binary
code
for 3
Binary
code
for 4
Binary
code
for 5
Sequence of binary codes that represent
the number of input pulses counted.
…and other functions such as code conversion
and storage.
Basic System Functions
One type of storage function is the shift register,
that moves and stores data each time it is clocked.
Serial bits
on input line
0101
010
01
0
0 0 0 0
1 0 0 0
0 1 0 0
1 0 1 0
0 1 0 1
Initially, the register contains onlyinvalid
data or all zeros as shown here.
First bit (1) is shifted serially into the
register.
Second bit (0) is shifted serially into
register and first bit is shifted right.
Third bit (1) is shifted into register and
the first and second bits are shifted right.
Fourth bit (0) is shifted into register and
the first, second, and third bits are shifted
right. The register now stores all four bits
and is full.
Integrated Circuits
Cutaway view of DIP (Dual-In-line Pins) chip:
Chip
Plastic
case
Pins
The TTL series, available as DIPs are popular
for laboratory experiments with logic.
Integrated Circuits
An example of laboratory prototyping is shown. The circuit
is wired using DIP chips and tested.
DIP chips
In this case, testing can
be done by a computer
connected to the system.
Integrated Circuits
DIP chips and surface mount chips
Pin 1
Dual in-line package
Small outline IC (SOIC)
Integrated Circuits
Other surface mount packages:
End view
SOIC
End view
PLCC
End view
LCCC
Test and Measurement Instruments
The front panel controls for a general-purpose oscilloscope
can be divided into four major groups.
VERTICAL
CH 1
CH 2
HORIZONTAL
TRIGGER
BOTH
SLOPE
Ð
POSITION
POSITION
VOLTS/DIV
VOLTS/DIV
+
LEVEL
POSITION
SEC/DIV
SOURCE
CH 1
CH 2
5V
2 mV
5V
2 mV
5s
5 ns
EXT
LINE
COUPLING
COUPLING
AC-DC-GND
AC-DC-GND
TRIG COUP
DC
DISPLAY
PROBE COMP
5V
INTENSITY
CH 1
CH 2
EXT TRIG
AC
Vertical section
Signal coupling
Volts/Di v
AC
DC
Ch 1
GND
For measuring digital
Summary
signals, use DC coupling
Amp
Display section
Conversion/storage
(Digital scopes only)
Test and Measurement Instruments
AC
Ch 2
DC
GND
Vertical
position
Amp
Analog
only
Intensity
Conversion/storage
(Digital scopes only)
Digital
only
Horizontal
section
Trigger section
External trigger
coupling
External
trigger
Trigger
source
AC
DC
Ch 1
Ext
Line
AC
Power supply
Trigger
level and
slope
Ch 2
Control and process
(Digital scopes only)
Sec /Div
Trigger
circuits
Time base
Horizontal
position
Normally, trigger on the slower of two
waveforms when comparing signals.
DC to all sec tions
Test and Measurement Instruments
The logic analyzer can display multiple channels of digital
information or show data in tabular form.
0.01 V
Test and Measurement Instruments
OFF
V
Hz
V
The DMM can make three basic
electrical measurements.
mV
A
Range
Autorange
Touc h/Hold
1s
1s
10 A
V
Voltage
40 m A
COM
Fused
Resistance
Current
In digital work, DMMs are useful for checking power
supply voltages, verifying resistors, testing continuity,
and occasionally making other measurements.
Programmable 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 than fixed function devices.
A PAL device is a form of PLD that uses a
combination of a programmable AND array and a
fixed OR array:
Programmable
AND array
Fixed OR
array and
output logic
Selected Key Terms
Analog Being continuous or having continuous values.
Digital Related to digits or discrete quantities; having a set
of discrete values.
Binary Having two values or states; describes a number
system that has a base of two and utilizes 1 and 0
as its digits.
Bit A binary digit, which can be a 1 or a 0.
Pulse 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.
Selected Key Terms
Clock
A basic timing signal in a digital system; a periodic
waveform used to synchronize actions.
Gate A logic circuit that performs a basic logic
operations such as AND or OR.
NOT A basic logic function that performs inversion.
AND A basic logic operation in which a true (HIGH)
output occurs only when all input conditions are
true (HIGH).
OR A basic logic operation in which a true (HIGH)
output occurs when when one or more of the input
conditions are true (HIGH).
Selected Key Terms
Fixed-function A category of digital integrated circuits having
logic functions that cannot be altered.
Programmable A category of digital integrated circuits capable of
logic being programmed to perform specified functions.
SELF TEST
Assignment No 1
• Learning Activity
• Study different types of number systems
– Binary
– Decimal
– Octal
– Hexadecimal