- Explain the basic differences between analog and digital technology.
- Explain the basic differences between the different numbering systems (binary, octal, hexadecimal, and decimal) presented in this unit.
EET 130– Digital Systems I
Digital Concepts
2
Outline of the lecture
Digital and Analog quantities
Binary Digits, logic levels and digital waveforms
Classification of Integrated Circuit( IC) Packages
Advantages and disadvantages of digital systems
Objective of the Lecture
After successful completion of the lecture students
will be able to: Name examples of analog and digital signals
Identify and define the differences between analog and digital signals
and their characteristics
Show how voltage levels are used to represent digital quantities
Identify typical digital signals & a timing diagram
Recognize the advantages and disadvantages of digital systems
Describe various parameters of pulse waveform
Introduction
Digital electronics is essential to understanding the
design and working of a wide range of applications
consumer and industrial electronics
Communications, embedded systems
Computers, security, military equipment
Integrated Circuits that operate on Digital Data are in
95% of every electrical powered device in the U.S
The job market for electronic designers and
technicians with Digital Design skills is at an all time
high and will continue growing
5
Analog and Digital Signals
The term “ signal will appear many times in
this course
It is anything which conveys information
It could be a voltage or current waveform from
electronic circuits
It could be one, two or three dimensional
Quantifying signals helps us to decide how
to store and transmit messages
Analog and Digital signals…
Signals are met in diverse fields of engineering
Elec. Eng. – voltages/currents in a circuit, speech signals,
image signals, video signals
Physics – radiation
Mech. Eng. – vibration studies
Astronomy – (2-D) pulsars, distant stars
Biomedicine – EEG, ECG, retinoscopy, MRI
Seismology – tectonic plate movement, earthquake
prediction
Economics – level of trading in stock market
Metrology – weather forecast, GPS
Analog and Digital Signals …
Examples of signals
Analog Signals and Digital Signals
Analog signals are signals in which the independent variable
is continuous
These signals are defined for a continuum of values of the
independent variable
They are continuous in value, in time, or both.
They are electrical signals whose values vary in analogy
with a physical quantity, e.g., temperature, force,
acceleration
Digital Signals are signals in which the independent variable
takes a discrete set of values
These signals are defined only at discrete times. Digital
signals are discrete in value, in time, or both.
Analog Signals
In analog representation a quantity is
represented by a voltage, current, or meter
movement that is proportional to the value of
that quantity
Analog quantities vary over a continuous
range of values
Digital Signals
In digital representation the quantities are
represented by discrete quantities (symbols)
called digits
Digital watch is the best example of digital
representation
Difference between analog and digital signal
ANALOG SIGNAL – continuous in value, in time, or both
It is an electrical signal whose value varies in an analogy with a physical quantity, e.g., temperature, force, acceleration
DIGITAL SIGNAL – discrete
in value, in time, or both
Analog signal- one whose output varies continuously in step with the input.
Example:
Analog
Digital signal- one whose output varies at discrete voltage levels commonly called HIGH or LOW (1 or 0).
Example:
Digital HIGH or 1
LOW or 0
Time
Difference between analog and digital signal
Difference between analog and digital signal
Difference between analog and digital signal
Analog signals could take any value at any given time
Digital signals take one of two values at any given time
Examples of Analog Signals
Sound: telephone, radio, CD
Examples of Digital Signals
• Serial transfer of data between computers
• Parallel transfer of data between computer & printer
Application of Analog and Digital Circuits
Public Address System
Is used to amplify sound so that it can be heard
by a large audience
It is a simple example of analog systems
Application of Analog and Digital Circuits…
Compact Disk Players
is an example of a system in which both digital and
analog circuits are used
Application of Analog and Digital Circuits…
Digital Watches: in our day to day activity we often see and
use these electronic devices
Application of Analog and Digital Circuits…
Robotics and control applications
digital circuits are widely applied in a wide range of applications
from the flight and propulsion systems of commercial airliners to
the cruise control present in many modern automobiles
Robotic systems could be applied in industries for different
applications where humans could not reach due to environmental
hazards and life hazards
Application of Analog and Digital Circuits…
Automation
digital systems are widely applied in process automation in industries
an automated tablet counting system for pharmaceutical industries is
shown in the next slide
22
23
Advantages and Disadvantages of Digital Systems
The most common advantages of digital systems over analog
systems are:
Easier to design – exact values of voltage or current are
not important, only the range (HIGH or LOW) in which
they fall.
Flexibility – a digital system can be reconfigured for some
other operations by simply changing the software program
and hardware change is not required
Accuracy- analog systems suffer from component
tolerance, breakdown etc, whereas accuracy in digital
systems is decided by the resolution of the A/D converter
and number of bits used to represent digital data.
24
Advantages and Disadvantages of Digital Systems
Easy storage- in digital systems storage is very easy and due to
which remote processing of digital signals is possible.
Mathematical Processing- complex mathematical algorithms
can be performed and implemented easily in digital systems
Cost- when there is large complexity in the application then
digital systems are cheaper compared to analog systems. In
digital systems the software algorithm may be complex but it
can be implemented accurately with less effort
Repeatability- Digital systems does not depend on strict
component tolerances and they can be duplicated easily
25
Advantages and Disadvantages of Digital Systems
Adaptability- digital systems are easily upgradable and they
can be reconfigured for other applications as they are software
controlled and no hardware change is required to adapt them
for other applications
Simplicity- some complex operations in analog systems can
be easily implemented using digital systems
Noise Immunity and security- digital systems have definite
and quantized levels and they are not corrupted by noise
Security systems such as encryption and scrambling can be easily done
in digital systems
Digital systems can be stored in magnetic tape and disks without
deterioration
Drawbacks of Digital Systems …
The real world is mainly analog
Most signals of practical interest are analog –
speech, image, video, sonar, radar etc…
To take advantage of digital techniques when dealing
with analog inputs and outputs, three steps must be
followed
Convert the real-world analog inputs to digital form (ADC)
Process (operate on) the digital information.
Convert the digital outputs back to real-world analog form.
(DAC)
Drawbacks of Digital Systems…
In a collective sense some of the drawbacks
of digital systems are: Digital techniques are limited to signals with relatively
low bandwidths. Currently digital systems are used for
signals up to video bandwidths (about 10 MHz)
The cost of high-speed ADCs and DACs and the amount
of digital circuitry required to implement very high-speed
designs (> 100 MHz) makes them impractical for many
applications.
The need for an ADC and DAC makes digital systems not
economical for simple applications (e.g., a simple filter)
Elements of digital systems
The figure below shows the most basic elements of digital
systems which allow the processing of analog signals
Reasons to the Shift to Digital Tech
Chief reasons for the shift to digital technology: Digital systems are generally easier to design.
Information storage is easy.
Accuracy and precision are easier to maintain throughout the
system.
Operations can be programmed.
Digital circuits are less affected by noise.
More digital circuitry can be fabricated on IC chips.
There have been remarkable recent advances in digital technology.
Advances will continue as digital technology expands and improves.
Binary Digits and Logic Levels
The two digits in the binary system, 1 and 0, are called bits
– a contraction of the words binary digit
In digital circuits two different voltage levels are used to
represent the two bits
Generally 1 is represented by the higher voltage, which we
will refer to as HIGH and a zero is represented by the
lower voltage level, which we will refer to as LOW –
Positive Logic
The reverse of the above notation where we represent 1
with LOW and 0 with HIGH is called Negative Logic
Logic Levels …
The voltages used to represent a 1 and a 0
are called logic levels
Ideally, one voltage level represents a
HIGH and another voltage level represents
a LOW
Type of logic Bit “1” Bit “0”
Positive Logic HIGH LOW
Negative Logic LOW HIGH
Logic Levels …
In practical digital circuits A HIGH can be any voltage between
a specified minimum value and a
specified maximum value
A LOW can be any voltage between
a specified minimum value and a
specified maximum
There is no overlap between the
accepted ranges of HIGH and LOW
levels
Logic Levels …
In digital systems there are two types of circuit
implementations:
TTL ( circuits made up of bipolar transistors)
CMOS ( circuits made up of MOSFET transistors)
In TTL circuits we adopt the following definitions for HIGH
and LOW levels.
LOW ≤ 15 % of the supply voltage ( VCC)
High ≥ 40 % of the supply voltage ( VCC)
For example, if the supply voltage is +5 volt then the logic
levels become
LOW ≤ 0.8 V and High ≥ 2 V
Logic Levels …
In CMOS circuits we adopt the following
definitions for HIGH and LOW levels.
LOW ≤ 30 % of the supply voltage (Vcc )
High ≥ 70 % of the supply voltage (Vcc)
For example, if the supply voltage is +5 volt
then the logic levels become
LOW ≤ 1.5 V, High ≥ 3.5 V
Logic levels …
The figure shows the defining levels of
HIGH and LOW for TTL and CMOS logic
Logic levels …
Binary values are represented by voltage levels
For ideal voltage levels as in the above figure has zero rise
time and fall time
This is not practically feasible
Components of Practical Digital Pulse
Major parts of a digital pulse
Base line
Amplitude
Rise time (tr)
Pulse width (tw)
Fall time (tf)
Digital Waveforms
tw = pulse width
T = period of the waveform
f = frequency of the waveform
The duty cycle of a binary waveform is defined as:
T
1 f
%100 T
t cycle Duty w
Integrated Circuits
An Integrated circuit (IC) is a number of logic
gates fabricated on a single silicon chip.
ICs can be classified according to how many
gates they contain as follows:
Small-Scale Integration (SSI): Contain 1 to 20 gates.
Medium-Scale Integration (MSI): Contain 20 to 200
gates. Examples: Registers, decoders, counters.
Large-Scale Integration (LSI): Contain 200 to 200,000
gates. Include small memories, some microprocessors,
programmable logic devices.
Very Large-Scale Integration (VLSI): Usually stated in
terms of number of transistors contained usually over
1,000,000. Includes most microprocessors and memories.
IC Packaging
IC packages are classified according to the
way they are mounted on the printed circuit
boards as
Through – hole mounted – example DIP
Surface mounted – example SOIC
SMT Package Examples
IC package styles
Dual in-line package (DIP) – through hole technology
Small-outline IC (SOIC) – surface mount technology
Fixed Function Integrated Circuits
Flat pack (FP)
Plastic-leaded chip carrier (PLCC)
Fixed Function Integrated Circuits
Leadless-ceramic chip carrier (LCCC)
Summary
Digital and Analog quantities
Binary Digits, logic levels and digital waveforms
Classification of Integrated Circuit( IC) Packages
Advantages and disadvantages of digital systems
Decimal Number System
Binary Number System
Decimal to Binary and Binary to Decimal Conversion
Binary Arithmetic
,
EET 130– Digital Systems I
Number Systems
2
Outline of the lecture
Decimal Number System
Binary Number System
Binary to decimal and Decimal to Binary conversions
Octal Number System
Hexadecimal Number system
1’s and 2’s complement of binary numbers
Signed numbers
Binary Coded Decimal ( BCD)
Digital Codes
Objective of the Lecture
After successful completion of the lecture students
will be able to: State the place values for decimal and binary number systems.
Convert decimal to binary and binary to decimal number system
Perform Binary Arithmetic Operations
State the place values for octal and hexadecimal number systems.
Convert octal to binary, octal to decimal, binary to octal and decimal
to octal number system
Convert hexadecimal to decimal, hexadecimal to binary, binary to
hexadecimal and decimal to hexadecimal
Determine 1’s and 2’s complement of a binary number
Express binary numbers in BCD form
Convert between binary system and Gray code
Interpret ASCII codes
Number Systems
Understanding digital systems requires an
understanding of the Number systems.
Many number systems are in use in digital
technology
The most common are the decimal, binary, octal,
and hexadecimal systems
The decimal system is clearly the most familiar to us
because it is a tool that we use every day
Most operations performed in decimal number
system are applied in other number systems too
Decimal Number System
The decimal system is composed of 10 numerals or symbols.
These 10 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; using these
symbols as digits of a number, we can express any quantity
The decimal system is also called the base-10 system
because it has 10 digits
The position of each digit in a decimal number indicates the
magnitude of the quantity represented and can be assigned a
weight:
… 105 104 103 102 101 100 . 10-1 10-2 10-3 10-4 10-5 …
Decimal Number System …
Example: Express the decimal number 47
as a sum of the values of each digit.
Solution:
The digit 4 has a weight of 10 (101), as indicated
by its position. The digit 7 has a weight of
1(100), as indicated by its position.
47 = (4 X 101) + (7 X 100)
= (4 X 10) + (7 X 1) = 40 + 7 Exercise: Determine the value of each digit in 939
Decimal Number System…
Example 2: Express the decimal number 568.25 as a sum
of the values of each digit.
Solution:
The whole number digit 5 has a weight of 100 (102), the
digit 6 has a weight of 10(101), the digit 8 has a weight
of 1(100)
the fractional digit 2 has a weight of 0.1 (10-1), and the
fractional digit 5 has a weight of 0.01 (10-2).
568.25 = (5 X 102) + (6 X 101) + (8 X 100) + (2 X 10-1) + (5 X 10-2)
= (5 X 100) + (6 X 10) + (8 X 1) + (2 X 0.1) + (5 X 0.01)
= 500 + 60 + 8 + 0.2 + 0.05
Exercise: Determine the value of each digit in 67.924
Binary Number System
In the binary system, there are only two symbols or possible
digit values, 0 and 1
This base-2 system can be used to represent any quantity that
can be represented in decimal or other number system
In a binary number system the number values are
determined by
The position of the digits multiplied by their positional weighting
Positive Powers of Two (whole numbers Negative Powers of Two (fractional numbers)
28 27 26 25 24 23 22 21 2 2-1 2-2 2-3 2-4 2-5 2-6
256 128 64 32 16 8 4 2 1 ½ 1/4 1/8 1/16 1/32 1/64
0.5 0.25 0.125 0.0625 0.03125 0.015625
Binary Counting
Binary to Decimal Conversion
Any binary number can be converted to its decimal equivalent
simply by
summing together the weights of the various positions in the binary
number which contain a 1
Example 1: Determine the decimal value of the binary whole
number 1101101
Solution:
Determine the weight of each bit that is a 1 and then find the
sum of the weights
Weight: 26 25 24 23 22 21 20
Binary number: 1 1 0 1 1 0 1
1101101 = 26 25 23 22 2 = 64 +32+ 8+ 4+ 1 = 109
Exercise: What is the decimal value of the binary number 10010001
Binary to Decimal Conversion …
Example 2: Determine the decimal value of
the fractional binary number 0.1011.
Solution:
First, determine the weight of each bit that is a 1,
and then sum the weights.
Weight: 2-1 2-2 2-3 2-4
Binary number: 0 . 1 0 1 1
0.1011 = 2-1 + 2-3 + 2-4 = 0.5 + 0.125 + 0.0625
= 0.6875
Exercise: Evaluate the binary number 10.111
Binary to Decimal Conversion …
The maximum value a binary number can have is
determined by the number of Binary digits or BITS present.
Therefore: Largest decimal number = 2n – 1
with five bits (n=5) the biggest decimal number that can be
represented is:
25 – 1 = 32 – 1 = 3110
To keep track of the digits in a binary numbering system
the Rightmost digit having the LOWEST weighting is
referred to as the Least Significant Bit, LSB
the Leftmost digit having the HIGHEST weighting is
referred to as the Most Significant Bit, MSB.
Decimal to Binary Conversion
Sum of weights method
Any decimal number can be converted to its
binary equivalent simply