Digital Systems I
EC 381
Fall 2017
Mohamed Elgalhud
Introduction
Course Description
This course will introduce the fundamentals of digital circuit
design. This includes Boolean algebra, simplification of
Boolean functions, combinatorial and sequential circuit design.
Textbook: Digital Design by M.Moris Mano.
Course Evaluation:
3 % Attendance
5 % Quiz
6 % Homework and Assignments
18% First Midterm Exam
18% Second Midterm Exam
50% Final Exam
2 Reference: Lecture Notes of Eng.Yusra Maatog 9/25/2017
Course Outline
1. Number Systems and Codes
Conversions between number systems.
Binary arithmetic.
2. Boolean Algebra.
Postulates of Boolean algebra.
Properties and theorems of Boolean algebra.
3. Logic gates and Minimization
Basic logic gates and their characteristics.
Canonical SOP and POS forms.
Using k-maps to obtain minimum SOP and POS
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expressions. 9/25/2017
Reference: Lecture Notes of Eng.Yusra Maatog
Course Outline
4. Combinational logic Networks
Half Adder and Full Adder.
Realization of ripple carry n-bit adders.
Encoders and decoders.
Multiplexers and demultiplexers.
Realizing switching functions using multiplexers, decoders, and
encoders.
Tri-state buffers and their applications.
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Reference: Lecture Notes of Eng.Yusra Maatog
Course Outline
5. Latches and Flip Flops
SR Latche
D flip flop
JK flip flop
T flip flop
General purpose registers
Ripple counters and synchronous counters
6. Analysis and design of small sequential logic systems
Finite State Machines (FSM)
Analysis of FSM
Synthesis of FSMs using different types of flip flops.
7. Introduction to PLDS, PLAs, FGA, ROM, and RAM.
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Course Website
This term we will be using Piazza for class discussion.
The system is highly catered to getting you help fast and
efficiently from classmates, and myself. Rather than
emailing questions to the teaching staff, I encourage you
to post your questions on Piazza.
Find our class page
at: http://piazza.com/uot.edu.ly/spring2017/ec381/home
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You can download course notes from Resouces
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Reference: Lecture Notes of Eng.Yusra Maatog
Digital Systems
Digital systems has a such a prominent role in
everyday life
They are used in communication, business
transactions, traffic control, weather monitoring,
medical treatment and so on.
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Reference: Lecture Notes of Eng.Yusra Maatog
Digital Systems
Takes a set of discrete information (inputs) and discrete internal
information (system state) and generates a set of discrete
information outputs.
Discrete Discrete
Inputs Information
Processing Discrete
System Outputs
System State
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Reference: Lecture Notes of Eng.Yusra Maatog
Analog versus Digital
Analog means continuous
Analog parameters have continuous range of values
Example: temperature is an analog parameter
Temperature increases/decreases continuously
Like a continuous mathematical function, No discontinuity
points
Other examples?
Digital means using numerical digits
Digital parameters have fixed set of discrete values
Example: month number {1, 2, 3, …, 12}
Thus, the month number is a digital parameter (cannot be 1.5!)
Other examples?
Reference: Lecture Notes of Dr Samir Elbuni
Analog versus 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
Reference: Lecture Notes of Dr. Samir Elbuni
Digitization of Analog Signals
Digitization is converting an analog signal into digital form
Example: consider digitizing an analog voltage signal
Digitized output is limited to four values =
{V1,V2,V3,V4}
Voltage
Time
Reference: Lecture Notes of Dr. Samir Elbuni
Digitization of Analog Signals – cont’d
Voltage
Time
Voltage
Time
Some loss of accuracy, why?
How to improve accuracy? Add more voltage values
Reference: Lecture Notes of Dr. Samir Elbuni
ADC and DAC Converters
input analog
Analog-to-Digital Converter (ADC) signals
Analog-to-Digital
Produces digitized version of analog signals
Converter (ADC)
Analog input => Digital output input digital
signals
Digital-to-Analog Converter (DAC) Digital System
Regenerate analog signal from digital form output digital
signals
Digital input => Analog output Digital-to-Analog
Converter (DAC)
Our focus is on digital systems only output analog
signals
Both input and output to a digital system are digital signals
Reference: Lecture Notes of Dr. Samir Elbuni
How do Computers Represent Digits?
Binary digits (0 and 1) are used instead of decimal digits
Using electric voltage High = 1
Voltage Level
Used in processors and digital circuits
Unused
High voltage = 1, Low voltage = 0
Using electric charge Low = 0
Used in memory cells
Charged memory cell = 1, discharged memory cell = 0
Using magnetic field
Used in magnetic disks, magnetic polarity indicates 1 or 0
Using light
Used in optical disks, surface pit indicates 1 or 0
Reference: Lecture Notes of Dr. Samir Elbuni
Number Systems
Representations of a number in a different
radix (base) [r]
1. Decimal (r=10) Digits € {0,1,2,3,4,5,6,7,8,9}
2. Binary (r=2) Digits € {0,1}
3. Octal (r=23=8) Digits € {0,1,2,3,4,5,6,7}
4. Hexadecimal (r= 24=16)
Digits € {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}
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Reference: Lecture Notes of Eng.Yusra Maatog
Binary Numbers
Each binary digit (called a bit) is either 1 or 0
Bits have no inherent meaning, they can represent …
Unsigned and signed integers
Fractions Most Least
Significant Bit Significant Bit
Characters
7 6 5 4 3 2 1 0
Images, sound, etc. 1 0 0 1 1 1 0 1
27 26 25 24 23 22 21 20
Bit Numbering
Least significant bit (LSB) is rightmost (bit 0)
Most significant bit (MSB) is leftmost (bit 7 in an 8-bit number)
Reference: Lecture Notes of Eng.Yusra Maatog
Decimal Value of Binary Numbers
Each bit represents a power of 2
Every binary number is a sum of powers of 2
Decimal Value = (dn-1 2n-1) + ... + (d1 21) + (d0 20)
27 + 24 + 23 + 22 + 1 = 157
Binary (10011101)2 =
7 6 5 4 3 2 1 0
1 0 0 1 1 1 0 1
27 26 25 24 23 22 21 20
Some common
powers of 2
Reference: Lecture Notes of Eng.Yusra Maatog
Special Powers of 2
23 = 8 bits => Byte
24 =16 bits or 2 bytes => word
210 (1024) is Kilobyte, denoted "KB”
220 (1,048,576) is Megabyte, denoted "MB”
230 (1,073, 741,824) is Gigabyte, denoted "GB”
240 (1,073, 741,824) is Terabyte, denoted “TB”
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Reference: Lecture Notes of Eng.Yusra Maatog
