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Goals and objectives 1
2

 The goal of this course is to:

 provide a good understanding of the digital systems.
 introduce the basic building blocks of digital design including
combinational logic circuits, combinational logic design,
arithmetic functions and circuits and sequential circuits.
Digital Design  Showing how these building blocks are employed in larger scale
2024 - 2025 digital systems

 Having successfully completed this course, the student

Dr. Aydın Tarık Zengin will:
Istanbul Technical University  acknowledge the importance of digital systems.
Faculty of Electrical and Electronics Engineering
Office Number: 6312  Design a digital circuit given a Boolean function.
E-mail: tarik.zengin@itu.edu.tr  Get familiar with typical combinatorial (adders, decoders,
multiplexers, encoders) and sequential (D flip-flops, counters,
registers, shift registers) components.
 Understand how larger systems are organized.

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References 1
3
Grading 1
4

Text Books : 1st Midterm - % 25

Digital Design, M. Morris Mano,  Nov. 8th 2024
Michael D. Ciletti, 2nd Midterm – % 25
Logic and Computer Design  Dec. 20th 2024
Fundamentals, 4/E, M. Morris 4 Homeworks - % 10
Mano and Charles Kime ,
Prentice Hall, 2008. Final Exam - % 40
VF : If Midterm avg < (class avg * 0.4)
FF : If Total avg < (class avg * 0.5) or
less than 30

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Overview of Chapter 1 1
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What is a Digital System? 1
6

 One characteristic:
Digital Systems, Computers  Ability of manipulating discrete elements of
information
Information Representation
 A set that has a finite number of elements contains
Number Systems [binary, octal and discrete information
hexadecimal]
 Examples for discrete sets
Arithmetic Operations  Decimal digits {0, 1, …, 9}
 Alphabet {A, B, …, Y, Z}
Base Conversion  Binary digits {0, 1}
Decimal Codes [BCD (binary coded  One important problem
decimal)]  how to represent the elements of discrete sets in
physical systems?
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DIGITAL & COMPUTER SYSTEMS - Digital System 1
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Types of Digital Systems 1
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 Takes a set of discrete information inputs and No state present
discrete internal information (system state) and
 Combinational Logic System
generates a set of discrete information outputs.
 Output = Function(Input)
State present
Discrete  State updated at discrete times
Discrete => Synchronous Sequential System
Inputs Information
Processing Discrete  State updated at any time
System Outputs =>Asynchronous Sequential System
 State = Function (State, Input)
 Output = Function (State)
or Function (State, Input)
System State

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Digital System Example:
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Analog – Digital Signals

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1 1
9 10
The physical quantities in real world like
A Digital Counter (e. g., odometer): current, voltage, temperature values
change in a continuous range.
Count Up The signals that can take any value
Reset 0 0 1 3 5 64 between the boundaries are called
analog signals.
Inputs: Count Up, Reset Information take discrete values in digital
Outputs: Visual Display systems.
State: "Value" of stored digits
Binary digital signals can take one of the
two possible values: 0-1, high-low, open-
closed.

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Signals 1
11
How to Represent? 1
12

 In electronics circuits, we have electrical signals

 voltage
 current
 Different strengths of a physical signal can be used to
represent elements of the discrete set.
Quantized Signal
 Which discrete set?
 Binary set is the easiest
 two elements {0, 1}
 Just two signal levels: 0 V and 4 V
 This is why we use binary system to represent the
information in our digital system.
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Binary System 1
13
How Many Bits? 1
14

 Binary set {0, 1}  What is the formulae for number of bits to represent a
 The elements of binary set, 0 and 1 are called “binary discrete set of n elements
digits”
 or shortly “bits”.  {0, 1, 2, 3}
 00  0, 01  1, 10  2, ands 11  3.
 How to represent the elements of other discrete sets
 Decimal digits {0, 1, …, 9}  {0, 1, 2, 3, 4, 5, 6, 7}
 Alphabet {A, B, …, Y, Z}  000  0, 001  1, 010  2, ands 011  3
 Elements of any discrete sets can be represented using  100  4, 101  5, 110  6, ands 111  7.
groups of bits.  The formulae, then,
 9  1001 ?
 A  1000001
 If n = 9, then 4 bits are needed