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ACOE161 – Digital Logic for
Computers
Dr. Konstantinos Tatas
General Information
• Instructors: K. Tatas, S. Savva
– [email protected]
– Library Building Office 116
• ECTS: 7 (approx. 175h)
• 3 hours/week Lectures
• 2 hours/week Labs
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Learning Outcomes
• Explain how and why information is coded and
manipulated in a variety of different ways.
• Apply Boolean algebra, Karnaugh maps and algorithmic
minimization techniques to analyze and design
combinational digital circuits.
• Use latches and flip flops to design and analyze
synchronous and asynchronous sequential digital circuits
such as counters and registers.
• Employ EDA tools and programmable logic devices for
the design and implementation of digital circuits.
• Simulate, build and test combinational and sequential logic
circuits using TTL ICs and programmable logic devices
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such as FPGAs.
Course Outline (1/2)
• Number systems and codes: Introduction to computer
numbering systems: Binary number representation.
Conversion from decimal to any base and from any base to
decimal. BCD representation. Fractional and negative
number representation: Sign-magnitude, radix –1 and radix
complement representation. Addition and subtraction using
radix complement. Excess and floating-point number
representations
• Combinational circuits: Basic digital components, truth
tables and logic functions Karnaugh maps and algorithmic
minimization techniques. Circuit implementation of logic
functions. Design of combinational MSI digital circuits
such as decoders, encoders, adders/subtracters,
multiplexers, comparators etc.
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Course Outline (2/2)
• Sequential circuits: Latches and Set/Reset, Data, JK and
Toggle flip-flops. Positive and negative edge triggered flip
flops. Asynchronous flip-flop inputs. Asynchronous
counters, synchronous counters and shift registers.
• Programmable Logic Devices: PLAs, PALs, CPLDs and
FPGAs. Programming of FPGAs using schematic
diagrams. Use of computer programs to design and
simulate digital circuits.
• Laboratory Exercises: Individual and small group
experiments including simulation of digital circuits and
implementation using TTL ICs.
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What is Digital (1/2)
• A digital signal is a signal that can only
have discrete values in time
– Most common are binary digital signals, where
only two values are allowed often designated as
0 and 1
• The opposite is analog signals that can take
infinite values
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What is Digital (2/2)
• A digital system processes digital signals
• Examples: computer, cellphone, DVD,
digital camera, etc.
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Okay, what is a signal then?
• A signal is a physical quantity (sound, light, voltage,
current) that carries information
– The power cable supplies power but no information
(not a signal)
– A USB cable carries information (files)
• Examples of quantities used as digital information signals
– Voltage: 5V (logic 1), 0V (logic 0) in digital circuits
– Magnetic field orientation in magnetic hard disks
– Pits and lands on the CD surface reflect the light from
the laser differently, and that difference is encoded as
binary data
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ANALOG VS DIGITAL
• Analog devices and systems: Process analog signals (timevarying signals that can take any value across a continuous
range known as dynamic range)
• Digital devices and systems: Process digital signals
(analog signals that are modeled as having at any time one
of two discrete values)
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Example of analog vs digital system
Digital
advantages:
Battery life
Programmability
Accuracy
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The world is analog
• Few systems like the watch can be
completely digital
• Systems that interact with the environment,
need to process analog information
• How? Analog signals must first be
converted to digital
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Example of analog vs digital
system
Analog
Digital
Temperature
sensor (analog)
A/D
Display
converter
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ANALOG GOES DIGITAL
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Photography
Video
Audio
Automobile applications
Telephony/Telecomunications
Traffic lights
Special effects
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WHY DIGITAL?
ADVANTAGES OF DIGITAL
PROCESSING
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Reproducibility of results
Ease of design
Programmability
Speed
Noise tolerance
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DIGITAL ABSTRACTION
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Example of using digital over
analog: Telecommunications
Noisy channel
Noisy channel
• Digital systems are less sensitive to noise
• As long as 0 is distinguishable from 1
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Binary Values: Other Physical
Quantities
• What are other physical quantities
represent 0 and 1?
– CPU Voltage
– Disk Magnetic Field Direction
– CD Surface Pits/Light
– Dynamic RAM Electrical Charge
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