ENSC-252
September 7, 2023
1
Fundamentals of Digital Logic & Design: Semester's plan
Lectures:
Tuesdays: 08:30 am – 10:20 am, Room C9002
Thursdays: 08:30 am – 10:20 am, Room WMC3520
Instructors:
Majid Shokoufi (mshokouf@sfu.ca)
Take your own notes during the lectures. The lecturers will not be recorded, and the filled slides will not be shared.
Teaching assistants:
Zihao Xie <zxa43@sfu.ca>
Aarya Pandya <aap19@sfu.ca>
Mahsa Tadrisinoor <mta161@sfu.ca>
Office hours:
• Instructor: Thursdays from 10:30 am to 11:30 am, Office number: ASB 9862
• (TA) office hours: TBA
Read the course information document on Canvas carefully. You can find all the information about the course on this
document such as course plan, quizzes, midterm, final exam and so forth:
ENSC252 Course information Fall 2023.pdf
September 7, 2023
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Fundamentals of Digital Logic & Design: Semester's plan
Laboratory sessions:
LA01: Mondays, 12:30 pm to 02:20 pm, Room ASB 10877 & ASB 10879
LA02: Mondays, 02:30 pm to 04:20 pm, Room ASB 10877 & ASB 10879
LA03: Mondays, 04:30 pm to 06:20 pm, Room ASB 10877 & ASB 10879
October 9th labs will be held on October 10th:
LA01: Tuesday, 12:30 pm to 02:20 pm, Room ASB 10877 & ASB 10879
LA02: Tuesday, 02:30 pm to 04:20 pm, Room ASB 10877 & ASB 10879
LA03: Tuesday, 04:30 pm to 06:20 pm, Room ASB 10877 & ASB 10879
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Labs are scheduled every week (starting from the third week of the semester).
You will work in groups of 3.
You must select your teammates by the end of the second week of the semester.
Teammates must stay unchanged during the entire semester.
You must select your teammate from the same lab session that you enrolled in.
You can sign out the development board during the second week of the semester. The date and time will be
announced on Canvas.
September 7, 2023
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Fundamentals of Digital Logic & Design: Semester's plan
Tentatively scheduled tutorial sessions: will be held according to the following schedule.
• Tutorial #1: Wednesday, Sep 27th, from 10:30 am to 12:20 pm
• Tutorial #2: Wednesday, Oct 26th, from 10:30 am to 12:20 pm
• Tutorial #3: Wednesday, Nov 15th, from 10:30 am to 12:20 pm
• Tutorial #4: Wednesday, Nov 29th, from 10:30 am to 12:20 pm
Please don't hesitate to ask questions if any part of the course material is unclear during the lectures. It's
important to ensure that everyone understands the subject matter, so please don’t let me move on until you
have a clear grasp of the concepts.
September 7, 2023
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Fundamentals of Digital Logic & Design: Objectives
• Get familiar with different type of number representation especially binary numbers
• Get familiar with fundamental components of digital logic gates, like AND, OR, XOR, …
• Get familiar with Combinational and arithmetic-circuit building blocks, like Encoder, Decoder, MAX, DEMAX,
adder, subtracter, ….
• Get familiar with fundamental components of memory, like Flip-flops, registers, and counters
• Get familiar with sequential circuits, like counters, shift registers, …
• Digital system design, like BUS structure, a simple processor
• Get familiar with digital logic circuits technology, CMOS
• You were able to construct complete VHDL models
• Generate logic functions using the VHDL
• Create hierarchical VHDL designs
By the end of the course, you will be able to design, simulate, build, and debug complex digital circuits using basic
digital gates as well as hardware description language (HDL).
September 7, 2023
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Fundamentals of Digital Logic & Design: Objectives
A synchronous up-down counter with load and clear
capabilities
September 7, 2023
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Fundamentals of Digital Logic & Design: Objectives
A 12-hour digital clock
Digital Fundamentals, by Thomas L. Floyd
September 7, 2023
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Fundamentals of Digital Logic & Design: Objectives
A VHDL code to perform 16 bit add operation
with carry out and overflow
-- 16-bit adder in VHDL
LIBRARY ieee;
USE ieee.std_logic_1164.all
USE ieee.std_logic_arith.all
ENTITY adder16 IS
PORT ( X, Y
: IN SIGNED ( 15 DOWNTO 0 );
S
: OUT SIGNED ( 15 DOWNTO 0 );
Cout, Overflow : STD_LOGIC
END adder16;
ARCHITECTURE Behavior OF adder16 IS
SIGNAL Sum : SIGNED ( 16 DOWNTO 0 );
BEGIN
Sum <= (‘0’ & X ) + (‘0’ & Y );
S <= Sum ( 15 DOWNTO 0 );
Cout <= Sum (16);
Overflow <= Sum (16) XOR X(15) XOR Y(15) XOR Sum(15);
END Behavior;
September 7, 2023
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Fundamentals of Digital Logic & Design: Objectives
• 1971
• 4-bit, 46 instructions, 740KHz
• roughly eight clock cycles per instruction cycle
(fetch, decode, execute)
• 2,300 transistors, 10 micron
September 7, 2023
https://wikimedia.org/
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Fundamentals of Digital Logic & Design: Course outline
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Introduction digital logic & design
Number representation and arithmetic circuits
Introduction to logic circuits
Combinational-circuit building blocks
Flip-flops, registers, and counters
Synchronous sequential circuits
Digital system design
Computer aided design tools
Implementation of digital logic circuits technology
Fundamentals of Digital Logic with VHDL Design 4th edition, Stephen Brown | Zvonko Vranesic, McGraw-Hill
Digital Design, by M. Morris Mano | Michael D. Ciletti
September 7, 2023
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Introduction to Digital Logic & Design : Lecture outline
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Digital hardware components
An overview of the design process
Binary numbers
Digital representation of information
Fundamentals of Digital Logic with VHDL Design 4th edition, Stephen Brown | Zvonko Vranesic, McGraw-Hill
September 7, 2023
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Introduction to Digital Logic & Design
In today’s world, the term digital has become part of our everyday vocabulary because of the dramatic
way that digital circuits and digital techniques have become so widely used in almost all areas of life:
computers, automation, robots, medical science and technology, transportation, telecommunications,
entertainment, space exploration, and on and on.
We start by introducing some underlying concepts that are a vital part of digital technology; these
concepts will be expanded on as they are needed later.
To understand the operation of each digital module, it is necessary to have a basic knowledge of digital circuits
and their logical function.
September 7, 2023
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Introduction to Digital Logic & Design
https://en.wikipedia.org/
September 7, 2023
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Introduction to Digital Logic & Design: Signals representation
An arbitrary analog voltage signal 𝑣𝑠 (𝑡)
Analog signals:
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can take on any value for amplitude
have continuous variation over its range
can be corrupted by noise
Discrete signals:
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can take on any value for amplitude
is defined at the sampling instance
no longer is a continuous function of time
Can be corrupted by noise
Example: A sample rate of 96KHz/44.1 kHz is commonly used for
music reproduction, the main source used for creating MP3 files.
Bit depth is a measure of the numerical detail used to describe each
audio sample. A bit Depth of 16-bit is commonly used for MP3.
7 September 2023
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Introduction to Digital Logic & Design: Signals representation
Digital signals:
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can take on a sequence of numbers (binary 2)
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Each number representing the signal magnitude at an instant of
time (binary 0 and 1)
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can withstand some noise while still being able to distinguish
between logic levels without any loss of information
7 September 2023
An arbitrary digital voltage signal 𝑣(𝑡)
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Introduction to Digital Logic & Design: Signals representation
There are basically two ways of representing the numerical value of quantities : analog and digital.
• Analog Representations :
In analog representation, a quantity is represented by a continuously variable, proportional indicator.
Analog quantities have an important characteristic, no matter how they are represented: they can vary
over a continuous range of values.
• Digital Representations :
In digital representation the quantities are represented not by continuously (discrete) variable indicators
but by symbols called digits.
September 7, 2023
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Introduction to Digital Logic & Design: Signals representation
Advantage of Digital Techniques
• Easy to design.
• Data storage is easy.
• Accuracy and precision are easier to maintain
throughout the system.
• Operation can be programmed.
• Digital circuits are less affected by noise.
• More digital circuitry can be fabricated on IC chips.
September 7, 2023
Limitations of Digital Techniques
• The real world is analog
• Processing digitized signals takes time.
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Introduction to Digital Logic & Design
Example:
Block diagram of a digital temperature control system
September 7, 2023
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Introduction to Digital Logic & Design
Example:
Microphone
Digital inputs
Speaker
Pre-Amp
ADC
Audio
processor
DAC
Amplifier
Power Amp
Digital outputs
7 September 2023
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Introduction to Digital Logic & Design
• Until the 1960s logic circuits were
constructed with bulky components, such as
transistors and resistors that came as
individual parts.
• By 1970 it was possible to implement all
circuitry needed to realize a microprocessor
on a single chip.
An estimate of the maximum number of
transistors per chip over time (Moore’s law).
September 7, 2023
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Introduction to Digital Logic & Design
Discrete digital gates and components
We can use discrete digital gates and components (such as TTL and CMOS) to design and implement our circuit.
For simple circuit we can use this approach but for complex
circuit this is not a practical approach.
Programmable Logic Devices (PLDs)
The most commonly-used type of PLD is known as a field-programmable gate array (FPGA).
Advantages:
• Flexible design
• Reprogrammable
• Easy prototyping
Drawbacks:
• Switches consume valuable chip area
• Switches limit the speed of operation of implemented circuits
Application-specific integrated circuits (ASICs)
• Costly
• Design and implementation process take considerable amount of time
• Large quantities
September 7, 2023
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Introduction to Digital Logic & Design
Required product
Design process
Define specifications
Initial design
Simulation
Redesign
Is design
correct?
No
Yes
Prototype implementation
Testing
Meets
specifications?
Make corrections
Yes
No
Minor
errors?
Yes
Finished product
September 7, 2023
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No
Introduction to Digital Logic & Design
Development kit will be used during the semester.
FPGA development board
• Altera
• DE2-115
Cyclone IV (4CE115 FPGA) :
Maximum Operating Frequency:200 MHz
Number of Logic Elements:114,480 LE
Number of I/Os:153 I/O
Computer aided design (CAD)
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Quartus II
Hardware description language
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VHDL
September 7, 2023
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Introduction to Digital Logic & Design: Digital Representation of Information
Many number systems are in use in digital technology. The most common are the decimal, binary, octal, and hexadecimal
systems.
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Decimal
Hexadecimal
Octal
Quaternary
Binary
– > 10 symbols (base-10)
–> 16 symbols (base-16)
–>
8 symbols (base-8)
–>
4 symbols (base-4)
–>
2 symbols (base-2)
The decimal system is a positional-value system in which the value of a digit depends on its position. For example, consider
the decimal number 453. We know that the digit 4 actually represents 4 hundreds, the 5 represents 5 tens, and the 3
represents 3 units. In essence, the 4 carries the most weight of the three digits; it is referred to as the most significant digit
(MSD). The 3 carries the least weight and is called the least significant digit (LSD).
September 7, 2023
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Introduction to Digital Logic & Design: Digital Representation of Information
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.
2 × 10+3 + (7 × 10+2 ) + (4 × 10+1 ) + (5 × 100 ) + (5 × 100 )
+ (2 × 10−1 ) + (1 × 10−2 ) + (4 × 10−3 ) = 2745.214
Most significant digit (MSD) & least significant digit (LSD)
In general, with N places or digits, we can count through 10N different numbers, starting with and including zero. The largest
number will always be 10N-1
September 7, 2023
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Introduction to Digital Logic & Design: Digital Representation of Information
The octal system is composed of 8 numerals or symbols . These 8 symbols are 0, 1, 2, 3, 4, 5, 6, 7.
Example:
(762)8 =?
(762)8 = 7 × 82 + (6 × 81 ) + (2 × 80 )
= (498)10
The hexadecimal system is composed of 16 numerals or symbols . These 16 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
Example:
(3𝐹𝐵)16 =?
(3𝐹𝐵)16 = 3 × 162 + (15 × 161 ) + (11 × 160 ) = (1019)10
The binary system is composed of 2 numerals or symbols . These 2 symbols are 0, 1.
Example:
(1001)2 =?
September 7, 2023
(1001)2 = 1 × 23 + (0 × 22 ) + (0 × 21 ) + (1 × 20 )
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Introduction to Digital Logic & Design: Digital Representation of Information
Binary Numbers (Base-2)
General formula to convert binary number to a decimal number
B = bn−1bn−2 · · · b1b0
an n-bit unsigned number
𝑛−1
V(B) = bn−1 ×
2n−1 +
bn−2 ×
2n−2 +·
· ·+b1 ×
21
+ b0 ×
20
= ෍ 𝑏𝑖 × 2𝑖
0
Example:
(1101)2 = (??)10
(0111)2 = (??)10
LSB, MSB, Byte, Nibble
September 7, 2023
(1000)2 = (??)10
(10000111)2 = (???)10
Decimal
(Base 10)
Hexadecimal
(base 16)
Binary
(base 2)
00
0
0000
01
1
0001
02
2
0010
03
3
0011
04
4
0100
05
5
0101
06
6
0110
07
7
0111
08
8
1000
09
9
1001
10
A
1010
11
B
1011
12
C
1100
13
D
1101
14
E
1110
15
F
1111
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Introduction to Digital Logic & Design: Conversion between Decimal and other base Systems
Consider converting a decimal number into an octal number.
Approach #1:
(35)10= (???)8 = a2 × 82 + a1 × 81+ a0 × 80=(a2a1a0)8
Approach #2:
Quotient
Remainder
35 ÷ 8
4
3
4÷8
0
4
(35)10= (???)8
= (43)8
Example: convert (153)10 into an octal number using both approach.
(153)10= (???)8 = a2 × 82+ a1 × 81+ a0 × 80=(a2 a1a0)8
September 7, 2023
Quotient
Remainder
153 ÷ 8
19
1
19 ÷ 8
2
3
2÷8
0
2
= (231)8
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Introduction to Digital Logic & Design: Conversion between Decimal and other base Systems
Example: convert (35)10 into a hexadecimal number using both approach.
Approach #1:
(35)10= (??)16 = a1 × 161+ a0 × 160=(a1a0)8
(35)10= (??)16
Approach #2:
Quotient
Remainder
35 ÷ 16
2
3
2 ÷ 16
0
2
= (23)16
Example: convert (153)10 into a hexadecimal number using both approach.
Approach #1:
Approach #2:
(153)10= (???)16
= a2 × 162+ a1 × 161+ a0 × 160=(a2 a1a0)16
September 7, 2023
Quotient
Remainder
153 ÷ 16
9
1
9 ÷ 16
0
9
= (91)16
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Introduction to Digital Logic & Design: Conversion between Decimal and other base Systems
Example: convert (35)10 into a binary number using both approach.
Approach #1:
(35)10= (?????)2 = b5 × 25+ b4 × 24+ b3 × 23+ b2 × 22+ b1 × 21+ b0 × 20=(b5b4b3b2b1b0)2
Approach #2:
Example: convert (857)10 into a binary number using both approach.
Convert (857)10 = (?????)2
September 7, 2023
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Introduction to Digital Logic & Design: Conversion between Decimal and other base Systems
Converting fractional decimal to other bases
(0.29)10= (0.???)2 = b-1 × 2-1+ b-2 × 2-2+ b-3 × 2-3=(0.b-1b-2b-3b-4b-5)2
0.29 × 2 =
0.58
0.58 × 2 =
1.16
0.16 × 2 =
0.32
0.32 × 2 =
0.64
0.64 × 2 =
1.28
0.28 × 2 =
0.56
0.56 × 2 =
1.12
0.12 × 2 =
0.24
.
.
.
.
.
.
September 7, 2023
(0.6875)10= (0.????)2
(0.6875)10= (0.????)8
0.6875 × 2 =
1.3750
0.6875 × 8 =
5. 50
0.3750 × 2 =
0.7500
0.50 × 8 =
4. 00
0.7500× 2 =
1.5000
0.5000 × 2 =
1.0000
=(0.54)8
=(0.1011)2
=(0.01001010…)2
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Introduction to Digital Logic & Design: Conversion between Decimal and other base Systems
Conversion between binary and hexadecimal, octal and quaternary systems
(10 110 001 101 011 . 111 100 000 11)2= (
.
(10 1100 0110 1011 . 1111 0000 011)2= (
(673.124)8= (
(3B6.D0)16= (
September 7, 2023
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.
)8
)16
)2
.
)2
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Introduction to Digital Logic & Design
ASCII Character Code
American Standard Code for
Information Interchange
September 7, 2023
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Introduction to Digital Logic & Design
An example of Digital system
September 7, 2023
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Questions?
September 7, 2023
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