Digital Principal 1
Spring 2022
© Zohreh Motamedi– ENGI10701(DP1)
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Course Information
Textbook:
• "Digital Electronics: a Practical Approach", 11th Edition, William Kleitz, Prentice Hall.
 Video: The author’s Youtube channel:
https://www.youtube.com/channel/UCFC56lANq_FESHes9j0NKnw
Labs: Will be posted on SLATE.
Class Plan: on SLATE.
© Zohreh Motamedi– ENGI10701(DP1)
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Evaluation Plan (Class Plan posted on SLATE)
• Labs (10 @ 3% each)
30%
• Midterm Exam
30%
• Final Exam
30%
• Quizzes (2 @ 5% each)
10% (Week 4th & Week 10th)
• Assignments,
will be posted on SLATE / Assignment
Lab attendance is mandatory
DUAL PASS PROVISION: Students must obtain at least 50% on the exams/Quizzes
and 50% on the labs component of this course in order to obtain a passing grade.
© Zohreh Motamedi– ENGI10701(DP1)
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Check the Class Plan Posted on SLATE
© Zohreh Motamedi– ENGI10701(DP1)
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Breach of Academic Integrity
• Zero-Tolerance!
• Study the Academic Integrity Policy & Procedure posted on SLATE.
(My apologies to all those of you that wouldn’t even think of it…)
© Zohreh Motamedi– ENGI10701(DP1)
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Evaluation Schedule
Make sure you are available for the quiz 1 and Midterm.
– Quiz 1: Week 4, Monday, May 30
– Midterm: Week 7, Monday, June 20
 Office Hour: TBA. Send an email to book an appointment.
© Zohreh Motamedi– ENGI10701(DP1)
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• Have a pen and paper during the Lectures
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This Week Lab 0
Multisim & Tinkercad
 Lab0 uploaded on SLATE already. If you have already installed them no need to install it
again. Simulate the circuits in Lab0 and upload your file on SLATE.
 Tinkercad Circuits: in an online platform. No need to install. Make an account and sign in
to use.
© Zohreh Motamedi– ENGI10701(DP1)
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Digital Electronics in your daily life
 Let’s list a few digital devices in our daily life:
•
……
•
……
•
……….
•
…………
•
………………
•
……………………
https://www.linkedin.com/learning/computer-science-principles-digital-information/yes-and-no-answers-with-binary?u=2272289
© Zohreh Motamedi– ENGI10701(DP1)
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Course Learning Outcomes
 The first Digital Electronics course
 Understand the main building blocks of digital circuits
Including:
Number systems, BCD, and ASCII code
Boolean Algebra.
Logic gates: Inverter, AND, and OR gates.
Apply various techniques for digital logic simplification.
Explain the design and operation of the building blocks of Digital Systems
© Zohreh Motamedi– ENGI10701(DP1)
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Analog Signal vs. Digital Signal
 An analog signal is continuous signal in both, time and amplitude.
 A digital signal refers to an electrical signal that is converted into a pattern of bits.
© Zohreh Motamedi– ENGI10701(DP1)
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Data Representation in the Computer
 Computers work with 0 and 1.
 All kinds of information such as, sounds, pictures, videos, numbers, and text
are converted into digital data, 0 and 1, to enter the digital world.
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Converting analog sound to digital (ADC)
& back digital to analog (DAC).
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Analog/Digital Conversion
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Number Systems
Number Systems:
• Decimal, Binary and Hexadecimal number systems
• BCD
Letters:
• ASCII Codes
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Numbering Systems
Base 10 (Decimal) — Represent any number using 10 digits [0–9]
Base 2 (Binary) — Represent any number using 2 digits [0–1]
Base 16 (Hexadecimal) — Represent any number using 10 digits and 6
characters [0–9, A, B, C, D, E, F]
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Decimal Numbering System (Base 10)
In the Base-10 world (Decimal), there are ten possible digits that each
position can take (0-9).
Example: 436
Most Significant Bit
MSB
LSB
Least Significant Bit
4
3
Value:
4*100
3*10
6*1
Exponential
Expression:
4*102
3*101
6*100
Number:
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Binary Numbering System (Base 2)
In the Base-2 world (Binary), there are 2 possible digits “0”, and “1”
S = {0, 1}
 The symbols in this system are referred to as bits (binary digit).
https://www.youtube.com/watch?v=s0pi-VoaZyU&list=PLE7E5C88AA6AEA0A2&index=3
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Binary Numbering System (Base 2)
• Example: 1012
Number:
1
0
1
Weight
22
21
20
Value:
1*4
+
0*2
+
1*1
© Zohreh Motamedi– ENGI10701(DP1)
=5
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Converting Base-2 to Base-10
1 0 0 1 12
Exponent:
Calculation:
16 0 0 2 1 1910
+
+
+
+
© Zohreh Motamedi– ENGI10701(DP1)
=
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Powers-of-2 Binary Weighting Factors
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Example
• Convert the binary number 100110 to decimal.
1 0 0 1 1 02
Exponent:
Calculation:
32 0 0 4 2 0
+
+
+
+
+
© Zohreh Motamedi– ENGI10701(DP1)
=
3810
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Practice
• Let's practice. Do not use a web converter!
• 00000000 -->
• 00001111 -->
• 01101011 -->
• 11111111 -->
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Converting Base-10 to Base-2
 STEP ONE: Find the largest exponent of two that is less than or equal to the
Base-10 number:
2210=
16 8
24 23
4
22
2
21
1
20
© Zohreh Motamedi– ENGI10701(DP1)
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Converting Base-10 to Base-2
 STEP Two: Place a “1” above the left-most position:
2210=
1
16 8
24 23
4
22
2
21
1
20
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Converting Base-10 to Base-2
 Step Three: Add left-most value to the next position. Put a “0” above is
the sum is greater than the number being converted, otherwise put a “1”
above:
2210=
1
0
16
24
8
23
4
22
2
21
1
20
© Zohreh Motamedi– ENGI10701(DP1)
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Converting Base-10 to Base-2
 Step Four: Add subsequent positions. If the sum is greater than the
number being converted, put a “0” above and disregard it. Otherwise,
put a “1” above and including it in your running total.
2210=
1
16
24
0
8
23
1
4
22
1
2
21
0
1
20
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Converting Base-10 to Base-2
 Step Five: The resulting 1s and 0s in the top row form the binary
equivalent of the Base-10 number with which we started:
2210 = 101102
MSB
Most significant bit
Least significant bit
© Zohreh Motamedi– ENGI10701(DP1)
LSB
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Converting Decimal to Binary, another Method
 Successive Division:
22/2=11
With a remainder of 0 (LSB)
11/2=5
With a remainder of 1
5/2=2
With a remainder of 1
2/2=1
With a remainder of 0
1/2=0
With a remainder of 1 (MSB)
2210 = 101102
© Zohreh Motamedi– ENGI10701(DP1)
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Example
• Convert the Decimal number 40 to binary.
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Example
• Convert these Decimal numbers to binary.
• 16
& 15
• 32
& 31
• 64
& 63
• 128
& 127
• 256
& 255
• 512
• 10000
& 1111
• 1 0000 0000 & 1111 1111
& 511
• 1024 & 1023
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Example
Convert the following decimal numbers into binary (no web converter).
• 70 
• 25 
• 49 
• 231 
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Binary Game
Click to play:
https://studio.code.org/projects/applab/iukLbcDnzqgoxuu810unLw
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Hexadecimal Numbering (Base 16)
• Hexadecimal number is a Base-16 numbering system.
• Hexadecimal is a convenient way to represent binary numbers.
• Base = 16 or ‘H’
16 symbols: { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}
{ 10=A, 11=B, 12=C, 13=D, 14=E, 15=F}
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Hexadecimal Numbering Systems
Decimal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Hexadecimal
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
Binary
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
© Zohreh Motamedi– ENGI10701(DP1)
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Hexadecimal Numbering Systems
• Repeated Division by 16
• Example
21310 = ( )16 ?
Divide-by -16
213 / 16
13 / 16
Quotient
13
0
Remainder
5
13
Hex digit
Lower digit = 5
Second digit =D
© Zohreh Motamedi– ENGI10701(DP1)
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Hexadecimal Numbering Systems
• How to convert D516 back to Decimal ?
• Use this table and multiply the digits with the position values.
Digit
8
167
Digit
7
166
Digit
6
165
Digit
5
164
Digit
4
163
Digit
3
162
Digit
2
161
Digit
1
160
……
……
…..
……
4096
256
16
1
D×161 + 5×160 = 13×16 + 5×1
= 208 + 5
= 213
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Example
 Convert A28H into a decimal number.
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Example
 Convert A28H into a decimal number.
Answer: 2560+32+8=2600
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Convert Binary to Hex
•
Group into 4's starting at least significant symbol (if the number of bits is
not evenly divisible by 4, then add 0's at the most significant end)
•
Write a hex digit for each group.
•
Example: 101 1110 0111 0000
0101 1110
5
E
0111 0000
7
0
© Zohreh Motamedi– ENGI10701(DP1)
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Example
 Convert 10010100110000 to Hex.
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Example
 Convert 10010100110000 to Hex.
Solution:
10 0101 0011 0000
This group has only two bits, to make it a group of 4
bits add zeros in MSB position
0010
2
0101 0011 0000
5
3
0
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Convert Hex to Binary
•
For each of the Hex digit write its binary equivalent (use 4 bits to represent)
• Example
Convert 25A0 to binary
0010 0101 1010 0000
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Example
 Convert A42F to Binary.
•
•
The Battery Service UUID: 0x180F
Battery Level Characteristic UUID: 0x2A19
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Example
 Convert A42F to Binary.
Solution:
1010 0100 0010 1111
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Binary Coded Decimal (BCD)
• With BCD code, each individual digit of the decimal number system
is represented by a corresponding binary number.
– Such as 19
0001 1001
0010 0010 : 0000 0011
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Binary-Coded-Decimal System
•
Simply, each individual digit of the decimal number system is represented
by a corresponding binary number.
Example:
Decimal number 71-33 is thus represented
0111 0001 - 0011 0011
BCD code
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Binary-Coded-Decimal System
Example:
Number 0101 : 0010 0111 in BCD code
represents 5 : 27 decimal number
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Example
 Convert 84:31 to BCD.
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Example
 Convert 84:31 to BCD.
Solution:
1000 0100:0011 0001
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Comparison of Numbering Systems
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MEET Tutoring
Digital Principles1 ENGI10701
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