Lesson Plan
Course Title: Computer Maintenance
Session Title: Numbering Systems
Lesson Duration: Lesson length is subjective and will vary from instructor to instructor
Performance Objective:
Upon completion of this assignment, the student will be able to identify the places in binary,
decimal, and hexadecimal numbers and know the value of each. The student will work with
powers of 16 and relate them to hexadecimal places, powers of 10 and relate them to decimal
places, as well as powers of 2 and relate them to binary places.
Specific Objectives:
· Demonstrate the ability to convert decimal numbers into binary and hexadecimal numbers.
· Demonstrate the ability to convert binary numbers into decimal and hexadecimal numbers.
· Demonstrate the ability to convert hexadecimal numbers into decimal and binary numbers.
Preparation
TEKS Correlations:
§130.273. Computer Maintenance
(4) The student acquires an understanding of computer technologies. The student is
expected to:
(F) explain the relationships relative to data-communications theory
Instructor/Trainer
References:
1. Cisco Systems Networking Academy Program: IT Essentials I: PC Hardware and
Software, Chapter 1: Information Technology Basics.
2. Cisco Systems Networking Academy Program: CCNA Semester 1, Chapter 1: Computing
Basics, and Chapter 6: Layer 2 Concepts.
3. JES and Co., A+ Certification: Introduction to Computer Hardware, Lesson 8: System
Settings: BIOS, IRQ, I/O, and DMA.
Instructional Aids:
1. PowerPoint Presentation: Numbering Systems
2. PowerPoint Presentation Handouts: Numbering Systems
3. Worksheet exercise: Binary numbers (and key)
4. Worksheet exercise: Binary to decimal conversion (and key)
5. Worksheet exercise: Decimal to binary conversion (and key)
6. Worksheet exercise: Hexadecimal conversion (and key)
7. Numbering Systems Exam (and key)
Materials Needed:
1. Copies of Worksheets for each student
2. Copies of Exam for each student
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Equipment Needed:
1. A projection system to display the PowerPoint presentation [PC/Monitor, PC/Projector, etc.]
Learner
Students should read the appropriate curriculum material for Numbering Systems [depending on
the text/curriculum being used for this course]. This lesson can be taught with only the
PowerPoint presentation and worksheet handouts.
Introduction
MI
Introduction (LSI Quadrant I):
Having sharp skills in number systems will aid you in your career as an IT
professional. With the ability to convert numbers without the use of a calculator, you
will be able to quickly and easily solve problems that may arise.
Computer systems use the binary numbering system to operate. Why do you think
binary is referred to as the “natural” numbering system for computers to accomplish
their tasks?
[Computers and networking equipment use binary numbers, a series of BITS (short
for binary digits) that are either ON (a binary 1) or OFF (a binary 0). They are
encoded internally in the PC on microchips and on the computer motherboard’s bus
as electrical voltages]. Understanding binary numbers and how they relate to
decimal numbers is critical to understanding how computers work internally.
Outline
MI
Outline (LSI Quadrant II):
Instructor Notes:
1. Introduce numbering systems to students using a
PowerPoint presentation.
a. Introduce the students to the base 10 numbering
system (decimal).
b. Introduce the students to the base 2 numbering
system (binary).
c. Introduce the students to the base 16 numbering
system (hexadecimal).
d. Compare and contrast decimal and binary counting.
e. Demonstrate decimal to binary conversion [two
methods].
f. Demonstrate binary to decimal conversion [two
methods].
g. Introduce hexadecimal to decimal conversion.
h. Discuss basic hexadecimal numbering.
i. Demonstrate hexadecimal to binary conversion.
j. Demonstrate decimal to hexadecimal conversion.
k. Demonstrate hexadecimal to decimal conversion.
l. Demonstrate binary to hexadecimal conversion.
2. Students practice number conversion exercise using
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worksheets.
a. Students complete the worksheet exercise for binary
numbers.
b. Students complete the worksheet exercise for binary
to decimal conversion.
c. Students complete the worksheet exercise for
decimal to binary conversion.
d. Students complete the worksheet exercise for
hexadecimal conversion.
Application
MI
Guided Practice (LSI Quadrant III):
1. Teacher works through the first conversion problem on each worksheet prior to
assigning the worksheet to the student for individual completion.
2. Have the students work through the second conversion problem on each
worksheet with their peers; rework if necessary.
3. Teacher assists student pairs, providing guidance as necessary or has students
volunteer to work/explain problem 2 for the class.
MI
Independent Practice (LSI Quadrant III):
1. Students work independently to complete number system worksheets:
a. Students complete the worksheet exercise for binary numbers
b. Students complete the worksheet exercise for binary to decimal conversion
c. Students complete the worksheet exercise for decimal to binary conversion
d. Students complete the worksheet exercise for hexadecimal conversion
Summary
MI
Review (LSI Quadrants I and IV):
1. Ask students summary questions.
a. What are the symbols used by base 2? [0, 1]
b. What are the symbols used by base 10? [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
c. What are the symbols used by base 16? [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C,
D, E, F]
d. Can you describe a method of converting a decimal number to binary?
e. Can you describe a method of converting a binary number to decimal?
2. Demonstrate [one more time] the conversion procedures the students have just
experienced.
a. Binary to decimal example
b. Decimal to binary example
c. Binary to hexadecimal example
d. Hexadecimal to binary example
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Evaluation
MI
Informal Assessment (LSI Quadrant III):
The teacher will monitor student progress during independent practice and provide
independent re-teach/redirection as needed.
MI
Formal Assessment (LSI Quadrant III, IV):
Administer the Numbering Systems Exam.
Extension
MI
Extension/Enrichment (LSI Quadrant IV):
1. Students that have mastered the conversion techniques can peer-tutor students
[one-on-one] that are having difficulty solving the conversions.
2. Students can show their conversion techniques on the board for the entire class
to observe.
3. Students can observe their computer’s network interface card (NIC) MAC
address in hexadecimal, and convert the MAC address to binary and decimal.
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Icon
MI
Verbal/
Linguistic
Logical/
Mathematical
Visual/Spatial
Musical/
Rhythmic
Bodily/
Kinesthetic
Intrapersonal
Interpersonal
Naturalist
Existentialist
Teaching Strategies
Personal Development
Strategies
Lecture, discussion, journal
writing, cooperative learning,
word origins
Reading, highlighting, outlining,
teaching others, reciting information
Problem-solving, number
games, critical thinking,
classifying and organizing,
Socratic questioning
Mind-mapping, reflective
time, graphic organizers,
color-coding systems,
drawings, designs, video,
DVD, charts, maps
Use music, compose songs
or raps, use musical
language or metaphors
Organizing material logically, explaining
things sequentially, finding patterns,
developing systems, outlining, charting,
graphing, analyzing information
Developing graphic organizers, mindmapping, charting, graphing, organizing
with color, mental imagery (drawing in
the mind’s eye)
Use manipulatives, hand
signals, pantomime, real life
situations, puzzles and board
games, activities, roleplaying, action problems
Reflective teaching,
interviews, reflective listening,
KWL charts
Cooperative learning, roleplaying, group brainstorming,
cross-cultural interactions
Natural objects as
manipulatives and as a
background for learning
Socratic questions, real life
situations, global
problems/questions
Creating rhythms out of words, creating
rhythms with instruments, playing an
instrument, putting words to existing
songs
Moving while learning, pacing while
reciting, acting out scripts of material,
designing games, moving fingers under
words while reading
Reflecting on personal meaning of
information, studying in quiet settings,
imagining experiments, visualizing
information, journaling
Studying in a group, discussing
information, using flash cards with
others, teaching others
Connecting with nature, forming study
groups with like-minded people
Considering the personal relationship to
the larger context
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Student Name:
Date:
Binary t o Decimal
This binary
number...
1 1 1 1 1 1 1 1
7
6
5
4
3
2
2 2
2
2
128 + 64 + 32 + 16 + 8
This binary
number...
2
+
2
4
1
+
2
2
0
+
2
1 = 255
1 0 0 1 0 1 0 1
7
6
2
2
128 + 0
5
+
2
0
4
+
3
2
2
16 + 0
2
+
2
4
1
+
2
0
E quals this
decimal number
E quals this
decimal number
0
+
2
1 = 14 9
C onvert each binary number int o a decimal number.
1.
110 0 10 0 1
=
9.
0 110 1110
=
2.
0 10 0 0 111
=
10.
0 0 0 10 111
=
3.
10 0 0 0 110
=
11.
111110 0 0
=
4.
0 0 0 10 0 0 1
=
12.
1110 0 0 10
=
5.
10 0 0 1 0 0 0
=
13.
0 0 0 1110 1
=
6.
0 0 111110
=
14.
0 110 1111
=
7.
0 10 10 10 1
=
15.
10 0 10 111
=
8.
10 10 10 10
=
16.
1110 0 10 1
=
Computer Maintenance I: Numbering Systems Binary to Decimal Worksheet
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Binary to Decimal Key
11001001
01000111
10000110
00010001
10001000
00111110
01010101
10101010
201
71
134
17
136
62
85
170
01101110
00010111
11111000
11100010
00011101
01101111
10010111
11100101
110
23
248
226
29
111
151
229
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Student Name:
Date:
Decimal t o Binary
151
128 128? YE S
23 6432?? NN OO
16 16? YE S
7 8? N O
4 4 ? YE S
3
2 2? YE S
1
1 1? YE S
0
Th is d ecim al
n u m b er...
64
32
16
8
151
128
1
2
7
=
Eq u als t h is
b in ar y n u m b er
2
4
1
0
0
1
0
1
1
6
5
4
3
2
1
2
2
2
2
2
2
1
2
0
C onvert each decimal number int o a binary number.
1.
137 =
11.
200 =
2.
128 =
12.
171=
3.
63 =
13.
150 =
4.
213 =
14.
27 =
5.
49 =
15.
19 =
6.
111=
16.
189 =
7.
24 2 =
17.
222 =
8.
192 =
18.
79 =
9.
89 =
19.
73 =
10.
2=
20.
136 =
Computer Maintenance I: Numbering Systems Decimal to Binary Worksheet
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Decimal to Binary Key
137
128
63
213
49
111
242
192
89
2
10001001
10000000
00111111
11010101
00110001
01101111
11110010
11000000
01011001
00000010
200
171
150
27
19
189
222
79
73
136
11001000
10101011
10010110
00011011
00010011
10111101
11011110
01001111
01001001
10001000
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Student Name:
Date:
HEXADECIMAL CONVERSIONS
INSTRUCTIONS:
Convert the following numbers to their appropriate base forms. Record your
answers in the spaces provided in the table.
BASE 10
BASE 2
BASE 16
243
10101100
AE
110110
131
3F
98
10010001
146
11000011
4D
11110001
172
E2
100100
195
31
1001111
7B
146
5A
11100000
223
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HEXADECIMAL CONVERSIONS
INSTRUCTIONS: Convert the following numbers to their appropriate base forms
BASE 10
BASE 2
BASE 16
243
11110011
F3
172
10101100
AC
174
10101110
AE
54
110110
36
131
10000011
83
63
111111
3F
98
11000010
62
145
10010001
91
146
10010010
92
195
11000011
C3
77
1001101
4D
241
11110001
F1
172
10101100
AC
226
11100010
E2
36
100100
24
195
11000011
C3
49
110001
31
79
1001111
4F
123
1111010
7B
146
10010010
92
90
1011010
5A
224
11100000
E0
223
11011111
DF
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Student Name:
Date:
In t rodu ct ion t o Bin ary N u m b ers
Part 1
Fill in t he rest of
t he numbers, in
order.
Decimal
0
1
Binary
Par t 2
N ow writ e t he
binary number
for each decimal
number
Par t 3
Fill in t he decimal and
binary equivalent s of
each exponent .
Decimal
Binary
0
2=
1
2=
2
2=
3
2=
4
2=
5
2=
6
2=
7
2=
32
64
128
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Introduction to Binary Numbers Key
Part 1
Decimal
Part 2
Binary
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
32
64
128
0
1
10
11
100
101
110
111
1000
1001
1010
1011
1100
1101
1110
1111
10000
100000
1000000
10000000
Part 3
Decimal
20
21
21
23
24
25
26
27
Binary
1
2
4
8
16
32
64
128
1
10
100
1000
10000
100000
1000000
10000000
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Student Name:
Date:
NUMBERING SYSTEMS EXAM
DIRECTIONS:
Circle the letter that corresponds to the one (1) best answer for each of the questions below.
Question 1: All functions of a computer are based upon the use and manipulation of numbers.
Which number system is most native to a computer?
A.
B.
C.
D.
binary
decimal
hexadecimal
octal
Question 2: What is the decimal conversion of the binary number 11011001?
A.
B.
C.
D.
221
193
217
192
Question 3: What is the hexadecimal conversion of the decimal number 224?
A.
B.
C.
D.
F0
E0
92
9E
Question 4: What is the decimal conversion of the hexadecimal number 7F?
A.
B.
C.
D.
115
134
201
127
Question 5: What is the binary conversion of the hexadecimal number CB?
A.
B.
C.
D.
10111001
11100001
11000100
11001011
Question 6: Which binary number represents the decimal number 133?
A.
B.
C.
D.
10001011
11000001
10000111
10000101
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Question 7: What is the hexadecimal equivalent of the decimal number 241?
A.
B.
C.
D.
E7
D3
F1
A9
Question 8: What is the decimal value of the binary number 11111111?
A.
B.
C.
D.
0
64
192
255
Question 9: What is the definition of a bit?
A.
B.
C.
D.
the section of a network that is bounded by bridges, routers, or switches
a binary digit used in the binary number system, either 0 or 1
the interface on an internetworking device, such as a router
the network areas within which data packets that have collided are propagated
Question 10: Which of the following phrases best describes the decimal numbering system?
A.
B.
C.
D.
It is also called the Base 100 Number System.
It is based on powers of 1.
It uses the 10 symbols 0 - 9.
It is the same as the ASCII numbering system.
Question 11: Which numbering system is based on powers of 2?
A.
B.
C.
D.
octal
hexadecimal
binary
ASCII
Question 12: What is the decimal number 151 in binary?
A.
B.
C.
D.
10010111
10010110
10101011
10010011
Question 13: What is the binary number 11011010 in decimal?
A.
B.
C.
D.
218
202
222
186
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Question 14: Convert the decimal number 43 to Hex.
A.
B.
C.
D.
2B
1F
EF
1A
Question 15: Hexadecimal is used to represent what kind of addresses?
A.
B.
C.
D.
IP
Octal
MAC
Digital
Question 16: What is 16 raised to the first power (16 1 )?
A.
B.
C.
D.
decimal 1
decimal 16
hex FF
hex 16
Question 17: Convert the decimal number 2989 to Hex.
A.
B.
C.
D.
FDD1
BAD
ED
CAD
Question 18: What is the decimal value of the hex number ABE?
A.
B.
C.
D.
2750
5027
2570
7250
Question 19: What is the hex value of the binary number 11100010?
A.
B.
C.
D.
D2
E2
G2
H20
Question 20: Which numbering system is based on powers of 10?
A.
B.
C.
D.
octal
hexadecimal
binary
decimal
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Numbering Systems Exam Key
Question 1: All functions of a computer are based upon the use and manipulation of numbers.
Which number system is most native to a computer?
A.
B.
C.
D.
binary
decimal
hexadecimal
octal
Question 2: What is the decimal conversion of the binary number 11011001?
A.
B.
C.
D.
221
193
217
192
Question 3: What is the hexadecimal conversion of the decimal number 224?
A.
B.
C.
D.
F0
E0
92
9E
Question 4: What is the decimal conversion of the hexadecimal number 7F?
A.
B.
C.
D.
115
134
201
127
Question 5: What is the binary conversion of the hexadecimal number CB?
A.
B.
C.
D.
10111001
11100001
11000100
11001011
Question 6: Which binary number represents the decimal number 133?
A.
B.
C.
D.
10001011
11000001
10000111
10000101
Question 7: What is the hexadecimal equivalent of the decimal number 241?
A.
B.
C.
D.
E7
D3
F1
A9
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Question 8: What is the decimal value of the binary number 11111111?
A.
B.
C.
D.
0
64
192
255
Question 9: What is the definition of a bit?
A.
B.
C.
D.
the section of a network that is bounded by bridges, routers, or switches
a binary digit used in the binary number system, either 0 or 1
the interface on an internetworking device, such as a router
the network areas within which data packets that have collided are propagated
Question 10: Which of the following phrases best describes the decimal numbering system?
A.
B.
C.
D.
It is also called the Base 100 Number System.
It is based on powers of 1.
It uses the 10 symbols 0 - 9.
It is the same as the ASCII numbering system.
Question 11: Which numbering system is based on powers of 2?
A.
B.
C.
D.
octal
hexadecimal
binary
ASCII
Question 12: What is the decimal number 151 in binary?
A.
B.
C.
D.
10010111
10010110
10101011
10010011
Question 13: What is the binary number 11011010 in decimal?
A.
B.
C.
D.
218
202
222
186
Question 14: Convert the decimal number 43 to Hex.
A.
B.
C.
D.
2B
1F
EF
1A
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Question 15: Hexadecimal is used to represent what kind of addresses?
A.
B.
C.
D.
IP
Octal
MAC
Digital
Question 16: What is 16 raised to the first power (16 1 )?
A.
B.
C.
D.
decimal 1
decimal 16
hex FF
hex 16
Question 17: Convert the decimal number 2989 to Hex.
A.
B.
C.
D.
FDD1
BAD
ED
CAD
Question 18: What is the decimal value of the hex number ABE?
A.
B.
C.
D.
2750
5027
2570
7250
Question 19: What is the hex value of the binary number 11100010?
A.
B.
C.
D.
D2
E2
G2
H20
Question 20: Which numbering system is based on powers of 10?
A.
B.
C.
D.
octal
hexadecimal
binary
decimal
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