Math-in-CTE Lesson Plan
Lesson Title: Binary Conversions – Base Numbers
Lesson #: IT04
Occupational Area: Information Technology
CTE Concept(s):
Binary basis of computers
Math Concepts:
Number systems with bases other than 10
Lesson
Objective:
Students will be able to:
 Understand how a computer interprets signals from
an input device.
 Convert binary numbers to decimal numbers and
decimal numbers to binary numbers.
Supplies
Computer, Power Point Presentation, White board,
Needed:
worksheets, pencils
Link to Accompanying Materials:
Information Technology IT04 Downloads
TEACHER NOTES
(and answer key)
1. Introduce the CTE lesson.
Explain to students that binary is
Ask students what is the smallest piece of a system founded on using 1s
data that a computer recognizes? What is a and 0s to encode information.
Bit? What is a Byte?
A bit (binary digit) equals a single
pulse in the digital encoding
system. It may have only one of
two values: 0 or 1.
THE "7 ELEMENTS"
A byte is eight bits of information.
In a digital signaling system,
broadly speaking, one byte
represents one piece of
information.
2. Assess students’ math awareness as it
relates to the CTE lesson.
Ask students: What is the base of a number?
What is an exponent? Base 10? Base 2?
Example: 23 = 8
A base is a number that is raised
to various powers to generate
the place values of the
numeration system.
An exponent is tells how many
Ask students if they know what conversion, times a base is used as a factor.
binary and decimal systems are?
Background for number systems
and binary systems:
The first arithmetic we were
taught consisted of ten symbols
called digits: 0, 1, 2, 3, 4, 5, 6, 7,
8, 9. These digits make up the
decimal number system, the
prefix deci- meaning ten.
The binary system consists of
only two digits: 0 and 1. These
two systems are based on
powers of ten and binary is
based on powers of 2.
For an expanded discussion:
Other number systems used in
computer topics are octal (eight
digits) and hexadecimal (deci10 +
hexa6 = 16 characters).
3. Work through the math example embedded in the Use the following
CTE lesson.
links for sample
Convert the decimal values to binary values. Use the blue questions and
actual worksheets
chart for conversions.
that you can use.
107
106
105
104
103
102
101
100
10000000
1000000
100000
1000
1000
100
10
1
27
26
25
24
23
22
21
20
128
64
32
16
8
4
2
1
Binary Values:
http://www.logicalch
ess.com/hayes/lect
urenotes/binaryexer
cise.html
Decimal Values:
00000000
0
10000000
128
11000000
192
11100000
224
11110000
240
11111000
248
11111100
252
11111110
254
11111111
255
4. Work through related, contextual Binary conversion walkthrough
math-in-CTE examples.
1. Compare the value of the
number with 128 at the left end of
Have students complete a walk through of
the table. If it is larger, then place
the method used to convert Decimal
a 1 in the column under 128.
numbers to Base 2. Our number for this
Next, subtract 128 from the
example is 231
original number. 231 is greater
Use the Base 2 conversion table below to
work out the Base 2 equivalent, using the
subtraction/remainder method.
128
64
32
16
8
4
2
1
1
1
1
0
0
1
1
1
than 128 so place a 1 in the 128
column and then subtract 128
from 231. This leaves a
remainder of 103.
2. Compare the 103 with 64. If it
is greater then place a 1 in the 64
column then subtract 64 from 103.
If it is smaller than 64, then move
to the 32 column and do the same
comparison. 103 is greater than
64 so place a 1 in the 64 column
and then subtract 64 from 103.
This leaves a remainder of 39.
3. Compare the 39 with 32. If it is
greater then place a 1 in the 32
column then subtract 32 from 39.
If it is smaller than 32, then move
to the 16 column and do the same
comparison. 39 is greater than 32
so place a 1 in the 32 column and
then subtract 32 from 39. This
leaves a remainder of 7.
4. Compare the 7 with 16. If it is
greater then place a 1 in the 16
column then subtract 7 from 16.
If it is smaller than 16, then move
to the 8 column and do the same
comparison. 7 is less than 16 so
move to the 8 column and
recompare. 7 is less than 8 so
move to 4 column. 7>4 so put a
1 in the 4 column, subtract 4
from 7 to get a remainder of 3.
5. Compare the 3 with 2. 3>2 so
put a 1 in the 2 column and
subtract 2 from 3. This gives us a
remainder of 1, which equals the
value in the last column, so we
can place a 1 in the 1 column to
finish up.
5. Work through traditional math / key
examples.
a. 125
a. 53 = ?
b. 16,807
b. 75 = ?
c. 512
c. 29 = ?
d. 40 = ?
d. 1 (anything to the power of
0 is always 1)
e. x2 =9, x=?
e. 3
f. 3n =27, n=?
f. 3
6.
Students
understanding.
demonstrate
their This is also a good time to show
students how to use the scientific
Have students convert their phone number calculator on their computer to
to binary to demonstrate their understanding also do these calculations. Using
the computer, click on Start,
of converting decimal to binary numbers.
Programs, Accessories,
Calculator, go to View, select
Scientific. Input a number (i.e.
123—make sure dec is selected).
This number will show up as the
following as bin (1111011), hex
(78), and oct (173).
7. Formal assessment.
As an additional activity:
 Do “Board Races” when
students come to the board
two at a time (class is divided
into two teams) and they race
to convert numbers from
decimal to binary.
 Have students look up ASCII
to Binary equivalent for their
name on the internet:
http://www.nickciske.com/tools
/binary.php (Each letter is
assigned a value of 8 bits).
Advanced: Have students use
Hex to look up their names.
Binary Numbers:
http://www.wwshs.org/academics/mat
Copy assessment from link given to assess hfiles/greenleefiles/C01ws1.pdf
students on converting decimal to binary
numbers.