Binary Number System
Student’s Name: Lauren Biffle & Michael Schoonover
Professor’s Name &Course: Mrs. Gaffner EDU 3338
Date: April 17, 2012
Grade Level: Birth to High School and Above & Beyond!
Content Area(s): Mathematics of binary number system, Applications of binary number
systems, Computers, Basic Hardware, Input and Output, Core Binary Machine Language, etc.
Title of Lesson: The Binary Number System as it relates specifically to Basic Computer
Information Systems and Input/Output.
TEKS Correlations:
§130.367. Mathematics and Technology.
(11)The student is expected to:
(C) convert between the binary, and decimal number systems.
§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
§120.23. Business Computer Information Systems
( c)(2)(A) Identify and explain the functions of various types of technology, hardware, and
software used in business.
Motivation/Objective:
Computers are not a recent invention. Fact is, the basic principles of computers go back to the
very basic principles of mathematics, dating back to the earliest days of mankind. All
information in a computer - documents, pictures, music, even 3D videos and more - are stored
and transmitted in and through computer systems as sequences of tiny “bits,” or “Binary
digITs” of data. A “bit” is the smallest unit of data in a computer, and each bit is translated as
either a zero or a one. Simply put and understood, computers at their most basic and
fundamental level, both “speak” and “hear” at the “binary” level. Our activities today will
demonstrate how sequences of these two symbols - zeros and ones - can be used to represent
virtually any number in the decimal system.
1. Students will first gain an appreciation for the vital importance of the binary numbering system in
computers.
2. They will begin to understand the basic physical hardware structure and organization of a
personal computer, and the overall relationship of the basic input/output devices – keyboard and
mice – to the core processing unit, or the CPU.
3. We will progress to where students will be able to compare, relate, and use both binary and
decimal numbers.
4. Students will begin to learn how to convert simple binary into the more common decimal
numbers.
5.By the end of our short session, hopefully student will begin to appreciate the big picture of small
bits of data.
Assessment:
As in much of our natural learning process, understanding of any given concept is built “line
upon line,” or “concept upon concept.” Our assessment will begin from the moment our lesson
begins, as students watch, interact, and “learn as they go” through the process of unraveling a
basic computer tower and its components.
Our initial learning experience will be verbal, visual, and “hands-on” and student will be given
the opportunity to explore the inner-workings of a basic personal computer, many for the very
first time.
The “assessment” of this portion of our exercises today will be measured by the attention level
of the class, the general interest level and expressed enthusiasm demonstrated on the part of
the class as a whole, and by the individual students themselves. Questions and Answers will be
strongly invited and encouraged.
Further assessment of basic binary math principles will be demonstrated as we distribute the
flashcards for students to use as a discovery exercise. Allowing student the opportunity for
hands on learning with a group will show their understanding of the lesson and help with peer
interaction.
During the second game – if time allows - students will show a clear understanding of the place
values and numerical values of the binary number system.
For after lesson, the Secret Numbers worksheet will be passed to each student and for quiet
work, they must complete with a partner. This will show and individual understanding of the
binary number system.
Rubric:
This lesson, both by its very design and nature, has been intentionally divided into two
introductory levels:
One, a brief introduction to the basic components of a personal computer tower; and
Two, an equally basic introduction to the concepts of the binary numbering system as it relates
to basic computer input, output and language.
Therefore, our rubric is both two-fold and very basic as well. We will not expect students to
gain a great deal of detailed understanding in this introductory lesson, rather, it is our hope to
create and excite some general enthusiasm for both of these dimensions presented in our
lesson so that we might further build upon these concepts with positive reception in future
lessons.
25 Possible Points -
5 Points
3 Points
2 Points
1 point
=============================================================================
Shows interest
Married
Verbally Participates
Engaged
Just Dating
Needs Motivation
Right Up-Front Main-Stream
Hangs Back
Needs Encouraging
Hands-On Involved
Dives Right In
Rolls-Up Sleeves
Reclines
Needs Invitation
Motivates Others
React Catalyst
Gets w/the Swing Goes Solo
Demos Desire 2 Learn Proactive Q&A Occasional Q&A
Gleans
Needs Some Love
Needs Add’l Fuel
==============================================================================
Grading Scale
25 – 20 = A
19 – 15 = B
14 - 8 = C
7 – 5 = Tutoring
Once again, this lesson plan is designed to be introductory, and our primary purpose is to set
the stage for an enthusiastic future of learning. As such, we are primarily concerned with
instilling a genuine interest in the students at this level of introductory instruction. In later
lessons, specific tasks and mastery of skills will be the object of instruction and testing.
Materials:
1. Genuine enthusiasm, excitement and interest on part of both presenters of this
material.
2. Prezi for guiding students to discover binary numbers.
3. Powers-of-2 flash cards and 0/1 cards for each student.
4. Large 0/1 flash cards (O on one side, 1 on the other).
5. Copy of the Secret Numbers worksheet for each student.
6. See through computer
7. Binary T-shirt
8.
Lesson Plan:
1. The first part of this lesson is a skit to catch the attention of the student. Michael wears
his binary t-shirt that has a joke of binary numbers. I ask what it means and it leads into
the discussion of binary. This leads into the application of how binary is used in
computers. Michael will demonstrate all this and more with the see-through computer.
2. The next part of this lesson is a discovery exercise, which should stimulate students to
learn to count in binary, as well as to reinforce their understanding of place value. Using
the PowerPoint questions students will be lead through a discovery discussion.
3. Explain the motivation for the lesson, and tell the students that we're now going to play
some games which will give us practice in writing binary numbers.
4. Divide students into small groups (optional - this lesson can be done by individuals, pairs
or small groups.).
5. Distribute flash cards, one set to each student or group. The set should look something
like this example: (The large cards are approximately 3in x 4in, and the small squares are
2.5in x 2.5in. Note that the small cards have a zero on one side and a one on the other.)
6. Have students sort the cards in descending order so that the largest is on the left and
the smallest is on the right.
7. Discussion: "What do you notice about the numbers on the cards?" For the younger kids
it is enough for them to notice that 1+1=2, 2+2=4, etc. Middle kids should recognize 1 x
2 = 2, 2 x 2 = 4, etc. High school kids should say something like "powers of 2." They
should also note that these are the place values discovered in the preliminary
discussion.
8. More discussion (optional):
a. "If I had given you another card, what would it have been?" (32)
b. "How many cards would I have given you if the maximum card were 128?" (8)
9. More optional discussion: Another fun thing to point out is that each card is one more
than the sum of all the cards lower than it. For example: 1 + 2 = 3 = 4 - 1, and 1 + 2 + 4 =
7 = 8 - 1. "Without taking the time to add up all the cards, can anyone tell me the sum of
all the cards?"
10. Game #1: Call out a number, and have the students place 1s above the cards which sum
to that number, and 0s above all other cards. For example, if you say 11, students place
1s above cards 8, 2, and 1, and 0s above 16 and 4. An easy one: 5 (answer 4, 1); harder:
22 (answer 16, 4, 2); last one: 15 (answer 8,4,2,1). If some students find the answers
quickly, challenge them to find another solution (they won't be able to do so). Have
older kids turn over the flash cards after the first example so they get to practice
remembering the values.
11. Ask if anyone in the class has a system for finding an answer. Upper grades should have
done so. Request that a student demonstrate the system to the group quickly. (A good
method for doing this is to subtract the largest power of two you can from the original
number, then subtract the largest power of two you can from that number, then
subtract the largest power of 2 you can from that number, etc. until you get down to
zero. For example, 37 - 32 = 5, 5 - 4 = 1, and 1 - 1 = 0. Then, write 1s in the places of the
powers of two you subtracted and 0s elsewhere: 37 = 100101.)
12. Discussion
a. "What's the largest number you can get?" (31)
b. "What's the smallest number you can get?" (0)
c. "Can you do your age?" (Sure, unless you're older than 31!)
d. "Can you suggest an impossible number which is between the smallest and largest
numbers?"
13. Explain that since we know the system we're using is binary, the 0s and 1s represent the
original number. Older kids should see the binary expansion as a sum of products where
the decimal value is equal to the sum of each binary digit multiplied by its corresponding
power of 2.
14. Spend a few minutes reemphasizing the connection between binary numbers to decimal
numbers. For example, the decimal value 453 is equal to four 100s plus five 10s plus
three 1s. Similarly, the binary value 111000101 is equal to one 256 plus one 128 plus
one 64 plus one 4 plus one 1. You may want to point out that just as the place values in
the decimal representation are powers of 10, the place values in the binary
representation are powers of 2.
15. Game #3: What number is (binary) 11001? 1011? Try to have the advanced students
visualize the cards.
16. Can we do all numbers up to the maximum discussed above? To answer this question
we need 4 volunteers, each of which holds a large 0/1 card. (We won't go all the way to
31. That would take too long. Instead we'll go to 15.) Each of these 4 students
represents one of the flash cards used in the earlier exercises. Have the remaining
students direct the 4 students to show 0s or 1s, and sit or stand accordingly. Start with
0, all 4 students should show 0s, and be seated. Next do 1, students should show 0001,
and the rightmost person should stand up. Then 2 should be 0010, etc. Try to elicit a
system for incrementing the numbers. Point out that this system is like adding 1 each
time. Younger kids may not see a system.
17. Discussion: Can all numbers be represented using only 0s and 1s if I gave you enough
cards? What's a simple proof of this? (Answer: we can always add 1, so we can start at
zero and get up to any number.)
Conclusion:
Ones and zeros are not explicitly written on the hard drive or transmitted over the modem.
Rather, they are represented by a magnetic orientation of the segments on a hard drive, and by
high and low tones in data transmission. Since bits by themselves don't represent much
information, they are commonly stored together in groups of size 8 called bytes.