Binary Numbers Activity
Barbara Ericson – ericson@cc.gatech.edu
Goal:
Demonstrate how to introduce binary numbers to teachers.
Standards:
CSTA K-12 Standards
L1.CT-5 – Demonstrate how 0s and 1s can be used to represent information
L2:CT-14 - Examine connections between elements of mathematics and computer
science including binary numbers, logic, sets and functions.
L3A:CT-5 - Describe the relationship between binary numbers and hexadecimal
numbers.
L3B:CT-7 - Discuss the interpretation of binary sequences in a variety of forms (e.g.,
instructions, numbers, text, sound, image).
CS Principles
Big Idea II (abstraction)-a - Learning Objectives 5 and 6.
Explanation of how data, information, or knowledge are represented for
computational use.
Procedure
1. Start by talking about the decimal number system (ask what 321 and 5749
mean and point out that the decimal number system uses powers of ten) and
by asking the participants to reflect on why we use the decimal number
system. Tell them that some cultures use other number systems like some
Native Americans used the spaces between fingers (8-based) and the Maya
used fingers and toes (20-based).
2. Demonstrate the CS Unplugged binary number cards with dots activity with a
small group (4 or 5 people in the group). Arrange the group in a line from left
to right with the largest number of dots on the left and the smallest on the
right facing the other participants.
3. Ask the small group to make some numbers by turning the cards face up so
that the dots show or face down so the dots don't show. Turn the cards so
that the sum of all the dots shown equals the number. Ask the group to make
some numbers like 4, 5, 7, and 11.
4. Have the group start showing all the numbers from 0 to the highest number
one at a time (count up slowly from 0 to 15 if 4 cards or 31 if 5 cards).
5. Ask if anybody noticed anything (like the one dot having to do lots of work or
the 8 dot mostly standing around till near the end, or that all the cards will be
face up before the next card to the left is turned face up and when that card
turns face up all the cards to the right are turned face down).
6. Count up again and this time ask one person to record the state of the cards
on the board using 0 to represent face down and 1 to represent face up.
Explain that this is the binary number system and show how the binary
number system is similar to the decimal number system except that it is
powers of 2 instead of 10.
7. Have all the participants break into groups of 4-5 people and do the activity.
8. Now ask the participants how high can they count with the fingers on one
hand. They have to count by 1 (not by 5 or 10) and the hand must look
different for each number. Tell groups higher if they guess less than 31.
Then ask how high can they count with the fingers on both hands. Explain
that the total is always 1 less than the next finger would be, so with 5 fingers
you can count to 1 less than what the 6th finger would be (2^6 is 32 and 2^11
is 1024).
9. Map this to computers by explaining that computers use binary numbers to
represent values. Each binary digit (bit) represents 1 digit and we group bits
into 8 bit bytes and use these to represent values. Ask how many different
numbers can you represent in 8 bits? Make the connection to digital cameras
using megapixels (a megapixel is 1 million pixels).
10. Show how to convert any binary number to a decimal number and if the
standards require it how to convert a decimal number to binary.
11. If the standards include octal and hexadecimal show how to convert from
binary to these number systems. Explain that web colors are often specified
in hexadecimal.
Tips:
 Use big cards with the number of dots on each page as well as the dots. You
can laminate the cards and reuse them.
 Step 1 is very important to help learners connect this to existing knowledge.
 Step 6 is very important for bridging the gap from the concrete (dots) to the
abstract (powers of 2).
 Have the participants practice the activity (step 7).
 To get "volunteers" pick one person and have that person pick the next one.
 Some learners will need more time on this concept.
References:
 http://csunplugged.com/binary-numbers - Count the Dots—Binary Numbers
 Blown to Bits Chapter 1 http://www.bitsbook.com/wpcontent/uploads/2008/12/B2B_3.pdf
 Web colors in hexadecimal http://www.webmonkey.com/2010/02/color_charts/
 Practice site for binary to decimal and decimal to binary
http://forums.cisco.com/CertCom/game/binary_game_page.htm
Follow-up questions:
 What would the next card in the sequence be?
 How could you represent the following: negative numbers, decimal numbers,
and alphabetic characters in binary?
 How many bits would you need for all English characters? How many for
Chinese characters?
 How would you represent pictures or sounds on a computer?
Follow-up activities:
1. Have people practice converting binary numbers to decimal and decimal to
binary using the CISCO on-line game:
http://forums.cisco.com/CertCom/game/binary_game_page.htm
2. CS Unplugged - Card Flip Magic—Error Detection & Correction http://www.csunplugged.org/error-detection
3. Binary magic trick http://www.mathmaniacs.org/lessons/01binary/Magic_Trick/
4. Talk about how pictures are stored in computers using binary numbers. One
way is to capture the amount of red, green, and blue at points (pixels) in the
picture. This is called the RGB model.
5. Talk about how sounds are stored in computers using binary numbers. One
way is to capture the air pressure readings over time.
6. Talk about what makes a good password and why it is important to have a
variety of items in a password (upper case letter, lower case letter, number,
etc).
7. Use beads to make a binary bracelet with your birthday encoded in binary.
Use two color beads one for 0 and one for 1.
8. Write a secret message to a friend using the decimal number for each ASCII
character. Have the friend decode the message.
9. Try to make binary numbers using flashlights instead of cards.
Notes: