Innovation Media Enrichment

Day One -- Binary Numbers For this activity, you will need to cut out the provided 5 cards with dots on one side and nothing on the other. Notice that each card has twice as many dots as the card to its right. Think about how many dots would be on the next card if we placed another card to the left. We can use these cards to make numbers by turning some of them face down and adding up the dots that are showing. When a binary number card is not showing, it is represented by a zero. When a binary number card is showing, it is represented by a one. This is the binary number system.

4 Photocopiable for classroom use only. © 2005 Computer Science Unplugged (www.unplugged.canterbury.ac.nz)

Binary Numbers

Introduction

Before giving out the worksheet on page 5, it can be helpful to demonstrate the principles to the whole group.

For this activity, you will need a set of five cards, as shown below, with dots on one side and nothing on the other. Choose five children to hold the demonstration cards at the front of the class. The cards should be in the following order:

Discussion

What do you notice about the number of dots on the cards? (Each card has twice as many as the card to its right.)

How many dots would the next card have if we carried on to the left? (32) The next…?

We can use these cards to make numbers by turning some of them face down and adding up the dots that are showing. Ask the children to make 6 (4-dot and 2-dot cards), then 15 (8-, 4-, 2- and 1-dot cards), then 21 (16, 4 and 1)…

Now try counting from zero onwards.

The rest of the class needs to look closely at how the cards change to see if they can see a pattern in how the cards flip (each card flips half as often as the one to its right). You may like to try this with more than one group.

When a binary number card is not showing, it is represented by a zero. When it is showing, it is represented by a one. This is the binary number system.

Ask the children to make 01001. What number is this in decimal? (9) What would 17 be in binary? (10001)

Try a few more until they understand the concept.

There are five optional follow-up extension activities, to be used for reinforcement. The children should do as many of them as they can.

Photocopiable for classroom use only. 5 © 2002 Computer Science Unplugged (www.unplugged.canterbury.ac.nz)

Worksheet Activity: Binary Numbers

Learning how to count So, you thought you knew how to count? Well, here is a new way to do it!

Did you know that computers use only zero and one? Everything that you see or hear on the computer—words, pictures, numbers, movies and even sound is stored using just those two numbers! These activities will teach you how to send secret messages to your friends using exactly the same method as a computer.

Instructions Cut out the cards on your sheet and lay them out with the 16-dot card on the left as shown here:

Make sure the cards are placed in exactly the same order.

Now flip the cards so exactly 5 dots show—keep your cards in the same order!

Find out how to get 3, 12, 19. Is there more than one way to get any number? What is the biggest number you can make? What is the smallest? Is there any number you can’t make between the smallest and biggest numbers?

Extra for Experts: Try making the numbers 1, 2, 3, 4 in order. Can you work out a logical and reliable method of flipping the cards to increase any number by one?

Day Two -- Binary Numbers Use your binary number knowledge to figure out the coded numbers.


Worksheet Activity: Working With Binary The binary system uses zero and one to represent whether a card is face up or not. 0 shows that a card is hidden, and 1 means that you can see the dots. For example:

Can you work out what 10101 is? What about 11111?

What day of the month were you born? Write it in binary. Find out what your friend’s birthdays are in binary.

Try to work out these coded numbers:

Extra for Experts: Using a set of rods of length 1, 2, 4, 8 and 16 units show how you can make any length up to 31 units. Or you could surprise an adult and show them

how they only need a balance scale and a few weights to be able to weigh those heavy things like suitcases or boxes!

Day Three -- Binary Numbers Use your knowledge of binary numbers to decode the message that Tom is sending using lights.


Worksheet Activity: Sending Secret Messages

Tom is trapped on the top floor of a department store. It’s just before Christmas and he wants to get home with his presents. What can he do? He has tried calling, even yelling, but there is no one around. Across the street he can see some computer person still working away late into the night. How could he attract her attention? Tom looks around to see what he could use. Then he has a brilliant idea—he can use the Christmas tree lights to send her a message! He finds all the lights and plugs them in so he can turn them on and off. He uses a simple binary code, which he knows the woman across the street is sure to understand. Can you work it out?

1 2 3 4 5 6 7 8 9 10 11 12 13

a b c d e f g h i j k l m 14 15 16 17 18 19 20 21 22 23 24 25 26

n o p q r s t u v w x y z

Day Four -- Binary Numbers Using the same code that Tom used when he was trapped in the department store, compose a message to a friend using binary numbers.


Worksheet Activity: E-mail and Modems Computers connected to the internet through a modem also use the binary system to send messages. The only difference is that they use beeps. A high-pitched beep is used for a one and a low-pitched beep is used for a zero. These tones go very fast—so fast, in fact, that all we can hear is a horrible continuous screeching sound. If you have never heard it, listen to a modem connecting to the Internet, or try calling a fax machine—fax machines also use modems to send information.

Using the same code that Tom used in the department store, try sending an e-mail message to your friend. Make it easy for yourself and your friend though—you don’t have to be as fast as a real modem!

Day Five -- Binary Numbers For this activity, you will think about how to count higher than 31 using binary numbers.


Worksheet Activity: Counting higher than 31 Look at the binary cards again. If you were going to make the next card in the sequence, how many dots would it have? What about the next card after that? What is the rule that you are following to make your new cards? As you can see, only a few cards are needed to count up to very big numbers.

If you look at the sequence carefully, you can find a very interesting relationship:

1, 2, 4, 8, 16… Try adding: 1 + 2 + 4 = ? What does it come to?

Now try 1 + 2 + 4 + 8 = ?

What happens if you add all the numbers up from the beginning?

Have you ever heard of “let your fingers do the walking”? Well now you can let your fingers do the counting, but you can get much higher than ten—no, you don’t have to be an alien! If you use the binary system and let each finger on one hand represent one of the cards with dots you can count from 0–31. That’s 32 numbers. (Don’t forget that zero is a number too!)

Try counting in order using your fingers. If a finger is up it is a one, and if it is down it is a zero.

You can actually get from 0–1023 if you use both hands! That’s 1024 numbers!

If you had really bendy toes (now you would have to be an alien) you could get even higher. If one hand can be used to count 32 numbers, and two hands can count to 32 × 32 = 1024 numbers, what is the biggest number Miss Flexi-Toes can reach?


Worksheet Activity: More on Binary Numbers 1. Another interesting property of binary numbers is what happens when a zero is

put on the right hand side of the number. If we are working in base 10 (decimal), when you put a zero on the right hand side of the number, it is multiplied by 10. For example, 9 becomes 90, 30 becomes 300.

But what happens when you put a 0 on the right of a binary number? Try this:

1001 → 10010 (9) (?)

Make up some others to test your hypothesis. What is the rule? Why do you think this happens?

2. Each of the cards we have used so far represents a ‘bit’ on the computer (‘bit’ is short for ‘binary digit’). So our alphabet code we have used so far can be represented using just five cards, or ‘bits’. However a computer has to know whether letters are capitals or not, and also recognise digits, punctuation and special symbols such as $ or ~.

Go and look at a keyboard and work out how many characters a computer has to represent. So how many bits does a computer need to store all the characters?

Most computers today use a representation called ASCII (American Standard Code for Information Interchange), which is based on using this number of bits per character, but some non-English speaking countries have to use longer codes.

Day Seven -- Binary Numbers Use your knowledge of binary numbers and the alphabet reference to crack the code and answer the questions.

1. What do you call a duck that gets all As?

00001-10111-01001-10011-00101-10001-10101-00001-00011 01011-00101-100102. How can you tell a vampire has a cold?

10011-01000-00101-10011-10100-00001-10010-10100-10011 00011-01111-00110-00110-01001-011103. Why can’t Elsa have a balloon?

00010-00101-00011-00001-10101-10011-00101-10011-01000 00101-10111-01001-01100-01100-01100-00101-10100-01001 10100-00111-011114. Why are ghosts bad liars?

00010-00101-00011-00001-10101-10011-00101-11001-01111 10101-00011-00001-01110-10011-00101-00101-10010-01001 00111-01000-10100-10100-01000-10010-01111-10101-00111 01000-10100-01000-00101-011015. How do you get a squirrel to like you?

00001-00011-10100-01100-01001-01011-00101-00001-01110 10101-10100

CRACK THE CODE BINARY CHALLENGE

12345678910111213

ABCDEFGHIJKLM

14151617181920212223242526

NOPQRSTUVWXYZ

00001

00010

00011

00100

00101

00110

00111

01000

01001

01010

01011

01100

01101

01110

01111

10000

10001

10010

10011

10100

10101

10110

10111

11000

11001

11010

BINARY CODE ALPHABET REFERENCE

Day Eight -- Binary Numbers Use each set of cards to convert the numbers into binary numbers.

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NATIONAL CENTER FOR WOMEN & INFORMATION TECHNOLOGY » ncwit.org Computer Science-in-a-Box: Unplug Your Curriculum

WORKSHEET 1 — BINARY NUMBERS

Represent each normal number by crossing out the cards you do not want to use. Then, convert each set of cards into strings of 1’s and 0’s! The first row has been completed for you, as an example.

Number Binary Number

2 00010

5

3

12

19

8

15

Day Nine -- Binary Numbers Use your knowledge of binary numbers to answer the questions on the following sheet.

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WORKSHEET 3 — CHECK YOUR UNDERSTANDING

1. What is the next number in the sequence?

00001 00010 00011 00100 ______

2. What decimal number is represented by 01011?

3. How would you write the number 20 in binary?

4. What is the largest number you can represent using 5 cards (i.e., 5 bits)?

5. What is the largest number you could represent if you had only 3 cards?

6. How many cards (bits) would you need to represent the number 63?

Day 10 -- Binary Numbers Computer scientists agreed on a standard way to represent letters and numbers. This encoding scheme is called ASCII (pronounced “as key”), which stands for American Standard Code for Information Interchange. It’s a system used to represent English characters. It uses 7 bits. ASCII includes 128 different characters, which includes numbers, lowercase letters, uppercase letters, and some special characters such as punctuation marks. ASCII characters are stored using 8 bits (each ASCII character uses an 8-digit binary number). The left-most 7 bits in a binary number in ASCII are used to represent the character. For example, the letter “A” is number 65 in decimal, or 1000001 in binary. The right-most digit is used to represent a parity bit, which helps a computer know whether an error has occurred. The parity bit is used to make any number have an even count of 1’s. Encode and decode messages using ASCII.

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WORKSHEET 1 — EXPLORING ASCIIASCII stands for the American Standard Code for Information Interchange. It’s a system used to represent English characters, and it was designed to encode 128 different characters. The table below maps the uppercase alphabet to 7-digit values.

A 1000 001 B 1000 010 C 1000 011 D 1000 100 E 1000 101 F 1000 110

G 1000 111 H 1001 000 I 1001 001 J 1001 010 K 1001 011 L 1001 100

M 1001 101 N 1001 110 O 1001 111 P 1010 000 Q 1010 001 R 1010 010

S 1010 011 T 1010 100 U 1010 101 V 1010 110 W 1010 111 X 1011 000

Y 1011 001 Z 1011 010

Part I. First try translating this message from binary numbers to English letters:

1000 010 1000 101 1000 111 1001 001 1001 110

________ ________ ________ ________ ________

Part II. Encode your own message using the binary representation of each alphabetic character that you use. Write each binary number on the lines below. Your message may be anywhere from 8 – 15 letters long. Then, trade with a friend, and see if you can decode each other’s messages.

________ ________ ________ ________ ________

________ ________ ________ ________ ________

________ ________ ________ ________ ________

Part III. Two friends named Alice and Bob are exchanging messages using ASCII code. It looks like Alice may have made a mistake when she converted her letters into binary. Can you find Alice’s mistake? Once you have found where she went wrong, describe Alice’s mistake on the lines below, and correct her binary message.

1001 000 1000 100 1001 100 1001 100 1001 111

1000 010 1001 111 1000 010

_________________________________________________________________________

_________________________________________________________________________

Day Eleven -- Finding the Best Solution This activity will help you understand how computers are used to find the best solutions for real-life problems, such as how to link power lines between houses. Pave enough streets in your city so that everyone can travel to everyone else's house along a paved path. Each block costs $1 to pave. Try to find the cheapest way to pave enough blocks to allow access to everyone's house along a paved path.

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WORKSHEET 1 — MUDDY CITYOnce upon a time, there was a city that had no roads. Getting around the city was particularly difficult after rainstorms, because the ground became very muddy — cars got stuck in the mud, and people got their boots dirty. The mayor of the city decided that some of the streets must be paved, but didn’t want to spend more money than necessary because the city also wanted to build a swimming pool. The mayor therefore specified two conditions:

1. Enough streets must be paved so that it is possible for everyone to travel from their house to anyone else’s house only along paved roads.

2. The paving should cost as little as possible. The cost to pave one block is $1.

The number of paving stones between each house represents the cost of paving that route. Find the best route that connects all of the houses, but uses as few counters (paving stones) as possible

.

Day Twelve -- Decorating the Town You need to decorate the streets in the town. You must decorate so that anyone from a house can travel to another house only on decorated paths. The number on the paths tells you how much it will cost to decorate that street. Try to decorate the streets using as little money as possible!

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WORKSHEET 2 — HALLOWEEN CANDYHalloween is coming! Your class at school is in charge of decorating the streets. You’ve been given money to do the decorating, and any money that you don’t spend is yours to keep.

The layout below shows what type of candy each house is giving out. The numbers between the houses represent the cost of decorating that street. You use the layout to decide which streets to decorate, based on two conditions:

1. Enough streets must be decorated so that it is possible for everyone to travel from their house to anyone else’s house only along decorated roads (so everyone can get all types of candy), and

2. The decorating should cost as little as possible.

On the layout below, circle all the streets that you plan to decorate.

Day Thirteen -- Edge Detection If we are trying to program a computer to identify objects in an image, it can be helpful to find the edges in an image. From these edges, we can pick out larger features such as shapes. Try to identify what the image is after you detect the edges. This technique is similar to what computers do. Before you detect the edges, it is very difficult to see the image. After, you have a clear idea of the dominant shape in the image.

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WORKSHEET 1 —EDGE DETECTION

One simple way to find edges is to look at two neighboring pixels and take the difference between their values. If it’s big, this means the colors are very different, so it’s an edge.

Try it yourself! The grid below is filled with numbers that represent a grayscale image. See if you can detect edges the way a computer would do it. If the values of two neighboring squares on the grid differ by more than 50, draw a thick line between them.

21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21

21 21 21 21 21 21 21 103 103 21 21 21 21 21 21 21

21 21 21 21 21 21 21 99 103 21 21 21 21 21 21 21

21 21 21 21 21 21 21 91 103 21 21 21 21 21 21 21

21 21 21 21 21 21 21 103 99 21 21 21 21 21 21 21

21 21 21 21 21 21 91 99 103 99 21 21 21 21 21 21

21 72 93 101 103 105 99 103 91 99 104 102 101 91 103 21

21 21 99 99 91 103 99 99 103 99 99 91 99 88 21 21

21 21 21 99 99 91 91 99 103 99 91 99 103 21 21 21

21 21 21 21 99 99 99 99 99 99 99 103 21 21 21 21

21 21 21 21 21 99 103 103 91 103 103 21 21 21 21 21

21 21 21 21 21 103 91 99 99 103 91 21 21 21 21 21

21 21 21 21 103 91 99 99 103 99 103 99 21 21 21 21

21 21 21 21 91 103 99 21 21 99 91 99 21 21 21 21

21 21 21 103 103 21 21 21 21 21 21 103 99 21 21 21

21 21 21 103 3 21 21 21 21 21 21 7 103 21 21 21

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WORKSHEET 2 —EDGE DETECTION

Given a grayscale image, one simple way to find edges is to look at two neighboring pixels and take the difference between their values. If it’s big, this means the colors are very different, so it’s an edge.

Try it yourself! The grid below is filled with numbers that represent a grayscale image. See if you can detect edges the way a computer would do it. If the values of two neighboring squares on the grid differ by more than 40, draw a thick line between them.

255 255 255 255 255 255 255 255 255 255 255 255 255 255 255 255

255 80 80 255 255 255 255 255 255 255 255 255 255 80 80 255

255 90 90 80 255 255 255 255 255 255 255 255 80 85 85 255

255 90 90 80 255 255 255 255 255 255 255 80 80 85 85 255

255 90 90 90 80 255 255 255 255 255 255 80 85 85 80 255

255 90 90 90 80 255 255 255 255 255 80 80 85 85 80 255

255 90 90 90 80 80 20 80 80 20 80 80 85 85 90 255

255 255 90 90 80 80 20 80 80 20 80 80 85 85 255 255

255 255 90 90 80 80 85 80 80 85 80 80 85 90 255 255

255 80 90 20 20 20 90 85 85 90 20 20 20 80 90 255

255 80 80 62 0 62 90 85 85 90 62 0 62 85 90 255

255 90 85 62 0 62 62 85 85 80 62 0 62 85 90 255

255 90 85 85 62 85 85 85 85 80 85 62 85 85 90 255

255 255 85 85 90 90 10 10 10 10 85 85 85 85 90 255

255 255 85 85 85 85 10 40 40 10 85 85 85 85 255 255

255 255 85 85 85 85 85 10 10 85 85 85 85 85 255 255

Day Fourteen -- Using Shapes to Identify Objects Another technique computers use to identify objects is to compare them to known shapes. On the attached worksheet, what shapes would be used to recognize the kangaroo? What are some reasons that a computer might want to be detailed? What are some reasons that a computer might want to be general?

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WORKSHEET 3 — KANGAROO SHAPE COMPARISON

Rectangle Circle Triangle Trapezoid Oval

SHAPE BANK

Computers look at things by breaking them down into shapes. Look at the elephant to see how a computer might break it down into basic shapes:

Now try to do the same with the image below:

Innovation Media Enrichment

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