Activity 1: Count the Dots — Binary Numbers

What is this about?
Computers store and send information using only two symbols: 0 and 1. How can we use just these two symbols to show words and numbers? Let's find out!

What you will learn

• Counting
• Matching
• Sequencing (putting things in order)

Who this is for
Ages 7 and up.

What you need

• A set of five special cards with dots on them (called "binary cards")
• Worksheets about binary numbers

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Binary Numbers — Let's Get Started!

Before starting the worksheet, it helps to show the class how this works first.

You will need five cards with dots on one side and nothing on the other side. Pick five children to hold the cards at the front of the class. Line the cards up in a special order.

Let's talk about it

Look at the dots on the cards. What do you notice? (Each card has twice as many dots as the card next to it on the right!)

If we added one more card to the left, how many dots would it have? (32!) What about the next one after that?

We can use these cards to make numbers. We turn some cards face-down and add up the dots we can still see.

Try making these numbers:

• 6 (use the 4-dot and 2-dot cards)
• 15 (use the 8-, 4-, 2-, and 1-dot cards)
• 21 (use the 16-, 4-, and 1-dot cards)

Now try counting from zero upwards using the cards!

The rest of the class should watch closely. Can they spot the pattern in how the cards flip? (Each card flips over half as often as the card to its right!)

When a card is turned face-down (hidden), we write it as 0. When a card is showing, we write it as 1. This is called the binary number system — a way of counting using only 0s and 1s.

Try making 01001 with the cards. What number is this in our normal counting (called decimal)? (It's 9!) What would 17 look like in binary? (10001)

Keep trying more numbers until everyone understands!

There are five extra activities after this to help you practice. Try as many as you can!

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Worksheet Activity: Binary Numbers

Learning a new way to count

Did you know computers only use two numbers — 0 and 1? Everything you see or hear on a computer — words, pictures, numbers, movies, and even sounds — is stored using just these two numbers! These activities will teach you how to send secret messages to your friends, just like a computer does.

What to do

Cut out your cards. Lay them out with the 16-dot card on the left.

Make sure your cards stay in this same order the whole time!

Now flip some cards so that exactly 5 dots are showing. Keep the cards in order!

Try making 3, 12, and 19. Is there more than one way to make any of these numbers?

What is the biggest number you can make? What is the smallest? Can you make every number in between, or are some missing?

Extra Challenge: Try making the numbers 1, 2, 3, 4 in order, one after another. Can you figure out a simple way to flip the cards so you always go up by one?

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Worksheet Activity: Working With Binary

In binary, 0 means a card is hidden, and 1 means you can see its dots.

Can you figure out what 10101 means? What about 11111?

What day of the month were you born? Write it using binary! Ask your friends their birthdays and write those in binary too.

Try to figure out some more coded numbers on your worksheet.

Extra Challenge: Get some rods of length 1, 2, 4, 8, and 16 units. Can you make any length from 1 all the way up to 31 units using these rods? You could even show a grown-up how to weigh something heavy, like a suitcase, using a balance scale and just a few weights!

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Worksheet Activity: Sending Secret Messages

Tom is stuck on the top floor of a store. It's almost Christmas, and he wants to get home with his presents! He has tried calling and yelling, but no one hears him. Across the street, he sees someone working late on a computer. How can he get her attention?

Tom looks around the store. Then he has a great idea! He can use the Christmas tree lights to send a message by turning them on and off. He uses a simple binary code that he's sure she'll understand.

Can you figure out his message too? (Use the code where each letter of the alphabet has a number — a=1, b=2, c=3, and so on up to z=26.)

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Worksheet Activity: E-mail and Modems

Computers connected to the internet used to use something called a modem, which also used binary — but with beeping sounds instead of lights! A high beep meant "1" and a low beep meant "0." These beeps happened so fast that they all blurred into one screechy sound. (Fax machines use modems too, so if you've ever heard a fax machine, you've heard this sound!)

Using the same code Tom used with the Christmas lights, try sending a message to a friend. You can go as slow as you like — you don't have to be as fast as a real modem!

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Worksheet Activity: Counting Higher Than 31

Look at your binary cards again. If you made the next card in the pattern, how many dots would it have? What about the card after that? What rule are you using to figure this out?

As you can see, just a few cards can help you count really high numbers!

Look closely at this pattern: 1, 2, 4, 8, 16...

Try adding: 1 + 2 + 4 = ? What do you get?
Now try: 1 + 2 + 4 + 8 = ?

What happens when you add up all the numbers from the start?

Have you heard the phrase "let your fingers do the walking"? Well, now your fingers can do the counting — and you can count higher than ten without being an alien! If each finger on one hand stands for one dot-card, you can count from 0 to 31. That's 32 different numbers (don't forget, zero counts too)!

Try counting in order with your fingers. A finger up means "1." A finger down means "0."

If you use both hands, you can count all the way from 0 to 1023 — that's 1024 numbers!

If you had super bendy toes (now that would make you an alien), you could count even higher! One hand can count to 32 numbers. Two hands can count to 32 × 32 = 1024 numbers. So, if Miss Flexi-Toes used her hands AND her toes, how high do you think she could count?

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Worksheet Activity: More on Binary Numbers

1. Something interesting happens when you add a zero to the right side of a number. In our normal counting system (called decimal), adding a zero to the right multiplies the number by 10. For example, 9 becomes 90, and 30 becomes 300.

But what happens when you add a 0 to the right side of a binary number? Try this:

1001 → 10010
(This is 9 in decimal → what number is this now?)

Make up a few more examples to test your idea. What's the rule? Why do you think this happens?

2. Each card we used is called a bit — short for "binary digit." Our alphabet code used just five cards, or five bits.

But computers need to do more than just show letters — they also need capital letters, numbers, punctuation marks, and symbols like $ or ~.

Look at a keyboard. How many different characters can you count? How many bits do you think a computer needs to store all of them?

Most computers today use a system called ASCII (say: "As-kee"), which stands for American Standard Code for Information Interchange. It uses a set number of bits for each character. Some countries that don't use English need even longer codes for their letters and symbols.

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What's It All About?

Computers use the binary system to store information. It's called "binary" because it only uses two symbols — 0 and 1. This is also called base two (people usually count in base ten).

Each 0 or 1 is called a bit (short for "binary digit"). Inside a computer, a bit is usually stored using a tiny switch called a transistor — it's either "on" or "off" — or a tiny battery-like part that is either charged or not charged.

When information travels over a phone line, high and low beeping sounds are used for the 1s and 0s — just like Tom's Christmas lights, but with sound!

On floppy disks, hard disks, and tapes, bits are stored using tiny magnets that point in different directions.

CDs and DVDs store bits using light — some spots reflect light, and some don't!

One bit alone can't show much. That's why bits are grouped together — usually in groups of 8. A group of 8 bits is called a byte, and it can represent any number from 0 to 255.

How fast a computer works depends on how many bits it can handle at once. A computer that handles 32 bits at a time can work faster than one that only handles 16 bits at a time, because the 16-bit computer has to break big numbers into smaller pieces first.

In the end, bits and bytes are how computers store and send everything — numbers, words, pictures, and more! Later activities will show you how other kinds of information can be stored this way too.