Count the Dots—Binary Numbers

What Is This About?

Computers store information. They use just two symbols. The symbols are 0 and 1. This is called binary. We can use 0 and 1 to show words and numbers.

Skills You Will Use

• Counting
• Matching
• Putting things in order

Who This Is For

Kids age 7 and up.

What You Need

You need five cards. Put a sticker dot on some. Each child needs a set of five cards. Cut them from the card page.

Binary Numbers

Let's Learn Together

First, show the class five cards. Each card has dots. Or no dots. Line up five children. Each child holds one card.

Let's Talk About It

Look at the dots on the cards. What do you see? Each card has two times more dots. The card is next to a smaller one.

What comes next? If we keep going left, the next card has 32 dots. Then 64!

We can flip cards over. Some show dots. Some do not. We add up the dots we see. This makes new numbers.

Let's make the number 6. Flip the 4-dot card and the 2-dot card.
Let's make 15. Flip the 8-, 4-, 2-, and 1-dot cards.
Let's make 21. Flip the 16-, 4-, and 1-dot cards.

Now let's count from zero. Watch how the cards flip. Do you see a pattern? Each card flips less than the one before it.

When a card is hidden, we write 0.
When a card shows, we write 1.
This is called the binary number system.

Let's make 01001. What number is this? It is 9.
What is 17 in binary? It is 10001.

Try more numbers. Keep practicing!

Worksheet: Binary Numbers

Learn a New Way to Count!

Did you know computers use only 0 and 1? Words. Pictures. Numbers. Movies. Sound. All of it is stored with just 0 and 1!

You can learn this too. Then you can send secret messages to your friends. Just like a computer does!

What To Do

Cut out your cards. Put the 16-dot card on the left.

Keep the cards in this same order every time.

Now flip cards so 5 dots show. Keep the same order!

Try to make 3. Try to make 12. Try to make 19.
Is there more than one way to make a number?

What is the biggest number you can make?
What is the smallest number?
Can you make every number in between?

Extra Challenge

Try making 1, 2, 3, 4 in order.
Can you find a way to add one each time?

Worksheet: Working With Binary

The binary system uses 0 and 1.
0 means the card is hidden.
1 means you can see the dots.

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

What day of the month were you born? Write it in binary.
Ask a friend. Find their birthday in binary too.

Try to solve these binary number codes.

Extra Challenge

Get rods that are 1, 2, 4, 8, and 16 units long.
Can you make any length up to 31 units?

You can also weigh heavy things, like suitcases. All you need is a scale and a few weights!

Worksheet: Sending Secret Messages

Tom is stuck on the top floor of a store. It is almost Christmas. He wants to go home with his gifts. He tries calling. He tries yelling. No one is around.

Across the street, he sees someone working late. She works with computers. How can he get her attention?

Tom looks around the store. He has an idea! He can use the Christmas tree lights. He can turn them on and off. He can send a message using binary code!

He knows the woman will understand the code. Can you figure it out too?

Worksheet: E-mail and Modems

Computers connect to the internet using a modem. Modems use binary too. But they use beeps instead of lights.

A high beep means 1.
A low beep means 0.

These beeps go very fast. So fast, it sounds like screeching! Have you heard this sound? Try calling a fax machine. Fax machines use modems too.

Use the same code Tom used. Try sending an email message to a friend. You can go slower than a real modem!

Worksheet: Counting Higher Than 31

Look at the binary cards again. What is the next card in line? How many dots does it have? What about the card after that?

What rule are you using to make new cards?

You only need a few cards to count very high numbers!

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

Try adding: 1 + 2 + 4 = ?
Now try: 1 + 2 + 4 + 8 = ?
What happens if you add all the numbers from the start?

Count With Your Fingers!

You can count higher than ten with your fingers! Just use binary.

Let each finger stand for a card with dots. Now you can count from 0 to 31. That's 32 numbers! (Remember, zero counts too!)

If a finger is up, it means 1.
If a finger is down, it means 0.

Try counting in order with your fingers.

Using both hands, you can count all the way to 1023! That's 1024 numbers!

What if you had bendy toes too? You could count even higher!

If one hand counts to 32, and two hands count to 1024... How high could you count with hands AND toes?

Worksheet: More on Binary Numbers

Part 1: Adding a Zero

In our normal number system, adding a 0 at the end makes a number bigger. Like this:
9 becomes 90.
30 becomes 300.

What happens when you add a 0 to a binary number?
Try this: 1001 becomes 10010.
1001 equals 9. What does 10010 equal?

Try more examples. What is the rule? Why do you think this happens?

Part 2: Bits and Letters

Each card we used is called a "bit." Bit is short for "binary digit."

We used 5 cards to make our letter code. That means 5 bits.

But computers need more than just letters. They need capital letters too. They need numbers. They need symbols like $ or ~.

Look at a keyboard. Count how many different characters there are. How many bits would a computer need to store them all?

Most computers use a code called ASCII. This code uses a set number of bits for each character. Some other countries need longer codes for their letters.

What's It All About?

Computers use binary to store information. Binary means only two digits are used: 0 and 1. We also call this base two. People usually count in base ten.

Each 0 or 1 is called a bit. That means "binary digit." Inside a computer, a bit can be a tiny switch. The switch is either on or off.

When computers send messages over phone lines, they use high and low beeps for 1 and 0.

On disks and tapes, bits are stored using magnets. The magnet points one way for 1. It points the other way for 0.

CDs and DVDs store bits with light. Some spots reflect light. Some spots do not.

One bit alone can't say much. So bits are grouped together. A group of 8 bits is called a byte. A byte can make numbers from 0 to 255.

A computer's speed depends on how many bits it handles at once. A 32-bit computer works with 32 bits at a time. A 16-bit computer is slower. It must break big numbers into smaller pieces.

Bits and bytes are how computers store all kinds of information. Numbers. Words. And more!