# The Dots

## What You Need

You will need to make a set of five binary cards (see page 6 for the demonstration). A4 cards with smiley face sticker dots work well.

Each child will need:

- A set of five cards.
- Copy Photocopy Master: Binary numbers page 6 onto card and cut out.
- Worksheet Activity: Binary numbers page 5

There are optional extension activities, for which each child will need:

- Worksheet Activity: Working with binary page 7
- Worksheet Activity: Sending secret messages page 8
- Worksheet Activity: Fax machines and modems page 9
- Worksheet Activity: Counting higher than 31 page 10
- Worksheet Activity: More on binary numbers page 11

Guide:

## What To Do

**Worksheet Activity: Binary Numbers **

Cut out the cards on your sheet and lay them out with the 16-dot card on the left as show in the manual. Make sure that 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's the biggest number you can make? What is the smallest? Is there any number you can't make between the biggest and smallest number?

**Optional Activity: Working with Binary**

The binary system uses zero and one to represent whether a card is face up or not. Zero shows that the card is hidden whereas one means you can see the dots. Using the binary system, try to figure out the coded numbers on the worksheet.

**Optional 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?

**Optional 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 email 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!

**Optional 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. Follow the worksheet to determine how high you can count using your fingers.

**Optional Activity: More on Binary Numbers**

- 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?
- 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.

## Discovery

#### What's Happening?

Computers today use the binary system to represent information. It is called binary because only two different digits are used. It is also known as base two (humans normally use base 10). Each zero or one is called a bit (binary digit). A bit is usually represented in a computer’s main memory by a transistor that is switched on or off, or a capacitor that is charged or discharged.

When data must be transmitted over a telephone line or radio link, high and low-pitched tones are used for the ones and zeros. On magnetic disks (floppy disks and hard disks) and tapes, bits are represented by the direction of a magnetic field on a coated surface, either North-South or South-North.

Audio CDs, CD-ROMs and DVDs store bits optically—the part of the surface corresponding to a bit either does or does not reflect light.

One bit on its own can’t represent much, so they are usually grouped together in groups of eight, which can represent numbers from 0 to 255. A group of eight bits is called a byte. The speed of a computer depends on the number of bits it can process at once. For example, a 32-bit computer can process 32-bit numbers in one operation, while a 16-bit computer must break 32-bit numbers down into smaller pieces, making it slower. Ultimately bits and bytes are all that a computer uses to store and transmit numbers, text, and all other information. In some of the later activities we will see how other kinds of information can be represented on a computer.

#### What's Happening?

Computers today use the binary system to represent information. It is called binary because only two different digits are used. It is also known as base two (humans normally use base 10). Each zero or one is called a bit (binary digit). A bit is usually represented in a computer’s main memory by a transistor that is switched on or off, or a capacitor that is charged or discharged.

When data must be transmitted over a telephone line or radio link, high and low-pitched tones are used for the ones and zeros. On magnetic disks (floppy disks and hard disks) and tapes, bits are represented by the direction of a magnetic field on a coated surface, either North-South or South-North.

Audio CDs, CD-ROMs and DVDs store bits optically—the part of the surface corresponding to a bit either does or does not reflect light.

One bit on its own can’t represent much, so they are usually grouped together in groups of eight, which can represent numbers from 0 to 255. A group of eight bits is called a byte. The speed of a computer depends on the number of bits it can process at once. For example, a 32-bit computer can process 32-bit numbers in one operation, while a 16-bit computer must break 32-bit numbers down into smaller pieces, making it slower. Ultimately bits and bytes are all that a computer uses to store and transmit numbers, text, and all other information. In some of the later activities we will see how other kinds of information can be represented on a computer.

#### Resources

**Guide:**

Attached files - Photocopiable for classroom use only. © 2002 Computer Science Unplugged

#### Resources

**Guide:**

Attached files - Photocopiable for classroom use only. © 2002 Computer Science Unplugged