Binary Challenge

What you need

Five cards (around the size of a playing card) that are blank on one side and have dots drawn on the other side (see below for instructions on drawing them). They could be created using cardboard from an old box, paper (fold it over if the dots can be seen on the back of the paper), a folder, or craft supplies.

Skills needed

Counting up to 31

Key question

Can you send information using just two symbols?

Activity steps

Step 1

Cut out 5 cards, ideally made of cardboard.

This can be done in advance for younger children.

Step 2

Child drawing dots on each of the cards.

Put one dot on one side of the right-most card, two dots on the card to its left...

It’s significant that the smallest is on the right; make sure the number of dots is increasing from right to left.

Step 3

Child placing the cards such that the number of dots is increasing from right to left.

...then 4, 8 and 16 dots. Can you describe the pattern in the number of dots on each card?

The child may recognise that the number of dots doubles each time.

Step 4

Adult pointing to where the next card in the sequence would go.

If there was one more card to the left, how many dots would it have?

They might be able to predict that if there was one more card it would have 32 dots on it. (This isn’t essential, but some children will enjoy extending the pattern, which would continue with 64, 128, 256 and so on.)

Step 5

Child flipping over some cards so that five dots are showing.

We can use these cards to represent numbers by turning some of them face down and counting up the number of dots that are showing. The rule is that each card is either fully visible, or fully hidden. How can you have exactly 5 dots showing?

Let the child experiment with flipping cards over. If they struggle, a good strategy is to start at the left, and ask them if they want the 16 dot card visible (no, because there would be too many dots), then the 8 card (still too many), then the 4 card (it’s less than 5, so looks hopeful), then the 2 card (let them count up the dots and realise that there would be 6 visible, which is more than 5), and finally the 1 card.

Step 6

So if we ask if each card is visible, it would be no, no, yes, no, yes?

Point to each card from left to right, and illustrate using "yes" and "no" to say if each card has the dots showing or not. The picture shows the only way to get exactly 5 dots visible.

Step 7

All cards are face up, showing all dots.

Now I’ll give you a number: yes, no, yes, yes, no

Get child to help put all 5 cards face up, then point to each card from left to right as you say "yes, no, yes, yes, no", and get child to hide the ones that are "no" (the pattern is shown in the next photo).

Step 8

How many dots are showing?

Allow the child to count up the dots (for younger children, they may need to point to each dot as they count it), or they can add the numbers, to get 16+4+2, or 22 dots visible. You’ve communicated the number 22 by saying "yes, no, yes, yes, no". Because you used just two words or symbols, you have used binary to convey information.

Step 9

Child flipping the cards so that eleven dots are showing.

Can you make exactly 11 dots visible?

Place all cards face up again, and let them experiment until they find the pattern shown.

Step 10

We can communicate numbers by just saying "yes" and "no"! Let’s make up more numbers for each other.

Take turns at showing each other numbers. These could be to communicate things like the day of the month they were born in, or the number of the month they’re thinking of. As an extension, try counting all the numbers possible, starting at 0, 1, 2, 3...up to 31, and look for patterns that occur.

Inside the computer

It’s usually cheaper and faster to build computers that only use two symbols (the "yes" and "no" we’ve been using, or sometimes they are written as 1 and 0). Modern digital systems use this binary representation, and the numbers in turn can be used to represent all sorts of things - text, pictures, videos and more. All these things are represented with combinations of the two digits, which is why we call them digital devices! The power and limitations of representing things using just "yes" and "no" dictate the power and limitations of the data that computers can store and send over networks, so understanding how they work is a gateway to understanding digital data.

By the way, the short word for the binary digits you've been working with is "bit" - the cards represent 5 bits. Many things about computers are measured in bits: download speeds are in bits per second (in fact, usually millions of bits per second), computers can be 16-bit or 32-bit based on how many bits they process at a time, Bitcoin is a cryptocurrency that represents money securely as bits, the quality of music and video is often chosen by their bit rate, the strength of a secure connection to your bank is measure by the number of bits in its cryptographic key, and so on. A bit is so simple that you can make one out of cardboard, and so powerful that nearly all our trading and communication is based on transferring bits.

Project

Where in the world does Arnold see Binary in use? For example, the number 98 in binary is often used to represent the letter "b" - what number is used for the other letters? Where else do you see the word "bit" used? Look up the meaning of "byte" to find out how it is made of bits, and then also look into where bytes are mentioned.