Pīkau 16: Representing data in binary


Why this matters

Binary plays a pivotal role in all things digital. Everything digital is based on it. Data representation (using binary) is in computational thinking Progress Outcomes 3, 4, and 5, while binary digits are specifically mentioned in Progress Outcomes 3 and 4. Even though binary is not mentioned until Progress Outcome 3 it is a concept that can easily be taught to young students.

Links to existing knowledge

You might already know some of this.

If you’ve ever played a game of 20 questions, you’ll be familiar with the idea of communicating information by simply giving yes/no answers. And if you carry a digital device you have probably noticed that exactly the same hardware can store a variety of information - text, images, sound, video, step counts and more. These are all ultimately stored as a binary representation, which means that you can use the same device to store - and transmit - all kinds of information.

The common point for all of these is that they are represented using just two symbols, or “states”. Because only two states are used, these two states are commonly referred to as binary (since the prefix “bi” means two).

Binary representation in the classroom

Watch the following video to see how relatively young students can engage with the idea of representing information using just two states - in this case, whether a card is face up or face down.

As you saw in this accelerated lesson, even students as young as 8-years-old can quite quickly understand the concept of using just two states to send many different kinds of information (data).

Quiz: Try this for yourself

Open the “cards” using the following link, and try the challenges below:

Work out which cards you need to flip over so that there are exactly 13 dots visible.

Now work out how to show 15 dots.

How about zero dots?

Try counting (show 1 dot, then 2, 3, 4, 5…). What patterns do you notice?

Is there any number from 0 to 31 that can’t be represented with these 5 cards?

Use this link to access a set with one more card (6 in total). What range of numbers is possible now?

Now try working out the range possible with 8 cards using the following link. It’s very common for binary digits, or bits, to be in groups of 8 like this - it’s called a byte.

Tip: Click on the black cards to flip them over

  • The range of numbers able to be shown with 6 binary cards is 0 to 63.
  • The range of numbers able to be shown with 8 binary cards is 0 to 253.
Optional extra resource

CS Unplugged - Binary digits (sample classroom lesson)

Video of how binary digits work being taught in a classroom situation:

Why is binary important?

Binary representation is used throughout digital technologies. This video shows how, including looking at the inside of a hard disk drive.

As we saw in this video everything digital uses binary in some form or another. This table shows how some different devices use binary.

Device Binary states
Hard drive Magnetism (North and South polarity)
CD Flat or uneven (reflects light or doesn’t)
Magnetic stripe card (e.g. bank card) Magnetism (North and South polarity)
Cell phone storage Lower and higher voltage in memory

Did you know that a whole book has been written using only two states? Jean-Dominique Bauby suffered from “locked-in syndrome” but by blinking (and not blinking), he was able to communicate, and write and edit a book.

Optional extra resources
  • Locked In - An activity based on “locked-in syndrome” which explores binary digits, algorithms and other computational thinking concepts

Two videos about how binary data is stored and read by a CD player.

How does a CD work?

How CD's work

How do hard drives work?

Video about how binary data is stored and read by a magnetic disk (hard disk drive)