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.

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).

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).

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.

**CS Unplugged - Binary digits (sample classroom lesson)**

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

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

VIDEO: Why is binary important? (339037521)

(no transcript)

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.

- 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?" (6 mins):

Youtube video "How CD's work" (2 mins):

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

Youtube video "How do hard drives work? - Kanawat Senanan" (5mins):

Students should understand how important the concept of binary digits is and how everything we do with digital devices really does rely on it. In this video find out how binary digits are used to represent pictures.

At Progress Outcome 3 students need to “...understand that digital devices store data using just two states represented by binary digits (bits).”

Progress Outcome 4 says “Students understand that digital devices represent data with binary digits…”

At Progress Outcome 5 students: “understand how computers store more complex types of data using binary digits.”

This Vimeo video demonstrates how audio is stored using just binary digits (2:54):

You can zoom in on your own photo using this web page (just drag your own photo on top of the one shown):

The RGB mixer used in the video is available here:

Binary digits can be used in the classroom in various ways. This video shows using beads and kōwhaiwhai patterns to represent binary digits.

Another way binary can be displayed in the classroom is with art. Students can create their names (and other messages) on posters.

This video shows some places that students may encounter binary representation in everyday life.

As we saw in this video, binary representations come up in many situations that students will encounter, including the Braille writing system, storing musical notes with MIDI, and inputs and outputs from programmable devices such as the micro:bit.

This video shows some examples of what can go wrong when people don’t take account of the limitations of binary representations.

Everything from popular YouTube clips to aeroplanes can go wrong if insufficient bits are allocated to storing numbers.

Which number do these binary cards represent?

The correct answer is 21.

Which set of cards represents 91 in binary?

A)

B)

C)

D)

C is the correct answer.

What is the largest decimal number that can be represented with 6 cards?

The correct answer is 63.

If A is 1, B is 2, C is 3 etc, what does this message say?

10100 00001 01101 00001 10010 01001 01011 01001

The correct answer is Tamariki.

Technological practice: students are able to work directly with binary representations for their own authentic contexts; for example, younger students can use the idea as the basis of artwork or hidden messages.

Technological knowledge: Understanding binary representation is a key concept that underpins how all digital systems work.

Nature of technology: The way that binary representation is used affects humans; for example, older systems with only 8-bit character representation excluded those whose language uses a different alphabet; and using too many bits to store an image can result in unacceptable download times.

There are several ideas for using ideas from binary representation for teaching and learning based around art, music and literacy here: CS Unplugged: Binary numbers

We’ve seen that binary is the basis of everything digital, and that students can find it an engaging topic. But binary representations are generally hidden under the surface of digital systems, so do we really need to know about them? A short answer is that it would be the same as saying we don’t really need to know about atoms and molecules - they underpin all physical objects, but we don’t think about them in daily life. Like atoms, binary is behind the scenes in so many things we use that while we can get by without knowing specifically about it, it is good to have some understanding of how it works so that students can understand and influence the digital world.

Binary representation affects so many things that we do. If you’re interested, here's a longer article about ways that binary representation comes up in everyday life.

Representing data in binary is discussed in more detail here: CS Field Guide: Data representation

- Binary cards and interactives are from http://csfieldguide.org.nz/ (Creative Commons (CC BY-NC-SA 4.0) license)
- "PaperTapes-5and8Hole" by TedColes - Own work. Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:PaperTapes-5and8Hole.jpg#mediaviewer/File:PaperTapes-5and8Hole.jpg
- CD rom image: https://upload.wikimedia.org/wikipedia/commons/9/9d/Afm_cd-rom.jpg https://commons.wikimedia.org/wiki/File:Afm_cd-rom.jpg#filehistory
- Magnetic disk image by Matesy GmbH - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=17014529
- Micro:bit image by Aruld - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=73117261
- Gangnam Style view count from https://www.youtube.com/watch?v=9bZkp7q19f0
- Year 2038 rollover by Monaneko - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=1711901
- Boeing 787 image by pjs2005 from Hampshire, UK - Boeing 787 N1015B ANA Airlines, CC BY-SA 2.0, https://commons.wikimedia.org/w/index.php?curid=71147495
- RIN 2120–AA64 Airworthiness directive from https://thefederalregister.org/82-FR/38629