# Binary numbers

## Unit Binary numbers

Year level: **5-6**
Topic: **Data representations**
Time: **2 hours**

The binary number system plays a central role in how information of all kinds is stored on computers. Understanding binary helps to unravel the mystery of computers, as students begin to understand that binary digits represent on and off. Binary cards can be used to introduce the binary number system. Students can see the connection between binary digits represented as dots and the corresponding decimal number. When cards are placed in sequence students can create a binary number displaying cards as on or off. Students explain how a standard system of encoding is used to represent numbers, text and other special characters.

### Flow of Activities

#### Computers use binary

Explore the way all data that is processed by a computer, is stored using binary.#### The binary system uses 0s and 1s

Examine how computer data is represented with binary, a number system that uses 0s and 1s.#### Characters as binary

Use the American Standard Code for Information Interchange (ASCII) to represent characters.#### Standards of encoding characters

Explore Unicode as an important character set that is used as standard worldwide.Activity Computers use binary

Why do digital systems need to convert sound, text, images and numbers to process them?

### Australian Curriculum Alignment

### What's this about?

All software, music, documents and any other information that is processed by a computer is stored using binary.

### Learning tasks

- Explore audio, video, text and image files to examine standard encoding formats such as MP3 for audio files, ASCII or Unicode for text, JPEG for images and MOV, AVI and WMV for video.
- Make a chart of the different formats. Share ideas and decide on common file types and ones with which students are familiar. Explain that all these files use the binary system of encoding.
- Provide resources to explore the binary number system with the aim of finding interesting information about the binary system and to raise questions for inquiry. As students explore the fundamentals of the binary system, challenge them to find out and share three things they have learned and any questions that arise.
- Write a list about what the class knows about binary. Then view an informative video about binary numbers. Update the list with revisions and new ideas.

### Supporting Resources

### Assessment

**Explain** how digital systems use whole numbers as a basis for representing a variety of data types.

Suggested approaches may include

- Refer to the three things they have learned

Activity The binary system uses 0s and 1s

How does the binary system work?

### Australian Curriculum Alignment

- Representation of data (ACTDIK015)

### What's this about?

Computer data is represented with binary, a number system that uses 0s and 1s. Binary digits can be grouped together into bytes (8 bits).

The binary system is based on the power of 2, the progression being 1, 2, 4, 8, 16, 32, 64, etc. In contrast, the base 10 system progresses by multiples of 10: 1, 10, 100, etc.

### Learning tasks

- Students explore the binary number system. Brainstorm to find out what students already know about binary. View the video ‘What are binary numbers?’
- Link with Mathematics and compare the base 10 system with base 2.
- Students explain what a binary number is, how to read it and identify the corresponding decimal number. Binary cards (cards with a dot for each 1, 2, 4, 8, 16 etc) enable us to see the connection between binary digits and the corresponding decimal number when placed in sequence.
- Students find out how to convert binary to decimal numbers. Use binary numbers in place of decimal numbers; for example, represent a calendar with months as binary numbers or a date of birth in binary.
- Use a programming board such as the B4 Primary School Starter Kit to experiment with representing binary, counting in binary and adding binary numbers. Alternatively use the BBC micro:bit or similar microcontroller to integrate data representation of binary numbers and programming.

### Supporting Resources

### Assessment

**Explain** how digital systems use whole numbers as a basis for representing a variety of data types.

Suggested approaches may include

- Adapted worksheet with binary numbers to be matched with a decimal number
- Explain using Think Aloud

### Assessment Resources

Activity Characters as binary

How are text characters represented?

### Australian Curriculum Alignment

### What's this about?

American Standard Code for Information Interchange (ASCII) is a 7-bit character set containing 128 characters. The upper and lower case English letters from A to Z are represented by binary numbers (eg 01100001 is a, and 01000001 is A). ASCII is only used for the English language.

### Learning tasks

- Students can use a basic binary character table to encode and decode messages.

### Supporting Resources

### Assessment

**Explain** how digital systems use whole numbers as a basis for representing a variety of data types.

Suggested approaches may include

- Artefact analysis: Accuracy of message written in binary using ASCII encoding

Activity Standards of encoding characters

What are standards of encoding characters?

### Australian Curriculum Alignment

### What's this about?

Hexadecimal is a shortcut for representing binary. ASCII and Unicode are important character sets that are used as standard.

### Learning tasks

- Students should be aware of other standards of encoding characters.
- Students create their own infographic about how text and numbers are encoded using patterns of binary digits. Provide a tool to create an infographic such as Canva or Piktochart.

### Supporting Resources

### Assessment

**Explain** how digital systems use whole numbers as a basis for representing a variety of data types.**Explain** how information systems and their solutions meet needs and consider sustainability.

Suggested approaches may include

- Artefact: Infographic