← Years 5–6 Data & Information

Writing small numbers in binary

To write a number in binary, put a 1 under each place value you add and a 0 under the rest. Place values are 8, 4, 2, 1. So 5 is 4 + 1, which is 0101.

Part of: 5-6 Digital Technologies Vic Curric - Data, Information and Privacy — Module 8, 7-8 Digital Technologies: Representing data with binary — Module 8, ACARA Digital Technologies Years 7–8 — Representing Text, Images and Sound — Module 9, ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 16

Understanding Writing small numbers in binary in Years 5–6 Data & Information

What it does: 8 is just the 8 place value on its own, so there is a 1 under 8 and 0 under 4, 2 and 1. 8 + 4 + 2 + 1 makes 15, so all four place values are used and every place gets a 1. 4 + 1 = 5, so you put a 1 under the 4 and a 1 under the 1. 5 = 4 + 1. That gives 0 under 8, 1 under 4, 0 under 2 and 1 under 1, so 0101. A 1 means the place value is added. A 0 means it is left out.

Common mistakes: 4 + 1 makes 5, not 6. To make 6 you add the place values 4 and 2, so the line should be Add: 4 + 2 = 6. 4 + 1 is 5, not 3. The place values that add up to 3 are 2 and 1, so the line should be 3 = 2 + 1.

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Learning
Duo
To write 5 in binary using the place values 8, 4, 2, 1, which place values do you add?
4 and 18 and 2
Matches
6 = 4 + 2 = 0111
↓
The 1 under the 1 place is wrong. 6 does not use the 1 place value, so it needs a 0 there. It should be 0110.
Applying
Meanings
Term
5 = 4 + 1 = 0101
Meaning
To write a number in binary, put a 1 under each place value you add and a 0 under the rest. Place values are 8, 4, 2, 1. So 5 is 4 + 1, which is 0101.
Practice
Place values: 8 4 2 1
Testing
Gaps
5 = 4 + 1 =
Check Answer
Spots
1Number: 6
2Add: 4 + 1 = 6

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Quick Questions

1. To write 5 in binary using the place values 8, 4, 2, 1, which place values do you add?
A. 4 and 1 ✓
B. 8 and 2
4 + 1 = 5, so you put a 1 under the 4 and a 1 under the 1.
2. Which is 5 written in binary?
A. 0101 ✓
B. 0110
5 = 4 + 1. That gives 0 under 8, 1 under 4, 0 under 2 and 1 under 1, so 0101.
3. In binary, what does a 0 under a place value mean?
A. That place value is not added ✓
B. That place value is added twice
A 1 means the place value is added. A 0 means it is left out.
4. Which is 3 written in binary?
A. 0101
B. 0011 ✓
3 = 2 + 1, so you put a 1 under the 2 and a 1 under the 1: 0011.
5. What is 8 written in binary using the place values 8, 4, 2, 1?
A. 0001
B. 1000 ✓
8 is just the 8 place value on its own, so there is a 1 under the 8 and 0s under the rest.

Match the Pairs

5 = 4 + 1 = 0101 → Add the place values 4 and 1 to make 5, so write 1 under 4 and 1, and 0 under 8 and 2
3 = 2 + 1 = 0011 → Add the place values 2 and 1 to make 3, so write 1 under 2 and 1, and 0 under 8 and 4
To write 8 in binary, you only need the 8 place value, so it gets a 1 and the others get 0 → 8 = 1000
To write 15 in binary, you add every place value, so every place gets a 1 → 15 = 8 + 4 + 2 + 1 = 1111
6 = 4 + 2 = 0111 → The 1 under the 1 place is wrong. 6 does not use the 1 place value, so it needs a 0 there. It should be 0110.
9 = 8 + 1 = 1100 → The 1s are under the wrong place values. 9 uses 8 and 1, not 8 and 4. It should be 1001.

Key Term

5 = 4 + 1 = 0101
To write a number in binary, put a 1 under each place value you add and a 0 under the rest. Place values are 8, 4, 2, 1. So 5 is 4 + 1, which is 0101.

Fill in the Blanks

1. 5 = 4 + 1 = 0101
Hint: Type the 4-bit binary number for 5 using place values 8, 4, 2, 1
2. Place values: 8, 4, 2, 1
Hint: Type the place value that sits between 8 and 2
3. 6 = 4 + 2 = 0110
Hint: Type the digit for the 4 place, which is added to make 6
4. 9 = 8 + 1 = 1001
Hint: Type the binary number: a 1 under 8 and under 1, a 0 under the rest
5. 3 = 2 + 1 = 0011
Hint: Type the two digits for the 2 and 1 places, which are both added

Spot the Error

Question 1
A Number: 6
B Add: 4 + 1 = 6
C Place values: 8 4 2 1
D Binary: 0110
Line B — 4 + 1 makes 5, not 6. To make 6 you add the place values 4 and 2, so the line should be Add: 4 + 2 = 6.
Question 2
A Place values: 8 4 2 1
B Number: 3
C 3 = 4 + 1
D Binary: 0011
Line C — 4 + 1 is 5, not 3. The place values that add up to 3 are 2 and 1, so the line should be 3 = 2 + 1.
Question 3
A Place values: 8 6 4 2
B 7 = 4 + 2 + 1
C Binary: 0111
Line A — The four binary place values are 8, 4, 2 and 1. Each one is double the place value to its right. The line should be Place values: 8 4 2 1.
Question 4
A Number: 9
B 9 = 8 + 2
C Place values: 8 4 2 1
D Binary: 1001
Line B — 8 + 2 makes 10, not 9. Nine is 8 + 1, so the line should be 9 = 8 + 1.
Question 5
A Number: 10
B Place values: 8 4 2 1
C 10 = 8 + 2
D Binary: 1100
Line D — 10 = 8 + 2, so put a 1 under 8 and under 2, and a 0 under 4 and under 1. That gives Binary: 1010. The broken line has 1s under 8 and 4, which is 12.

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