← Years 5–6 Data & Information

Reading binary numbers

To read a binary number, add up the place values (1, 2, 4, 8...) that have a 1 under them and ignore the 0s. For example, 1011 is 8 + 2 + 1 = 11.

Part of: 5-6 Digital Technologies Vic Curric - Data, Information and Privacy — Module 9, 7-8 Digital Technologies: Representing data with binary — Module 7, IGCSE Computer Science 0478 — 1.1 Number Systems — Module 6, ACARA Digital Technologies Years 7–8 — Representing Text, Images and Sound — Module 10, ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 15

Understanding Reading binary numbers in Years 5–6 Data & Information

What it does: In 110 the 1s are under the 4 and the 2. The 0 is under the 1, so it is ignored. 4 + 2 = 6. The 1s in 1001 are under 8 and 1. Adding them gives 9, so the answer checks out. Add the place values that have a 1. Here the 1s are under 4 and 1, and the 0 is ignored. So 101 is 5. The 1s are under 8, 2 and 1. So 8 + 2 + 1 = 11. The 4 place has a 0, so it is not added. The 1s are in the 8 and 4 places. The 2 and 1 places have 0s, so they are ignored. So 1100 is 12.

Common mistakes: Binary place values double each time, starting at 1. For three digits they are 4, 2, 1, not 5, 3, 1. The 1s are under 8, 4 and 1. 8 + 4 + 1 = 13, so the decimal answer is 13, not 14.

Class: _____________________  ·  Name: _____________________  ·  Date: _________

Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

🖨 Print worksheet + answer key Add Reading binary numbers to a class →

This module's key terms are also in a printable crossword (Modules 1–10) and word search (Modules 1–20).

Take this worksheet further — free with Cloodit

Each concept is reinforced from every angle — learned, then applied, then tested.

Learning
Duo
To read the binary number 101, which place values do you add?
1 + 0 + 1 = 2, because you just count the digits4 + 1 = 5, because the 1s are under 4 and 1
Matches
1010 = 8 + 2 + 1 + 0 = 11
↓
The 1 place value was added even though it has a 0 under it. Only add place values that have a 1. The correct answer is 8 + 2 = 10.
Applying
Meanings
Term
Add the place values that have a 1
Meaning
To read a binary number, add up the place values (1, 2, 4, 8...) that have a 1 under them and ignore the 0s. For example, 1011 is 8 + 2 + 1 = 11.
Practice
Binary: 1011
Testing
Gaps
1011 = 8 + 2 + = 11
Check Answer
Spots
1Binary: 101
2Place values: 5 3 1

Cloodit turns curriculum-aligned coding content into journeys students work through one biome at a time.

The 'Horned Lizard' badge — Bug Squasher, one of Cloodit's 106 collectible badges
Students earn collectable badges

Over 100 of them, across seven natural biomes.

Study Buddy
Students build a real study resource

Turns their work into revision material ready for Flash Cards and Exam study.

Diamond Dash — one of Cloodit's live, competitive Sprint games
Students lock in with Sprints

Live, competitive practice for the start of the lesson or a teacher-led lesson finisher.

A Cloodit certificate of achievement, ready to personalise and print
Custom printable certificates

Honour your top performers, or encourage a student who's trying hard — ready to print in seconds.

Add to class →

Quick Questions

1. To read the binary number 101, which place values do you add?
A. 4 + 1 = 5, because the 1s are under 4 and 1 ✓
B. 1 + 0 + 1 = 2, because you just count the digits
Add the place values that have a 1. Here the 1s are under 4 and 1, and the 0 is ignored. So 101 is 5.
2. What is 1011 in decimal?
A. 11 ✓
B. 13
The 1s are under 8, 2 and 1. So 8 + 2 + 1 = 11. The 4 place has a 0, so it is not added.
3. What do you do with a place value that has a 0 under it?
A. Add it twice
B. Ignore it and do not add it ✓
A 0 means that place value is not used. Only add the place values that have a 1.
4. Which is the right way to read 1100?
A. 8 + 4 = 12 ✓
B. 2 + 1 = 3
The 1s are in the 8 and 4 places. The 2 and 1 places have 0s, so they are ignored. So 1100 is 12.
5. Do leading zeros change the value of a binary number? Look at 0011 and 11.
A. Yes, 0011 is bigger than 11
B. No, both are 3 because the zeros add nothing ✓
Leading zeros are 0s on the left. They add nothing, so 0011 and 11 both equal 2 + 1 = 3. Computers often use them to keep numbers the same length.

Match the Pairs

1011 = 8 + 2 + 1 = 11 → Add the place values that have a 1 (8, 2 and 1) and ignore the 0 to get the decimal number 11
0101 = 5 → Leading zeros do not change the value, so 0101 is the same number as 101
Write 110 as a decimal number by adding the place values that have a 1 → 4 + 2 = 6
Check your answer: the binary number 1001 should add up to 9 → 8 + 1 = 9
1010 = 8 + 2 + 1 + 0 = 11 → The 1 place value was added even though it has a 0 under it. Only add place values that have a 1. The correct answer is 8 + 2 = 10.
0011 = 1 + 2 + 3 = 6 → The place values were counted as 1, 2, 3 instead of 1, 2, 4, 8. Only 2 + 1 should be added, so the answer is 3.

Key Term

Add the place values that have a 1
To read a binary number, add up the place values (1, 2, 4, 8...) that have a 1 under them and ignore the 0s. For example, 1011 is 8 + 2 + 1 = 11.

Fill in the Blanks

1. 1011 = 8 + 2 + 1 = 11
Hint: Type the place value of the right-most column.
2. 0101 has the same value as 101
Hint: Type the binary number with the leading zero removed.
3. Place values: 8, 4, 2, 1
Hint: Type the missing place value between 4 and 1.
4. 1101 = 8 + 4 + 1 = 13
Hint: Type the total of the place values that have a 1.
5. A 1 means add the place value above it
Hint: Type the binary digit that tells you to add the place value.

Spot the Error

Question 1
A Binary: 101
B Place values: 5 3 1
C Add 4 + 1
D Decimal: 5
Line B — Binary place values double each time, starting at 1. For three digits they are 4, 2, 1, not 5, 3, 1.
Question 2
A Binary: 1101
B Place values: 8 4 2 1
C Add 8 + 4 + 1
D Decimal: 14
Line D — The 1s are under 8, 4 and 1. 8 + 4 + 1 = 13, so the decimal answer is 13, not 14.
Question 3
A Binary: 110
B Place values: 4 2 1
C Add 4 + 2 + 1
D Decimal: 6
Line C — The last digit is 0, so the place value 1 is ignored. Only add 4 + 2.
Question 4
A Binary: 1001
B Add 8 + 2 + 1
C Answer: 9
Line B — Only the place values with a 1 are added. 1001 has 1s under 8 and 1, so the sum is 8 + 1. The 2 has a 0 under it.
Question 5
A Binary: 111
B Place values: 4 2 1
C Add 4 + 2 + 1 = 7
D Check: 3 bits is at most 8
Line D — With 3 bits the biggest number is 4 + 2 + 1 = 7. The answer must be 7 or less, so the check should say 7.

Student with a class code? Join your class →