← ACARA Digital Technologies Years 7–8

Counting in binary from 8 to 15 (Representing Text, Images and Sound)

Four bits count from 0 to 15. After 0111 (7) the fourth bit turns on, so 8 is 1000. Each column flips half as often as the column to its right, and the rightmost column flips every number.

Part of: ACARA Digital Technologies Years 7–8 — Representing Text, Images and Sound — Module 7

Understanding Counting in binary from 8 to 15 (Representing Text, Images and Sound) in ACARA Digital Technologies Years 7–8

What it does: Going from 8 (1000) to 9 (1001), only the rightmost bit changes, and it flips every time we count up by one. After 0111 (7) all three right bits are full, so the fourth bit turns on and the others reset: 1000 is 8. 0111 is 7. The rightmost column alternates 0, 1, 0, 1 with every step. It is the fastest column. 1111 = 8 + 4 + 2 + 1 = 15. Four bits count from 0 to 15, which is 16 different values. 111 = 4 + 2 + 1 = 7. To count 8 we need a fourth bit, giving 1000.

Common mistakes: 9 is 8 + 1, so it is 1001. The pattern 1010 is the code for 10, not 9. 13 is 8 + 4 + 1, so it is 1101. The pattern 1110 is 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 Counting in binary from 8 to 15 (Representing Text, Images and Sound) to a class →

This module's key terms are also in a printable crossword (Modules 69–124) and word search (Modules 69–152).

Take this worksheet further — free with Cloodit

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

Learning
Duo
What is the number 8 written in 4-bit binary?
01111000
Matches
8 = 0111
↓
0111 is 7, not 8. To count 8 you need a fourth bit, so 8 is 1000.
Applying
Meanings
Term
0000 to 1111
Meaning
Four bits count from 0 to 15. After 0111 (7) the fourth bit turns on, so 8 is 1000. Each column flips half as often as the column to its right, and the rightmost column flips every number.
Practice
8 = 1000
Testing
Gaps
8 =
Check Answer
Spots
18 = 1000
29 = 1010

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

The 'Anglerfish' badge — Deep Diver, 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. What is the number 8 written in 4-bit binary?
A. 1000 ✓
B. 0111
After 0111 (7) all three right bits are full, so the fourth bit turns on and the others reset: 1000 is 8. 0111 is 7.
2. Which binary number comes right after 1001 (9)?
A. 1010 ✓
B. 1100
1001 + 1 = 1010 (10). The rightmost bit flips from 1 to 0 and the next bit turns on. 1100 is 12.
3. How often does the rightmost column change as you count up?
A. Every number (0, 1, 0, 1...) ✓
B. Every 2 numbers (0, 0, 1, 1...)
The rightmost column alternates 0, 1, 0, 1 with every step. It is the fastest column.
4. What is 1111 in decimal?
A. 16
B. 15 ✓
1111 = 8 + 4 + 2 + 1 = 15. Four bits count from 0 to 15, which is 16 different values.
5. Why can't 3 bits show the number 8?
A. 3 bits only go up to 111, which is 8
B. 3 bits only go up to 111, which is 7 ✓
111 = 4 + 2 + 1 = 7. To count 8 we need a fourth bit, giving 1000.

Match the Pairs

1000 → The number 8: the fourth bit turns on after 0111 (7) and the other three bits reset to 0
1111 → The biggest number four bits can show: 15
The rightmost column flips between 0 and 1 on every single number, so 9 follows 8 like this → 1000 -> 1001
The second column from the right flips every 2 numbers, so it stays the same for two numbers then changes (10 and 11 both have 1 there) → 1010 1011
8 = 0111 → 0111 is 7, not 8. To count 8 you need a fourth bit, so 8 is 1000.
12 = 1010 → 1010 is 10. Twelve is 1100, because the 8 and 4 columns are on and the 2 and 1 columns are off.

Key Term

0000 to 1111
Four bits count from 0 to 15. After 0111 (7) the fourth bit turns on, so 8 is 1000. Each column flips half as often as the column to its right, and the rightmost column flips every number.

Fill in the Blanks

1. 7 = 0111 8 = 1000
Hint: After 0111 the fourth bit turns on and the other three columns reset to zero. Type the 4-bit pattern for 8.
2. 8 = 1000 9 = 1001
Hint: Only the rightmost column changes from the line above. Type the 4-bit pattern for 9.
3. 12 = 1100 13 = 1101 14 = 1110
Hint: The rightmost column flips every number, so it goes from 1 back to 0 here. Type the 4-bit pattern for 14.
4. 10 = 1010 11 = 1011
Hint: The rightmost column alternates 0 and 1 every number. Type the single digit that comes after a 0 in that column.
5. Four bits count from 0000 to 1111
Hint: Type the largest 4-bit number, where every column is switched on. It stands for 15.

Spot the Error

Question 1
A 8 = 1000
B 9 = 1010
C 10 = 1010
Line B — 9 is 8 + 1, so it is 1001. The pattern 1010 is the code for 10, not 9.
Question 2
A 11 = 1011
B 12 = 1100
C 13 = 1110
Line C — 13 is 8 + 4 + 1, so it is 1101. The pattern 1110 is 14.
Question 3
A Bit 1 flips every number
B Bit 2 flips every 4 numbers
C Bit 4 flips every 4 numbers
Line B — Each column flips half as often as the column to its right. Bit 1 flips every number, so bit 2 flips every 2 numbers, not every 4.
Question 4
A Rightmost column, 8 to 11:
B 8 ends in 0, 9 ends in 1
C 10 ends in 0, 11 ends in 0
Line C — The rightmost column alternates every number. After 10 (1010) ending in 0, 11 (1011) must end in 1.
Question 5
A Four bits count 0 to 15
B Smallest: 0001
C Largest: 1111
Line B — The smallest four-bit number is 0000, which is 0. The pattern 0001 is 1.

Student with a class code? Join your class →