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Counting in binary from 0 to 7 (Binary Number Representation)

Binary counting: when a column is 1 and must go up, it resets to 0 and the next column on the left becomes 1, like carrying from 9 to 10 in decimal.

Part of: ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 7

Understanding Counting in binary from 0 to 7 (Binary Number Representation) in ACARA Digital Technologies Years 7–8

What it does: Reading the last digit of each number gives 0, 1, 0, 1, 0, 1, 0, 1, so the right-hand column alternates every step. Just as 9 + 1 = 10 resets the ones column to 0, 011 + 1 resets the two right columns to 0 and makes the left column 1. In decimal, 9 is the highest digit, so it resets to 0 and carries 1 to the next column. In binary, 1 is the highest digit, so 001 resets to 0 and carries to give 010. Binary uses only 0 and 1. The number 7 is written as 111, which is the biggest value that fits in 3 bits.

Common mistakes: One in binary is 001, not 010. The right-hand column is the only one that is 1. 010 is the number two. After 100 (four), the right-hand column goes from 0 to 1, so five is 101. 110 is six.

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This module's key terms are also in a printable crossword (Modules 173–188) and word search (Modules 153–188).

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Learning

Duo

What comes right after 011 when counting in binary?

100012

Matches

000, 001, 002, 003

↓

Binary only uses the digits 0 and 1. When a column reaches 1 it must reset to 0 and carry, so 001 is followed by 010.

Applying

Meanings

Term

000 001 010 011 100

Meaning

Binary counting: when a column is 1 and must go up, it resets to 0 and the next column on the left becomes 1, like carrying from 9 to 10 in decimal.

Practice

000

Testing

Gaps

000, 001, 010, , 100, 101, 110, 111

Check Answer

Spots

10 = 000

21 = 010

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Quick Questions

1. What comes right after 011 when counting in binary?

A. 100 ✓

B. 012

Binary only has the digits 0 and 1. The right two columns are both 1, so they reset to 0 and the next column on the left becomes 1. That gives 100.

2. Which is the correct 3-bit binary counting order?

A. 000, 001, 002, 003

B. 000, 001, 010, 011 ✓

There is no 2 in binary. After 001 the right-hand column resets to 0 and the next column becomes 1, giving 010.

3. What does the right-hand column do as you count up in binary?

A. It stays 0 until the very end

B. It alternates 0, 1, 0, 1, 0, 1 ✓

The right-hand column flips on every step: 000, 001, 010, 011, 100, 101, and so on.

4. Which decimal step is like binary 001 going to 010?

A. 9 going to 10 ✓

B. 5 going to 6

In decimal, 9 is the highest digit, so it resets to 0 and carries 1 to the next column. In binary, 1 is the highest digit, so 001 resets to 0 and carries to give 010.

5. When a binary column is 1 and needs to go up, what happens?

A. It resets to 0 and the next column on the left becomes 1 ✓

B. It becomes 2 and stays in the same column

A binary column can only hold 0 or 1. Going up means resetting to 0 and carrying 1 to the left, like 9 to 10 in decimal.

Match the Pairs

001 + 1 = 010 → The right-hand column was 1, so it resets to 0 and carries 1 into the middle column.

010, 011, 100 → Each step up: the right-hand column flips, and a full column carries a 1 into the next column on the left.

The right-hand column alternates 0 1 0 1 every time you count up by one. → 000, 001, 010, 011, 100, 101, 110, 111

Binary carrying is like decimal going from 9 to 10: the full column resets to 0 and the next column on the left goes up. → 011 + 1 = 100

000, 001, 002, 003 → Binary only uses the digits 0 and 1. When a column reaches 1 it must reset to 0 and carry, so 001 is followed by 010.

001, 011, 010, 100 → The order is wrong. After 001 comes 010 (carry into the middle column), then 011, then 100.

Key Term

000 001 010 011 100

Binary counting: when a column is 1 and must go up, it resets to 0 and the next column on the left becomes 1, like carrying from 9 to 10 in decimal.

Fill in the Blanks

1. 000, 001, 010, 011, 100, 101, 110, 111

Hint: Type the 3-bit number that comes after 010 and before 100.

2. Right-hand column: 0, 1, 0, 1, 0, 1, 0, 1

Hint: The right-hand column alternates. Type the digit that comes after the 0 in this spot.

3. 011 + 1 = 100

Hint: Add 1 and carry through each column. Type the 3-bit result.

4. A column of 1 that must go up resets to 0

Hint: Type the digit a column becomes when it resets and carries.

5. 9 + 1 carries to 10 in decimal 1 + 1 carries to 10 in binary

Hint: Binary carries just like decimal. Type what 1 + 1 becomes when the column resets and carries.

Spot the Error

Question 1

A 0 = 000

B 1 = 010

C 2 = 010

D 3 = 011

Line B — One in binary is 001, not 010. The right-hand column is the only one that is 1. 010 is the number two.

Question 2

A 3 = 011

B 4 = 100

C 5 = 110

D 6 = 110

Line C — After 100 (four), the right-hand column goes from 0 to 1, so five is 101. 110 is six.

Question 3

A 4 = 100

B 5 = 101

C 6 = 110

D 7 = 011

Line D — Seven uses all three columns set to 1, so it is 111. 011 is three.

Question 4

A Right column for 0 to 7:

B 0 0 1 1 0 0 1 1

C It flips every count

Line B — The right-hand column alternates 0 1 0 1 0 1 0 1. The pattern 0 0 1 1 0 0 1 1 belongs to the middle column.

Question 5

A Counting from 011 to 100:

B Right column 1 stays at 1

C Middle column 1 resets to 0

D Left column 0 becomes 1

Line B — When a column at 1 has to go up, it resets to 0 and carries to the left. The right column becomes 0, not stays 1.

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