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

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Quick Questions

Shade in the A or B circle for each question.

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

A 100

B 012

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

A 000, 001, 002, 003

B 000, 001, 010, 011

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

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

A 9 going to 10

B 5 going to 6

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

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1001 + 1 = 010		AThe order is wrong. After 001 comes 010 (carry into the middle column), then 011, then 100.
2010, 011, 100		B011 + 1 = 100
3The right-hand column alternates 0 1 0 1 every time you count up by one.		CEach step up: the right-hand column flips, and a full column carries a 1 into the next column on the left.
4Binary carrying is like decimal going from 9 to 10: the full column resets to 0 and the next column on the left goes up.		DBinary 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.
5000, 001, 002, 003		E000, 001, 010, 011, 100, 101, 110, 111
6001, 011, 010, 100		FThe right-hand column was 1, so it resets to 0 and carries 1 into the middle column.

Definitions

000 001 010 011 100

Fill in the Blanks

Complete each line of code by filling in the missing parts.

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

Right-hand column: 0, 1, 0, 1, 0, _, 0, 1

011 + 1 = ___

A column of 1 that must go up resets to _

9 + 1 carries to 10 in decimal 1 + 1 carries to __ in binary

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A 0 = 000

B 1 = 010

C 2 = 010

D 3 = 011

Question 2

A 3 = 011

B 4 = 100

C 5 = 110

D 6 = 110

Question 3

A 4 = 100

B 5 = 101

C 6 = 110

D 7 = 011

Question 4

A Right column for 0 to 7:

B 0 0 1 1 0 0 1 1

C It flips every count

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

Answer Key

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

Section A: Quick Questions

A — 100

B — 000, 001, 010, 011

B — It alternates 0, 1, 0, 1, 0, 1

A — 9 going to 10

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

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

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

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

011 + 1 = 100

A column of 1 that must go up resets to 0

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

Section E: Spot the Error

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

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

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

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.

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.