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Counting in binary from 0 to 7 (Representing Text, Images and Sound)

Counting in binary uses only 0 and 1, so after 1 the next number needs a new column: 1 + 1 = 10. Three bits count from 000 (0) up to 111 (7).

Part of: ACARA Digital Technologies Years 7–8 — Representing Text, Images and Sound — Module 6

Understanding Counting in binary from 0 to 7 (Representing Text, Images and Sound) in ACARA Digital Technologies Years 7–8

What it does: Binary only has 0 and 1, so counting past 1 needs a new column. Binary 10 means one two and no ones, which is 2 in decimal. Each step adds 1. After 011 (3) every column is full up to that point, so the next number, 4, needs a new column and is written 100. 101 has a 4, no 2 and a 1: 4 + 0 + 1 = 5. Binary digits can only be 0 or 1. After 001 comes 010. Three bits count from 000 (0) up to 111 (7): 4 + 2 + 1 = 7.

Common mistakes: Zero in three bits is 000, not 001. 001 is the number 1. Six is 110 in binary. 101 is the number 5.

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

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Learning

Duo

What is 101 in binary as a decimal number?

Matches

0, 1, 2, 3 in binary is 0, 1, 2, 3

↓

Binary can only use the digits 0 and 1, so 2 and 3 cannot be written as single digits. Two is 10 and three is 11.

Applying

Meanings

Term

000 001 010 011 100 101 110 111

Meaning

Counting in binary uses only 0 and 1, so after 1 the next number needs a new column: 1 + 1 = 10. Three bits count from 000 (0) up to 111 (7).

Practice

000 = 0

Testing

Gaps

000 001 010 100 101 110 111

Check Answer

Spots

10 = 001

21 = 001

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Quick Questions

1. What is 101 in binary as a decimal number?

A. 5 ✓

B. 3

101 has a 4, no 2 and a 1: 4 + 0 + 1 = 5.

2. In binary, what comes right after 1?

A. 10 (a new column is needed) ✓

B. 2

Binary only has the digits 0 and 1, so after 1 we add a new column and write 10. The digit 2 never appears in binary.

3. Which list counts from 0 to 3 correctly in binary?

A. 000, 001, 002, 003

B. 000, 001, 010, 011 ✓

Binary digits can only be 0 or 1. After 001 comes 010.

4. What is the biggest number that three bits can show?

A. 111, which is 7 ✓

B. 111, which is 3

Three bits count from 000 (0) up to 111 (7): 4 + 2 + 1 = 7.

5. What is the binary number for 4 using three bits?

A. 011

B. 100 ✓

4 is the first number that needs the third column, so it is 100. 011 is 3.

Match the Pairs

010 → The decimal number 2, written with three bits

111 → The biggest number three bits can show, which is 7

After 1 you run out of digits, so you add a new column: 1 + 1 makes two, written as 10 → 1 + 1 = 10

Counting from 0 to 7 with three bits starts at 000 and reaches 100 for the number 4 → 000, 001, 010, 011, 100

0, 1, 2, 3 in binary is 0, 1, 2, 3 → Binary can only use the digits 0 and 1, so 2 and 3 cannot be written as single digits. Two is 10 and three is 11.

011 + 1 = 012 → There is no digit 2 in binary. Adding 1 to 011 carries over to give 100, which is 4.

Key Term

000 001 010 011 100 101 110 111

Counting in binary uses only 0 and 1, so after 1 the next number needs a new column: 1 + 1 = 10. Three bits count from 000 (0) up to 111 (7).

Fill in the Blanks

1. 000 001 010 011 100 101 110 111

Hint: Type the 3-bit binary number that comes right after 010 in the count.

2. 1 + 1 = 10 in binary

Hint: Type the two-digit binary result when 1 is added to 1, because a new column is needed.

3. 101 in binary is 5 in decimal

Hint: Type the decimal value of binary 101 (one four, no twos, one one).

4. Three bits count from 000 up to 111

Hint: Type the largest number that fits in three bits, where every bit is 1.

5. Decimal 4 is written 100 in binary

Hint: Type the 3-bit binary number that starts a new column after 011.

Spot the Error

Question 1

A 0 = 001

B 1 = 001

C 2 = 010

D 3 = 011

Line A — Zero in three bits is 000, not 001. 001 is the number 1.

Question 2

A 4 = 100

B 5 = 101

C 6 = 101

D 7 = 111

Line C — Six is 110 in binary. 101 is the number 5.

Question 3

A Count: 000, 001, 010

B After 001 comes 002

C After 010 comes 011

D After 011 comes 100

Line B — Binary only has the digits 0 and 1, so 002 is not possible. After 001 comes 010 because 1 + 1 needs a new column.

Question 4

A 000 = 0

B 001 = 1

C 010 = 2

D 011 = 4

Line D — 011 means 2 + 1, which is 3 in decimal. Four is 100.

Question 5

A Three bits: 000 to 111

B 000 is 1 in decimal

C 111 is 7 in decimal

Line B — 000 has no 1s in it, so its value is 0, not 1.

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