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Decimal (base-10) and binary (base-2)

Decimal is base-10 and uses ten digits, 0 to 9. Binary is base-2 and uses only 0 and 1. People use decimal every day, but computers use binary.

Part of: ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 5

Understanding Decimal (base-10) and binary (base-2) in ACARA Digital Technologies Years 7–8

What it does: Decimal has ten digits, from 0 up to 9, and people use it every day. Binary has just two digits, 0 and 1, which suits the on/off states in computers. Decimal is base-10 because it has ten different digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Everyday numbers like prices, scores and ages are written in decimal. Binary can only contain 0 and 1. The digit 3 is not allowed, so 1031 is not binary. The base is about how many digits there are (0 and 1), not about the biggest number. Binary can write numbers much bigger than 2.

Common mistakes: Decimal is base-10 because it uses ten digits (0 to 9). Line 1 should be decimal_base = 10. Base 2 belongs to binary. The base is how many different digits a system uses. Binary has only two digits, so binary_base must be len(binary_digits), which is 2. Using decimal_digits would give 10.

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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

Which number system uses the ten digits 0 to 9?

Binary (base-2)Decimal (base-10)

Matches

Binary (base-2) digits: 0 1 2

↓

Binary only has two digits, 0 and 1. The digit 2 does not exist in binary.

Applying

Meanings

Term

decimal base-10, binary base-2

Meaning

Decimal is base-10 and uses ten digits, 0 to 9. Binary is base-2 and uses only 0 and 1. People use decimal every day, but computers use binary.

Practice

decimal: base 10, digits 0 to 9

Testing

Gaps

decimalBase ←

Check Answer

Spots

1decimal_base = 2

2binary_base = 2

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Quick Questions

1. Which number system uses the ten digits 0 to 9?

A. Decimal (base-10) ✓

B. Binary (base-2)

Decimal is base-10 because it has ten different digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

2. Which number system uses only the digits 0 and 1?

A. Decimal (base-10)

B. Binary (base-2) ✓

Binary is base-2 because it has just two different digits, 0 and 1.

3. What does the 'base' of a number system tell you?

A. How many different digits the system uses ✓

B. How big the largest number can be

The base is the count of different digits. Base-10 has ten digits and base-2 has two.

4. Your phone shows the price of a game as $25. Which system is this price written in?

A. Binary

B. Decimal ✓

Everyday numbers like prices, scores and ages are written in decimal.

5. Which system do computers use to store and process data?

A. Binary ✓

B. Decimal

Computers use binary because their hardware has two states, which are written as 0 and 1.

Match the Pairs

base-10 → The decimal system, which uses ten different digits: 0 to 9

base-2 → The binary system, which uses only two different digits: 0 and 1

Everyday numbers like prices and scores are written in decimal, using digits 0 to 9 → Decimal: 0 1 2 3 4 5 6 7 8 9

Computers store numbers using only two digits, so they use binary → Binary: 0 1

Binary (base-2) digits: 0 1 2 → Binary only has two digits, 0 and 1. The digit 2 does not exist in binary.

Decimal is base-2 and uses 0 and 1 → Decimal is base-10 and uses ten digits, 0 to 9. Base-2 is binary.

Key Term

decimal base-10, binary base-2

Decimal is base-10 and uses ten digits, 0 to 9. Binary is base-2 and uses only 0 and 1. People use decimal every day, but computers use binary.

Fill in the Blanks

1. decimalBase ← 10

Hint: Type the number of different digits that decimal uses.

2. binaryBase ← 2

Hint: Type the number of different digits that binary uses.

3. FOR digit ← 0 TO 9 DISPLAY digit END FOR

Hint: Type the largest digit that decimal uses.

4. FOR digit ← 0 TO 1 DISPLAY digit END FOR

Hint: Type the largest digit that binary uses.

5. base ← 2 IF base = 2 THEN DISPLAY "binary"

Hint: Type the variable name that stores the number of digits in the system.

Spot the Error

Question 1

A decimal_base = 2

B binary_base = 2

C print(decimal_base)

Line A — Decimal is base-10 because it uses ten digits (0 to 9). Line 1 should be decimal_base = 10. Base 2 belongs to binary.

Question 2

A decimal_digits = "0123456789"

B binary_digits = "01"

C binary_base = len(decimal_digits)

Line C — The base is how many different digits a system uses. Binary has only two digits, so binary_base must be len(binary_digits), which is 2. Using decimal_digits would give 10.

Question 3

A computers_use = "decimal"

B people_use = "decimal"

C print(computers_use, "is base-2")

Line A — Computers use binary, not decimal. Line 1 should be computers_use = "binary", which matches the base-2 message on line 3.

Question 4

A bits = ["0", "1"]

B base = len(bits)

C print("Binary is base", base)

D print("Computers use decimal")

Line D — The program is about binary, which has two digits (base-2) and is what computers use. Line 4 should say "Computers use binary".

Question 5

A digits = "0123456789"

B base = len(digits) - 1

C print("Base", base)

Line B — The base is the number of different digits. Decimal has ten digits (0 to 9), so base = len(digits) gives 10. Subtracting 1 gives 9, which is wrong.

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