GCSE Computer Science: Number Systems

πŸ“š Learning Outcomes

  • Understand the concept of Denary, Binary, and Hexadecimal number systems.
  • Convert positive Denary numbers to Binary (up to 8 bits).
  • Convert positive Binary numbers to Denary.
  • Convert between Binary and Hexadecimal.
  • Convert between Denary and Hexadecimal.
  • Explain the uses of different number systems in computing.


Starter Activity: Why Other Number Systems?

Denary (Base-10) to Binary (Base-2)

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Denary (Base-10)

Our everyday number system using 10 digits (0-9). Column values are powers of 10.

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Binary (Base-2)

The computer's language using 2 digits (0-1). Column values are powers of 2.

Interactive Example: Convert 150 to Binary

Practice Questions

Binary (Base-2) to Denary (Base-10)

Interactive Example: Convert 11010011 to Denary

Practice Questions

Introduction to Hexadecimal (Base-16)

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Hexadecimal (Base-16)

Uses 16 digits (0-9 and A-F) as a human-friendly shorthand for binary. One hex digit represents four binary digits (a nibble).

Uses: MAC Addresses, Colour Codes (#FF5733), Memory Dumps.

Hexadecimal Values

A=10, B=11, C=12, D=13, E=14, F=15

Binary to Hexadecimal

Interactive Example: Convert 11101001 to Hex

Practice Questions

Hexadecimal to Binary

Interactive Example: Convert 7C to Binary

Practice Questions

Denary to Hexadecimal

Method 1: Divide by 16

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Method 2: Pro Strategy (via Binary)

This two-step process is often faster and less prone to errors:

  1. Convert the Denary number to Binary first.
  2. Then, convert that Binary number to Hexadecimal.

Interactive Example: Convert 210 to Hex (via Binary)

Practice Questions

Hexadecimal to Denary

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Pro Strategy

To convert from Hex to Denary, use place values that are powers of 16. For a two-digit hex number like 'B4', the columns are 16s and 1s.

Interactive Example: Convert B4 to Denary

Practice Questions

⚠️ Common Mistakes

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Forgetting the 1s Column

The rightmost binary column is 20, which equals 1, not 2. A common error is starting the columns at 2 instead of 1.

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Mixing up Hex Letters

It's easy to forget the values for A-F. Write them down! A=10, B=11, C=12, D=13, E=14, F=15.

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Incomplete Nibbles

When converting Hex to Binary, each Hex digit MUST become a 4-bit nibble. Hex '7' is `0111`, not `111`.

Key Takeaways

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Denary (Base 10)

0-9. Used by humans. Powers of 10.

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Binary (Base 2)

0-1. Used by computers (on/off). Powers of 2.

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Hexadecimal (Base 16)

0-9, A-F. Human-friendly shorthand for binary. Powers of 16.

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Key Strategy

When converting between Denary and Hexadecimal, it's often easiest to use Binary as a middle step.

Infinite Practice Zone

Denary to Binary Practice

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Binary to Denary Practice

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Binary to Hex Practice

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Hex to Binary Practice

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Denary to Hex Practice

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Hex to Denary Practice

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πŸ† My Achievements

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