Number Bases — Binary, Decimal & Hexadecimal
Learn how to convert between decimal, binary, and hexadecimal, and understand why different number bases are used in computing.
📚 Learning Steps
💡 Study Tips
- • Read through at your own pace
- • Try the interactive simulators hands-on
- • Study the pseudocode — it appears in exams
- • Quiz yourself before moving on
Step 1: Why Do Computers Use Different Bases?
📖 TheoryComputers operate using binary (base 2) because electronic circuits have two states: ON (1) and OFF (0). But binary is hard for humans to read — long strings of 0s and 1s are error-prone.
The three number bases you need:
•Binary (base 2) — digits 0 and 1. Used internally by all digital computers.
•Decimal (base 10) — digits 0–9. The everyday number system humans use.
•Hexadecimal (base 16) — digits 0–9 and A–F. A compact way to represent binary.
Hexadecimal is used because:
•Each hex digit represents exactly 4 binary bits
•8-bit byte = just 2 hex digits (e.g., 11111111 = FF)
•Memory addresses, colour codes (#FF00AA), MAC addresses all use hex
•Much easier for humans to read and type than binary
🎯 Key Points
- •Binary (base 2): used by computers — two states (0/1)
- •Decimal (base 10): used by humans — ten digits (0–9)
- •Hexadecimal (base 16): compact representation — 16 digits (0–F)
- •1 hex digit = 4 binary bits exactly
- •Hex is used for memory addresses, colour codes, MAC addresses, and error codes
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