Topic 1 · pp. 25–31 · Free
Topic Notes · Easy summaries with diagrams
Chapter 2 — Chapter 2 — Number Systems
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Topic 1 of 6
📘Easy summary
Base (radix) = number of digits. Decimal base 10 (0–9); binary base 2 (0, 1); octal base 8 (0–7); hexadecimal base 16 (0–9, A–F). Decimal → other base: repeatedly divide by the base, write remainders bottom-to-top: 25₁₀ = 11001₂ = 31₈ = 19₁₆. Other base → decimal: multiply each digit by base^position and add: 1011₂ = 8+0+2+1 = 11. Binary ↔ octal by groups of 3 bits; binary ↔ hex by groups of 4 bits (1111 1010₂ = FA₁₆).
⭐Key points
- Remainders read upward.
🔬Diagram
🌿Real-life example
13 → 1101₂.
💡Exam tip
- Valid binary contains only 0 and 1.
✅Quick check
1. Valid binary:
2. Hex digits:
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