Show understanding of different number systems

1.1 Data Representation – Understanding Number Systems

Binary (Base‑2)

Binary is the language computers speak. It uses only two digits: 0 and 1. Think of it as a light switch – off (0) or on (1). Every piece of data is ultimately a string of these bits.

Conversion to Decimal: Multiply each bit by 2 raised to its position (starting from 0 on the right) and sum.

1. Write the binary number: 1101₂
2. Positions: 3  2  1  0
3. Values: 2³  2²  2¹  2⁰
4. Multiply: 1×8 + 1×4 + 0×2 + 1×1 = 13
5. Result: 1101₂ = 13₁₀

Octal (Base‑8)

Octal uses digits 0–7. It’s like grouping binary bits in threes. Computers sometimes use octal for compactness, especially in older systems.

Conversion Example: 17₈ → 1×8¹ + 7×8⁰ = 15₁₀.

Hexadecimal (Base‑16)

Hexadecimal uses digits 0–9 and letters A–F (A=10, B=11, …, F=15). It’s popular for representing memory addresses and colours in web design (e.g. #FF5733).

Conversion Example: 2F₁₆ → 2×16¹ + 15×16⁰ = 47₁₀.

Decimal (Base‑10)

Decimal is the system we use every day. It has ten digits (0–9). Computers convert everything to decimal for human readability.

Key Takeaways for the Exam

• Know how to convert between binary, octal, decimal, and hexadecimal.
• Remember the base notation: 101₁₀, 101₂, 101₈, 0x101₁₆.
• Practice writing conversion tables; they help with quick mental calculations.
• Use the “powers of the base” method for conversions (e.g., 2ⁿ, 8ⁿ, 16ⁿ).
• Check your work by converting back to the original base.

Quick Conversion Cheat Sheet