§1 Positional value
In base b, each digit is multiplied by b raised to its position (starting at 0 on the right). 175₈ = 1·8² + 7·8¹ + 5·8⁰ = 125.
§2 Conversion methods
| From → To | Method |
|---|---|
| Decimal → base b | Divide repeatedly by b; read remainders bottom to top |
| Base b → decimal | Sum digit × bᵖᵒˢⁱᵗⁱᵒⁿ |
| Binary ↔ hex | Group bits in fours from the right (1011 0111 = B7) |
| Binary ↔ octal | Group bits in threes from the right (101 110 = 56₈) |
| Decimal fraction → binary | Multiply the fraction by 2; record integer parts top to bottom |
§3 Signed numbers
§4 Worked examples
Example 1
Convert 156₁₀ to binary and hexadecimal.
- 156 ÷ 2 → remainders 0,0,1,1,1,0,0,1 (bottom to top: 10011100).
- Group in fours: 1001 1100 = 9C.
Answer 10011100₂ = 9C₁₆
! Common traps
- Reading remainders in the wrong direction.
- Forgetting that A–F stand for 10–15 in hexadecimal.
Coverage source: 2023 ICT Proficiency Certification Examination FAQs (file dated 14 Feb 2023) (third-party copy)