01 Chapter Map - Number Systems & Arithmetic
Chapter 1 Overview & Map of Content (MOC)
Foundational number representations, arbitrary base conversions, base complements (1’s & 2’s), and 8-bit signed two’s complement computer arithmetic.
📚 Study Notes Index
Read in order — each note assumes the previous one.
| # | Note | What it covers | PYQ years | Typical marks |
|---|---|---|---|---|
| 1.01 | 1.01 Positional Number Systems & Base Conversions | Positional radix theory, successive division/multiplication, unusual bases (3, 4, 7, 12), hex↔octal↔binary, fractional precision | 2015, 2016, 2017, 2021, 2022, 2023, 2025 | 12 |
| 1.02 | 1.02 Base Complements & Subtraction Mechanics | ’s and ‘s complements, 1’s/2’s complement subtraction, end-around carry, direct base-6 and base-8 multiplication | 2015, 2018, 2019, 2024 | 8–13 |
| 1.03 | 1.03 Signed Representation, Overflow & Two’s Complement | Sign-magnitude vs 1’s vs 2’s complement, 8-bit signed arithmetic, overflow detection () | 2016, 2017, 2020, 2021, 2025 | 8–13 |
🎯 Exam Weight
This chapter is the highest-yield-per-hour block in the course
Chapter 1 supplies roughly 20–25 marks of every paper and the questions are almost purely mechanical — no proofs, no design judgement, just algorithms executed correctly. Three questions recur relentlessly:
- Base conversion (every paper, 2015–2025) → 1.01 Positional Number Systems & Base Conversions
- 8-bit two’s complement arithmetic (5 of 10 papers) → 1.03 Signed Representation, Overflow & Two’s Complement
- Complement subtraction with straight-subtraction check (3 of 10 papers) → 1.02 Base Complements & Subtraction Mechanics
The examiner recycles the same handful of numbers (, , , ) with digits shuffled, and in 2020 tied the operands to your roll number specifically to defeat memorisation. Drill the algorithms, not the answers.
🔗 Related Resources
- Course Teaching Plan: ECE 2103 - Digital Electronics and Logic Circuits
- Next chapter: 02 Chapter Map - Digital Codes & Error Detection — applies these conversions to BCD, Excess-3, Gray and weighted codes.