Theory — Data-representation

Data Representation — How Computers Store Everything as Numbers: 14 topics and 36 interactive cards with runnable examples and quizzes.

Topics

  1. Why Computers Use Binary — Everything Is a Number · Why Only Two Digits?
  2. Counting in Binary — Place Value, Base 2 · Binary → Denary, in Code · Denary → Binary · Your Turn: Convert It
  3. Hexadecimal — Shorthand for Binary — Why Hex Exists · Binary ↔ Hex in Four-Bit Chunks · Quick Check
  4. Binary Addition & Overflow — Adding Bits · Overflow
  5. Negative Numbers — Two's Complement — The Problem with Minus Signs · Making a Negative Number · Range and a Common Trap
  6. Logical Binary Shifts — Shifting Left and Right
  7. Representing Text — Character Sets: ASCII · Unicode: Beyond English
  8. Representing Images — Bitmaps: A Grid of Pixels · Resolution & File Size
  9. Representing Sound — Sampling a Wave · Sound File Size
  10. Storage Units & Compression — Units of Storage · Lossless vs Lossy Compression
  11. Floating-Point Numbers (A Level) — Storing Fractions · Normalisation & Its Trade-offs
  12. More Number Representations — Binary Subtraction · Binary-Coded Decimal (BCD) · Unicode in Bytes: UTF-8 · Normalisation, Worked (A Level)
  13. File Organisation & Access (A Level) — Records, Fields & Files · File Organisation · File Access & Hashing
  14. Check Your Understanding — Number Systems · Two's Complement · Media & Compression · You've Got the Foundation