Ch 11 · Floating-Point Numbers (A Level) · Theory

Topic 11 of 14 in Data Representation — How Computers Store Everything as Numbers — 2 lessons.

Storing Fractions

Two's complement handles whole numbers, but how do you store 3.75 or 0.0001? Computers use floating-point: a number split into a mantissa (the significant digits) and an exponent (where the binary point sits) — binary's version of scientific notation like 3.75 × 10².

Normalisation & Its Trade-offs

To use the bits efficiently, floating-point numbers are normalised — the mantissa is shifted so it has no wasted leading digits, giving maximum precision for the bits available.

All topics in Theory Data-representation

  1. Why Computers Use Binary
  2. Counting in Binary
  3. Hexadecimal — Shorthand for Binary
  4. Binary Addition & Overflow
  5. Negative Numbers — Two's Complement
  6. Logical Binary Shifts
  7. Representing Text
  8. Representing Images
  9. Representing Sound
  10. Storage Units & Compression
  11. Floating-Point Numbers (A Level)
  12. More Number Representations
  13. File Organisation & Access (A Level)
  14. Check Your Understanding