Integers, Floating Points or Exotic Representations ...
summary
Explains why binary (base‑2) is preferred for hardware despite an information-theory optimum near e states, shows two’s‑complement uses less hardware than ones’ complement and gives concrete integer ranges (e.g. 8‑bit signed −128..127). Compares floating‑point versus fixed‑point: floats are approximate and can be slower on some CPUs, while fixed‑point (example: scale 256) speeds a rotozoom on a 486 by using integer addresses; demos include the fast inverse square root (≈0.001 precision), Bresenham’s line algorithm implemented as one add plus one branch per pixel, and LFSR counters with up to 255 states.
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chapters (12)
- 0:00Number representation intro
- 4:31Optimal base choice
- 8:02Binary and positional notation
- 10:29Negative numbers
- 15:24Floating point limits
- 23:46Fixed-point applications
- 27:18Bresenham line algorithm
- 32:58Exotic representations
- 36:46Finance number formats
- 38:16Counters and shift registers
- 43:09Representation choices recap
- 45:36Q&A
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