Incomplete list of numbers systems with practical usage

numberSystems.txt

Incomplete list of numbers systems with practical usage

(dynamic) https://en.wikipedia.org/wiki/Radix
- combinatorics: enumerate combinations/variations/permutations of recursive+discrete structures

https://en.wikipedia.org/wiki/Mixed_radix
- date (year-month-day), time (hour-minute-second)
- combinatorics: enumerate combinations/variations/permutations of non-recursive+discrete structures

https://en.wikipedia.org/wiki/Signed_number_representations
- 2s complement most popular and used in hardware to compute on numbers
- Google's Protocol Buffers "zig-zag encoding" (sign bit at xxxxs) enables variable-length quantity encoding

https://en.wikipedia.org/wiki/Binary-coded_decimal
- rounding behavior to match how a human doing base-10 arithmetic might behave

https://en.wikipedia.org/wiki/Fixed-point_arithmetic
- represent the domain of interest exactly and not accumulate error

Rational numbers
- Without restrictions they have unbounded size when you start mixing denominators

https://en.wikipedia.org/wiki/Floating-point_arithmetic
- wide dynamic range and lots of precision for small values
- simple to use

https://en.wikipedia.org/wiki/Logarithmic_number_system
- Multiply/divide are fast, and addition/subtraction have tradeoffs:
  addition/subtraction are not very precies or are very slow
- signal processing: almost all operations are multiply/divide

Symbolic number systems
- represent computable numbers exactly