display | more...
Radix economy is a way of measuring the relative efficiency of various number systems. The economy is measured as a product of the radix (r) and the width, (w), where rw equals some constant value, compared across different radices.

Why is this a useful measure? The economy measures how much space is required to store given values. For instance, taking the number one thousand, in various radices:

  1. width 1000, economy 1000 (obviously not useful)
  2. width 9.97, economy 19.9
  3. width 6.29, economy 18.9 (The lowest)
  4. width 4.98, economy 19.9
  5. width 4.29, economy 21.5
  6. width 3.86, economy 23.1
  7. width 3.55, economy 24.8
  8. width 3.32, economy 26.6
  9. width 3.14, economy 28.3
  10. width 3.00, economy 30.0
Taking radices as a continuous spectrum, the most efficient base is e, but it's hard to build computers using base-e logic. Which is the whole point of radix economy - building hardware. Unfortunately, Moore's Law has put binary computers so far ahead in optimization that the 5% increase in efficiency of base 3 is not worth discarding decades of advances in base 2 efficiency.

Log in or register to write something here or to contact authors.