Radix economy

From Wikipedia, the free encyclopedia

Radix economy is the efficiency of expressing a number in a particular base. The economy for any particular number N in a given base b is equal to the number of digits needed to express it in that base, multiplied by the radix [1]:

E(b,N) = b \lceil \log_b (N) \rceil

For example, 11001002 (100) has radix economy 7×2 = 14, while in base 3 100 is written 102013, with an economy of 15. The decimal representation of 100 has an economy of 30 (larger numbers are worse), and the economy of 2S36 (100 in Base 36) is 72.

Bases b1 kaj b2 may be compared for the same (large) N:

{{E(b_1,N)} \over {E(b_2,N)}} \approx {{b_1 {\log_{b_1} (N)} } \over {b_2 {\log_{b_2} (N)}}} = { {b_1 {\log (N)} \over {\log (b_1)} }\over {b_2 {\log (N)} \over {\log (b_2)}} } = {{b_1 \log (b_2)} \over {b_2 \log (b_1)}}

In general, base 3 is the most economic of any integral base [1], followed by binary and base 4.

This would theoretically allow computers to be for 5% more powerful if they used ternary [1], but considerable development would be needed to reach the processing power of modern binary hardware.

[edit] External links

  1. ^ a b c "Radix economy" at Everything2
 This mathematics-related article is a stub. You can help Wikipedia by expanding it.
Languages