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Radix economy : ウィキペディア英語版
Radix economy
The radix economy of a number in a particular base is the number of digits needed to express it in that base, multiplied by the radix (the number of possible values each digit could have). Various proposals have been made to quantify the relative costs between using different radices in representing numbers, especially in computer systems. Radix economy also has implications for organizational structure, networking, and other fields.
==Definition==
The radix economy ''E''(''b'',''N'') for any particular number ''N'' in a given base ''b'' is equal to the number of digits needed to express it in that base (using the floor function \lfloor \rfloor), multiplied by the radix:
: E(b,N) = b \lfloor \log_b (N) +1 \rfloor \, .
The radix economy measures the cost of storing or processing the number ''N'' in base ''b'' if the cost of each "digit" is proportional to ''b''. A base with a lower average radix economy is therefore, in some senses, more efficient than a base with a higher average radix economy.
For example, 100 in decimal has three digits, so its radix economy is 10×3 = 30; its binary representation has seven digits (11001002) so it has radix economy 2×7 = 14 in base 2; in base 3 its representation has five digits (102013) with a radix economy of 3×5 = 15; in base 36 (2S36) its radix economy is 36×2 = 72.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Radix economy」の詳細全文を読む



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