底数经济度

底数经济度是一种将某数作为进位制的底数时，该进位制表达数的效率，其定义为数在某进位制下表达的位数与底数或该计数系统中每个位数可能的符号之数量的乘积。为量化不同底数的进制或计数系统在表示一个数时的效率的一种方法，尤其用于计算机系统，评估特定计数系统的储存效率。

底数经济度的概念亦用于组织结构、网路等领域。

定义

对一数N在特定的底数b下，底数经济度 $E(b,N)$定义为：

$E(b,N)=b\lfloor \log _{b}(N)+1\rfloor \,$

其中，$\lfloor \,\rfloor$表示下取整函数；$\log _{b}$表示以$b$为底的对数。

若b和N皆为正整数，则底数经济度$E(b,N)$值与$N$在以$b$为底的进制下的位数与$b$的乘积。

底数经济度列表

底数 b	N = 1 to 6 E(b,N)平均	N = 1 to 43 E(b,N)平均	N = 1 to 182 E(b,N)平均	N = 1 to 5329 E(b,N)平均	${{E(b)} \over {E(e)}}$	E (b )/E (e )的 相对大小
1	3.5	22.0	91.5	2,665.0	$\infty$	—
2	4.7	9.3	13.3	22.9	1.0615	1.0615
e	4.5	9.0	12.9	22.1	1.0000	1
3	5.0	9.5	13.1	22.2	1.0046	1.0046
4	6.0	10.3	14.2	23.9	1.0615	1.0615
5	6.7	11.7	15.8	26.3	1.1429	1.1429
6	7.0	12.4	16.7	28.3	1.2319	1.2319
7	7.0	13.0	18.9	31.3	1.3234	1.3234
8	8.0	14.7	20.9	33.0	1.4153	1.4153
9	9.0	16.3	22.6	34.6	1.5069	1.5069
10	10.0	17.9	24.1	37.9	1.5977	1.5977
12	12.0	20.9	25.8	43.8	1.7765	1.7765
15	15.0	25.1	28.8	49.8	2.0377	2.0377
16	16.0	26.4	30.7	50.9	2.1230	2.123
20	20.0	31.2	37.9	58.4	2.4560	2.456
30	30.0	39.8	55.2	84.8	3.2449	3.2449
40	40.0	43.7	71.4	107.7	3.9891	3.9891
60	60.0	60.0	100.5	138.8	5.3910	5.391

延伸阅读

• S.L. Hurst, "Multiple-Valued Logic-Its Status and its Future", IEEE trans. computers, Vol. C-33, No 12, pp. 1160–1179, DEC 1984.
• J. T. Butler, "Multiple-Valued Logic in VLSI Design, ” IEEE Computer Society Press Technology Series, 1991.
• C.M. Allen, D.D. Givone “The Allen-Givone Implementation Oriented Algebra", in Computer Science and Multiple-Valued Logic: Theory and Applications, D.C. Rine, second edition, D.C. Rine, ed., The Elsevier North-Holland, New York, N.Y., 1984. pp. 268–288.
• G. Abraham, "Multiple-Valued Negative Resistance Integrated Circuits", in Computer Science and Multiple-Valued Logic: Theory and Applications, D.C. Rine, second edition, D.C. Rine, ed., The Elsevier North-Holland, New York, N.Y., 1984. pp. 394–446.

外部链接

• The Optimum Radix In Multiple-Valued Logic Systems