底數經濟度

底數經濟度是一種將某數作為進位制的底数時，該進位制表達數的效率，其定義為數在某進位制下表達的位數與底數或該計數系統中每個位數可能的符號之數量的乘積。為量化不同底數的進制或計數系統在表示一個數時的效率的一種方法，尤其用於計算機系統，評估特定計數系統的儲存效率。

底數經濟度的概念亦用於組織結構、網路等領域。

對一數N在特定的底數b下，底數經濟度 ${\displaystyle E(b,N)}$定義為：

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

其中，${\displaystyle \lfloor \,\rfloor }$表示下取整函數；${\displaystyle \log _{b}}$表示以${\displaystyle b}$為底的對數。

若b和N皆為正整數，則底數經濟度${\displaystyle E(b,N)}$值與${\displaystyle N}$在以${\displaystyle b}$為底的進制下的位數與${\displaystyle b}$的乘積^[1]。

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	${\displaystyle {{E(b)} \over {E(e)}}}$	E (b )/E (e )的 相對大小
1	3.5	22.0	91.5	2,665.0	${\displaystyle \infty }$	—
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（英语：Septenary）	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（英语：Pentadecimal）	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

• 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.

• The Optimum Radix In Multiple-Valued Logic Systems