Giant Brains; or, Machines That Think

Biquinary or Two-Five Numbers

Another kind of notation for numbers is biquinary notation, so called because it uses both 2’s and 5’s. Essentially this notation is very like Roman numerals, ancient style. By ancient style we mean, for example, VIIII instead of IX. In the following table we show the first two dozen numbers in decimal, biquinary, and ancient Roman notation:

Decimal	Biquinary	Roman
0	0
1	1	I
2	2	II
3	3	III
4	4	IIII
5	10	V
6	11	VI
7	12	VII
8	13	VIII
9	14	VIIII
10	100	X
11	101	XI
12	102	XII
13	103	XIII
14	104	XIIII
15	110	XV
16	111	XVI
17	112	XVII
18	113	XVIII
19	114	XVIIII
20	200	XX
21	201	XXI
22	202	XXII
23	203	XXIII

The biquinary columns alternate in going from 0 to 4 and from 0 to 1. The digits from 0 to 4 are not changed. The digits from 5 to 9 are changed into 10 to 14. We see that the biquinary digits are 0 to 4 in odd columns and 0, 1 in even columns, counting from the right.

This is the notation actually expressed by the abacus. The beads of the abacus show by their positions groups of 2 and 5 (see Fig. 1).