Babylonian Numerals

In mesopotamian/babylonian number system, numbers have to be converted to base 60. Numbers are written in a cuneiform style with | and <. Each vertical bar | (pipe) equals a unit and each < (corner wedge or bracket) equals a tenth. The change of power of sixty (60 ^ 1 = 60, 60 ^ 2 = 3600, 30 ^ 3 = 216000, etc.) is represented by a space.

Example: 23 is written with 2 tenths and 3 units so <<||| or

Example: 61 is written 1 sixtieth and 1 unit as | | or (with a space separator)

dCode uses the recent system (from the 3rd century civilization in Babylon) which introduce the writing or 0 (before the concept of zero did not exist, it was replace by an ambiguous empty space).

Since Unicode 5 (2006) cuneiform symbols can be represented on compatible browsers, here is the table of characters used by dCode:

Converting is easy by counting symbols and considering it in base 60 to get numbers into classical Hindu-Arabic notation.

Example: <<||| is 2 < and 3 | so $ 2 \times 10 + 3 \times 1 = 23 $

Example: | | (note the space) is 1 | and then 1 | so $ 1 \times 60 + 1 = 61 $

TO convert a number $ n $ from base $ 10 $ to base $ b=60 $ apply the algorithm:

$$ q_0=n; i=0; \mbox{ while } q_i > 0 \mbox{ do } (r_i = q_i \mbox{ mod } 60; q_{i+1}= q_i \mbox{ div } 60 ; i = i+1 ) $$

Example: $$ q_0 = 100 \\ r_0 = 100 \mbox{ mod } 60 = 40 \;\;\; q_1 = 100 \mbox{ div } 60 = 1 \\ r_1 = 1 \mbox{ mod } 60 = 1 \;\;\; q_2 = 0 \\ So \{1,0,0\}_{(10)} = \{1, 40\}_{(60)} $$

Babylonians did not use the zero (this concept had not been invented), but from the 3rd century they used the symbol

Babylonian numbers chart (base60)

0 (zero)		1		2		3		4
5		6		7		8		9
10		11		12		13		14
15		16		17		18		19
20		21		22		23		24
25		26		27		28		29
30		31		32		33		34
35		36		37		38		39
40		41		42		43		44
45		46		47		48		49
50		51		52		53		54
55		56		57		58		59

For other numbers, use the form above.

60 has the advantage of having many divisors.

Today the time system of hours still uses the base sixty: 60 seconds = 1 minute, 60 minutes = 1 hour = 3600 seconds

Convert the Babylonian numbers to Hindu-Arabic numerals (1,2,3,4,5,6,7,8,9,0), then use the Roman numeral converter of dCode.