Tool to convert babylonian numbers (Babylonian Numerals). The Mesopotamian numeral system uses a mix of base 60 (sexagesimal) and base 10 (decimal) by writing wedges (vertical or corner wedge).
Babylonian Numerals - dCode
Tag(s) : Numeral System, History, Symbol Substitution
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Tool to convert babylonian numbers (Babylonian Numerals). The Mesopotamian numeral system uses a mix of base 60 (sexagesimal) and base 10 (decimal) by writing wedges (vertical or corner wedge).
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:
π | 1 | π | 2 | π | 3 | π | 4 | π | 5 | π | 6 | π | 7 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
π | 8 | π | 9 | π | 10 | π | 20 | π | 30 | π | 40 | π | 50 |
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.
dCode retains ownership of the online 'Babylonian Numerals' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Babylonian Numerals download for offline use on PC, tablet, iPhone or Android !
Please, check our community Discord for help requests!