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

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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 number system, numbers have to be converted in 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.

Example: 23 is written <<||| or

Example: 61 is written | | 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).

Converting is easy by counting symbols and considering it in base 60.

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)}

Babylonnians 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.

Convert the babylonian numbers to 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 source code of the script Babylonian Numerals online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Babylonian Numerals script for offline use on PC, iPhone or Android, ask for price quote on contact page !

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Source : https://www.dcode.fr/babylonian-numbers

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