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/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 tenthes 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:

𒐕 | 1 | 𒐖 | 2 | 𒐗 | 3 | 𒐘 | 4 | 𒐙 | 5 | 𒐚 | 6 | 𒐛 | 7 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

𒐜 | 8 | 𒐝 | 9 | 𒌋 | 10 | 𒎙 | 20 | 𒌍 | 30 | 𒐏 | 40 | 𒐐 | 50 |

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.

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 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 released for free. To download the online Babylonian Numerals script for offline use on PC, iPhone or Android, ask for price quote on contact page !

- Babylonian to Hindu-Arabic Numbers Converter
- Hindu-Arabic to Babylonian Numbers Converter
- How to write babylonian numbers?
- How to convert babylonian numbers?
- How to convert from base 10 to base 60?
- How to write the number zero 0?
- How to count using babylonian numerals?
- Why the base 60?
- How to convert babylonian numbers into roman numerals?

babylonian,mesopotamian,numeral,babylon,cuneiform,writing,civilization,wedge,bracket,pipe,bar,arabic,roman

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

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