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 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!

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

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