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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Babylonian numeration is a numbering system used by the ancient Babylonians/Sumerians in Mesopotamia to represent numbers. In mesopotamian/babylonian/sumerian number system, our current number system, called *hindu-arabic* (0,1,2,3,4,5,6,7,8,9) did not exist. Numbers are written in a cuneiform style with `|` (pipe or nail) and `<` (corner wedge or bracket), written in base 60.

The number is written in base 60, the 60 digits are broken down into vertical bars `π` (often noted `|`) which are worth one unit (1) and chevrons `π` (often noted `<`) which are worth ten (10) in base 10.

The power change of sixty ($ 60^1 = 60 $, $ 60^2 = 3600 $, $ 60^3 = 216000 $ etc.) is represented by a space.

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:

`// pseudo-code`

q[0] = n

i = 0

while (q[i] > 0) {

r[i] = q[i] mod 60

q[i+1] = q[i] div 60

i = i+1

}

return q

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

60 has the advantage of having many divisors: 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

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.

Clay tablets played a crucial role in understanding Babylonian numbers, as they were the medium on which the ancient Babylonians wrote their numerations. These tablets have survived through the centuries, providing a valuable source of information about the numerical and mathematical systems of the time.

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Cite as source (bibliography):

*Babylonian Numerals* on dCode.fr [online website], retrieved on 2024-10-04,

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