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Babylonian Numerals

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).

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Babylonian Numerals -

Tag(s) : Numeral System, History, Symbol Substitution

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Babylonian Numerals

Converter From Babylonian Numbers 𒐕,π’Œ‹ β†’ 1,2,3

Converter To Babylonian Numbers 1,2,3 β†’ 𒐕,π’Œ‹







Answers to Questions (FAQ)

What are babylonian numbers? (Definition)

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.

How to write babylonian numbers?

The number is written in base 60, the 60 digits are broken down into vertical bars 𒐕 (often noted |) which are worth one unit (1) and chevrons π’Œ‹ (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.

Example: 23 is written with 2 tenths and 3 units so <<||| or char(66)char(51)

Example: 61 is written 1 sixtieth and 1 unit as | | or char(49)char(49) (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:

𒐕1𒐖2𒐗3π’˜4𒐙5π’š6𒐛7
π’œ8𒐝9π’Œ‹10π’Ž™20π’Œ30𒐏40𒐐50
NB: The double chevron character π’Ž™ (20) has been forgotten in Unicode 5 (it existed as βŸͺ) and was added in Unicode 8 (2015) but may appear unknown (?) on some devices.

How to convert babylonian numbers?

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 $

How to convert from base 10 to base 60?

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

How to write the number zero 0?

Babylonians did not use the zero (this concept had not been invented), but from the 3rd century they used the symbol char(48)

How to count using Babylonian numerals?

Babylonian numbers chart (base60)

0 (zero)char(48)1char(49)2char(50)3char(51)4char(52)
5char(53)6char(54)7char(55)8char(56)9char(57)
10char(65)11char(65)char(49)12char(65)char(50)13char(65)char(51)14char(65)char(52)
15char(65)char(53)16char(65)char(54)17char(65)char(55)18char(65)char(56)19char(65)char(57)
20char(66)21char(66)char(49)22char(66)char(50)23char(66)char(51)24char(66)char(52)
25char(66)char(53)26char(66)char(54)27char(66)char(55)28char(66)char(56)29char(66)char(57)
30char(67)31char(67)char(49)32char(67)char(50)33char(67)char(51)34char(67)char(52)
35char(67)char(53)36char(67)char(54)37char(67)char(55)38char(67)char(56)39char(67)char(57)
40char(68)41char(68)char(49)42char(68)char(50)43char(68)char(51)44char(68)char(52)
45char(68)char(53)46char(68)char(54)47char(68)char(55)48char(68)char(56)49char(68)char(57)
50char(69)51char(69)char(49)52char(69)char(50)53char(69)char(51)54char(69)char(52)
55char(69)char(53)56char(69)char(54)57char(69)char(55)58char(69)char(56)59char(69)char(57)

For other numbers, use the form above.

Why using the base 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

How to convert Babylonian numbers into roman numerals?

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.

What traces remain of Babylonian numbers?

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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Babylonian Numerals on dCode.fr [online website], retrieved on 2024-06-16, https://www.dcode.fr/babylonian-numbers

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