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
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Babylonian Numerals
Converter From Babylonian Numbers π,π β 1,2,3
Converter To Babylonian Numbers 1,2,3 β π,π
Answers to Questions (FAQ)
What are babylonian numbers? (Definition)
In mesopotamian/babylonian 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?
Each vertical bar | equals a unit and each < 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 .png)
.png)
Example: 61 is written 1 sixtieth and 1 unit as | | or .png)
(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 |
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 .png)
How to count using Babylonian numerals?
Babylonian numbers chart (base60)
| 0 (zero) | | 1 | | 2 | .png) | 3 | | 4 | .png) |
|---|---|---|---|---|---|---|---|---|---|
| 5 | .png) | 6 | .png) | 7 | .png) | 8 | .png) | 9 | .png) |
| 10 | .png) | 11 | | 12 | | 13 | | 14 | |
| 15 | | 16 | | 17 | | 18 | | 19 | |
| 20 | | 21 | | 22 | | 23 | | 24 | |
| 25 | | 26 | | 27 | | 28 | | 29 | |
| 30 | .png) | 31 | | 32 | | 33 | | 34 | |
| 35 | | 36 | | 37 | | 38 | | 39 | |
| 40 | .png) | 41 | | 42 | | 43 | | 44 | |
| 45 | | 46 | | 47 | | 48 | | 49 | |
| 50 | .png) | 51 | | 52 | | 53 | | 54 | |
| 55 | | 56 | | 57 | | 58 | | 59 | |
For other numbers, use the form above.
Why using the base 60?
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
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.
Source code
dCode retains ownership of the "Babylonian Numerals" source code. Except explicit open source licence (indicated Creative Commons / free), the "Babylonian Numerals" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Babylonian Numerals" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Babylonian Numerals" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
Cite dCode
The copy-paste of the page "Babylonian Numerals" or any of its results, is allowed (even for commercial purposes) as long as you cite dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Babylonian Numerals on dCode.fr [online website], retrieved on 2023-09-21,
- Converter From Babylonian Numbers π,π β 1,2,3
- Converter To Babylonian Numbers 1,2,3 β π,π
- What are babylonian numbers? (Definition)
- 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 using the base 60?
- How to convert Babylonian numbers into roman numerals?
