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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 To Babylonian Numbers 1,2,3 → 𒐕,𒌋

 Output result as images/symbols (as above) with Unicode characters 𒐕𒌋 with | and < in base 60 (sexagesimal form) in base 60 (with calculation details)

### 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

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 𒐖 𒐗 𒐘 𒐙 𒐚 𒐛 1 2 3 4 5 6 7 8 9 10 20 30 40 50
NB: The double chevron character 𒎙 (20) has been forgotten in Unicode 5 (it existed as ) 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-codeq[0] = ni = 0while (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

### How to count using Babylonian numerals?

Babylonian numbers chart (base60)

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.

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