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|Numeral systems by culture|
|East Asian numerals|
|List of numeral system topics|
|Positional systems by base|
|2, 4, 8, 16, 32, 64|
|1, 3, 9, 12, 20, 24, 30, 36, 60, more…|
A numeral system (or system of numeration) is a way to write numbers. Roman numerals and tally marks are examples. "11" usually means eleven, but if the numeral system is binary, then "11" means three.
A numeral is a symbol or group of symbols, or a word in a natural language that represents a number. Numerals differ from numbers just as the word "rock" differs from a real rock. The symbols "11", "eleven" and "XI" are different numerals, all representing the same number. This article tries to explain the different systems of numerals. Greek numerals and Roman numerals are among the systems that were long used, before the Hindu–Arabic numeral system largely replaced them.
Various symbols are used as numerals to make numbers. A system with base 10 (the normal decimal system), normally uses the symbols 0,1,2, 3, 4, 5,6, 7, 8, and 9. The numbers 0 to 9 can be written as one symbol, 0 ... 9. To count past 9, symbols have to be put together. 10 can be seen as 1 in the tens' place and 0 in the ones' place, or as 1 times 101 plus 0 times 100. With a base of 2, only the symbols 0 and 1 are used. 10 in base 2 notation is therefore 1 times 21 plus 0 times 20. This is the same as 2, in the base 10 notation.
Today, mainly base 10 is in use. Computers use binary and people who study computers often use octal and hexadecimal numeral systems. Ancient Sumer used sexagesimal (base 60). Mesoamerica used base 20.