Numeral system

:Occasionally the term "number system" is used for this concept, but that is also the name of an altogether different concept; see number system.

Bases used

The base-10 system is the one most commonly used today. It is assumed to have originated because humans have ten fingers.

Related Topics:
Human - Finger

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A base-eight system was devised by the Yuki of Northern California, who used the spaces between the fingers to count. There is also linguistic evidence that the Bronze Age Proto-Indo Europeans (from whom most European and Indic languages descend) replaced a base 8 system (or a system which could only count up to 8) with a base 10 system. The evidence is that the word for 9, newan, appears to derive from the word for 'new', newo, suggesting that the number 9 had been recently invented and called the 'new number'. (In French, the word neuf still means both 9 and 'new').

Related Topics:
Yuki - Proto-Indo European

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The Maya civilization and other civilizations of Pre-Columbian Mesoamerica used base 20 (possibly originating from the number of a person's fingers and toes). Base 60 was used by the Sumerians and their successors in Mesopotamia and survives today in our system of time (hence the division of an hour into 60 minutes and a minute into 60 seconds) and in our system of angular measure (a degree is divided into 60 minutes and a minute is divided into 60 seconds). 60 is a useful base because it has large number of factors, including all of the first six counting numbers. Base-12 systems were popular because multiplication is easier in them than in base-10 (addition is just as easy), and because the year has twelve months; we still have a special word for "dozen" and use 12 hours for every night and day.

Related Topics:
Maya civilization - Pre-Columbian - Mesoamerica - Sumerians - Mesopotamia - Factors - Counting numbers

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Switches (and their electronic successors, built of vacuum tubes, or later of transistors) have only two possible states: "open" and "closed". Substituting open=1 and closed=0 (or the other way around) yields the entire set of binary digits. (In modern transistors, it is more accurate to say that the voltages are high and low instead of 'on' and 'off'). This binary system is the basis for digital computers. It is used to perform integer arithmetic in almost all digital computers, the only exception being the exotic base-3 and base-10 designs that were discarded very early in the history of computing hardware. Note however that a computer does not treat all of its data as integers — some of it may be treated as text and program data. Real numbers (which include numbers other than integers) are usually stored and treated as floating point numbers, which have different rules of arithmetic.

Related Topics:
Vacuum tube - Transistor - Binary system - Computers - History of computing hardware - Real number - Integer - Floating point - Arithmetic

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The bases that were used in past or used today are 2, 3, 4, 5, 6, 7, 8, 10, 12, 16, 20, 60.

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