Radix point

In mathematics and computing, a radix point or radix character is a symbol used in the display of numbers to separate the integer part of the value from its fractional part. In English and many other languages (including many that are written right-to-left), the integer part is at the left of the radix point, and the fraction part at the right of it.^[1]

A radix point is most often used in decimal (base 10) notation, when it is more commonly called the decimal point (the prefix deci- implying base 10). In English-speaking countries, the decimal point is usually a small dot (.) placed either on the baseline or halfway between the baseline and the top of the digits^[2] In many other countries, the radix point is a comma (,) placed on the baseline.^[2] These conventions are generally used both in machine displays (printing, computer monitors) and in handwriting. It is important to know which notation is being used when working in different software programs. The respective ISO standard defines both the comma and the small dot as decimal markers, but does not explicitly define universal radix marks for bases other than 10.

Fractional numbers are rarely displayed in other number bases, but, when they are, a radix character may be used for the same purpose. When used with the binary (base 2) representation, it may be called "binary point".

Examples[edit]

In base 10 (decimal): 13.625

In this example, 13 is the integer to the left of the radix point, and 625 (i.e. 625/1000) is the fractional part to the right.

In base 2 (binary): 1101.101

The binary number 1101.101 has the following digits:

Power of 2	3	2	1	0		−1	−2	−3
Binary digit	1	1	0	1	.	1	0	1

Hence, its decimal value can be calculated as:

{\begin{aligned}1101.101_{2}&=1\times 2^{3}+1\times 2^{2}+0\times 2^{1}+1\times 2^{0}+1\times 2^{-1}+0\times 2^{-2}+1\times 2^{-3}\\&=1\times 8+1\times 4+0\times 2+1\times 1+1\times 0.5+0\times 0.25+1\times 0.125\\&=8+4+0+1+0.5+0+0.125\\&=13.625_{10}\end{aligned}}

It is now seen that 1101, which is to the left of the radix point, is the binary representation of the decimal number 13. To the right of the radix point is 101, which is the binary representation of the decimal fraction 625/1000 (or 5/8).

References[edit]

^ Van Verth, James M.; Bishop, Lars M. (2008), Essential Mathematics for Games and Interactive Applications: A Programmer's Guide (2nd ed.), CRC Press, p. 7, ISBN 9780123742971.
^ ^a ^b "International Language Environments Guide". Oracle Corporation Docs. Archived from the original (html) on 15 January 2012. Retrieved 19 December 2018. Great Britain and the United States are two of the few places in the world that use a period to indicate the decimal place. Many other countries use a comma instead. The decimal separator is also called the radix character. Likewise, while the U.K. and U.S. use a comma to separate groups of thousands, many other countries use a period instead [...]

[1] Van Verth, James M.; Bishop, Lars M. (2008), Essential Mathematics for Games and Interactive Applications: A Programmer's Guide (2nd ed.), CRC Press, p. 7, ISBN 9780123742971.

[oracle-2] "International Language Environments Guide". Oracle Corporation Docs. Archived from the original (html) on 15 January 2012. Retrieved 19 December 2018. Great Britain and the United States are two of the few places in the world that use a period to indicate the decimal place. Many other countries use a comma instead. The decimal separator is also called the radix character. Likewise, while the U.K. and U.S. use a comma to separate groups of thousands, many other countries use a period instead [...]

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Radix point

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