Radix point

In mathematics and computing, a radix point (or radix character) is the symbol used in numerical representations to separate the integer part of a number (to the left of the radix point) from its fractional part (to the right of the radix point). "Radix point" applies to all number bases. In base 10 notation, the radix point is more commonly called the decimal point, where the prefix deci- implies base 10. Similarly, the term "binary point" is used for base 2.

In English-speaking countries, the radix point is usually a small dot (.) placed either on the baseline or halfway between the baseline and the top of the numerals. In many other countries, the radix point is a comma (,) placed on the baseline. 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.

Examples

• 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).

See also

• Floating point
• Fixed point
• Positional notation