Radix point

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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" is a general term that 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 other regions, a comma (,) is usually used instead (see decimal mark for further information).

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{align}
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{align}

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[edit]