Radix point
Encyclopedia
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 base
s. 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 separator
for further information).
Hence, its decimal value can be calculated as:
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).
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and computing
Computing
Computing is usually defined as the activity of using and improving computer hardware and software. It is the computer-specific part of information technology...
, a radix
Radix
In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...
point (or radix character) is the symbol used in numerical representations to separate the integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
part of a number (to the left of the radix point) from its fractional
Fraction (mathematics)
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists...
part (to the right of the radix point). "Radix point" is a general term that applies to all number base
Radix
In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...
s. In base 10
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
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
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 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
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
. In other regions, a comma is usually used instead (see decimal separator
Decimal separator
Different symbols have been and are used for the decimal mark. The choice of symbol for the decimal mark affects the choice of symbol for the thousands separator used in digit grouping. Consequently the latter is treated in this article as well....
for further information).
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:
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).