For other uses see Data type (disambiguation).
In certain technical fields (especially computer programming and statistics), a data type is a classification identifying one of various types of data, such as real-valued, integer or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of that type can be stored.  Most data types in statistics have comparable types in computer programming, and vice-versa, as shown in the following table:
|real-valued (interval scale)||rowspan=2||floating-point|
|real-valued (ratio scale)|
|count data (but, usually non-negative)||integer|
|categorical data||enumerated type|
|random vector||list or array|
|random matrix||two-dimensional array|
The rest of this article addresses data types from a computer science perspective. For their use in statistics, see statistical data type.
Data types are used within type systems, which offer various ways of defining, implementing and using them. Different type systems ensure varying degrees of type safety. Formally, a type can be defined as "any property of a programme we can determine without executing the program".
Almost all programming languages explicitly include the notion of data type, though different languages may use different terminology. Common data types may include:
For example, in the Java programming language, the "int" type represents the set of 32-bit integers ranging in value from -2,147,483,648 to 2,147,483,647, as well as the operations that can be performed on integers, such as addition, subtraction, and multiplication. Colors, on the other hand, are represented by three bytes denoting the amounts each of red, green, and blue, and one string representing that color's name; allowable operations include addition and subtraction, but not multiplication.
Most programming languages also allow the programmer to define additional data types, usually by combining multiple elements of other types and defining the valid operations of the new data type. For example, a programmer might create a new data type named "complex number" that would include real and imaginary parts. A data type also represents a constraint placed upon the interpretation of data in a type system, describing representation, interpretation and structure of values or objects stored in computer memory. The type system uses data type information to check correctness of computer programs that access or manipulate the data.
All data in computers based on digital electronics is represented as bits (alternatives 0 and 1) on the lowest level. The smallest addressable unit of data is usually a group of bits called a byte (usually an octet, which is 8 bits). The unit processed by machine code instructions is called a word (as of 2011, typically 32 or 64 bits). Most instructions interpret the word as a binary number, such that a 32-bit word can represent unsigned integer values from 0 to
There is a specific set of arithmetic instructions that use a different interpretation of the bits in word as a floating-point number.
Machine data types need to be exposed or made available in systems or low-level programming languages, allowing fine-grained control over hardware. The C programming language, for instance, supplies integer types of various widths, such as
long. If a corresponding native type does not exist on the target platform, the compiler will break them down into code using types that do exist. For instance, if a 32-bit integer is requested on a 16 bit platform, the compiler will tacitly treat it as an array of two 16 bit integers.
In higher level programming, machine data types are often hidden or abstracted as an implementation detail that would render code less portable if exposed. For instance, a generic
numeric type might be supplied instead of integers of some specific bit-width.
The Boolean type represents the values: true and false. Although only two values are possible, they are rarely implemented as a single binary digit for efficiency reasons. Many programming languages do not have an explicit boolean type, instead interpreting (for instance) 0 as false and other values as true.
unsignedin C and C++). May also have a small number of predefined subtypes (such as
longin C/C++); or allow users to freely define subranges such as 1..12 (eg. Pascal/Ada).
Character and string types can store sequences of characters from a character set such as ASCII. Since most character sets include the digits, it is possible to have a numeric string, such as
"1234". However, many languages would still treat these as belonging to a different type to the numeric value
Character and string types can have different subtypes according to the required character "width". The original 7-bit wide ASCII was found to be limited, and superseded by 8 and 16-bit sets, which can encode a wide variety of non-latin alphabets (Hebrew, Chinese) and other symbols.Strings may be either stretch-to-fit or of fixed size, even in the same programming language. They may also be subtyped by their maximum size.
Note: strings are not primitive in all languages, for instance C: they may be composed from arrays of characters.
The enumerated type. This has values which are different from each other, and which can be compared and assigned, but which do not necessarily have any particular concrete representation in the computer's memory; compilers and interpreters can represent them arbitrarily. For example, the four suits in a deck of playing cards may be four enumerators named CLUB, DIAMOND, HEART, SPADE, belonging to an enumerated type named suit. If a variable V is declared having suit as its data type, one can assign any of those four values to it. Some implementations allow programmers to assign integer values to the enumeration values, or even treat them as type-equivalent to integers.
Types can be based on, or derived from, the basic types explained above.
The main non-composite, derived type is the pointer, a data type whose value refers directly to (or "points to") another value stored elsewhere in the computer memory using its address. It is a primitive kind of reference. (In everyday terms, a page number in a book could be considered a piece of data that refers to another one). Pointers are often stored in a format similar to an integer; however, attempting to dereference or "look up" a pointer whose value was never a valid memory address would cause a program to crash. To ameliorate this potential problem, pointers are considered a separate type to the type of data they point to, even if the underlying representation is the same.
Composite types are derived from more than one primitive type. This can be done in a number of ways. The ways they are combined are called data structures. Composing a primitive type into a compound type generally results in a new type, eg. array-of-integer is a different type to integer.
Many others are possible, but they tend to be further variations and compounds of the above.
Any type that does not specify an implementation is an Abstract data type. For instance, a stack (which is an abstract type) can be implemented as an array (a contiguous block of memory containing multiple values), or as a linked list (a set of non-contiguous memory blocks linked by pointers).
Abstract types can be handled by code that does not know or "care" what underlying types are containedin them. Programming that is agnostic about concrete data types is called generic programming. Arrays and records can also contain underlying types, but are considered concrete because they specify how their contents or elements are laid out in memory.
For convenience, high-level languages may supply ready-made "real world" data types, for instance times, dates and monetary values, even where the language allows them to be built from primitive types.
See main article: Type system. A type system associates types with each computed value. By examining the flow of these values, a type system attempts to prove that no type errors can occur. The type system in question determines what constitutes a type error, but a type system generally seeks to guarantee that operations expecting a certain kind of value are not used with values for which that operation does not make sense.
A compiler may use the static type of a value to optimize the storage it needs and the choice of algorithms for operations on the value. In many C compilers the data type, for example, is represented in 32 bits, in accord with the IEEE specification for single-precision floating point numbers. They will thus use floating-point-specific microprocessor operations on those values (floating-point addition, multiplication, etc.).
The depth of type constraints and the manner of their evaluation affect the typing of the language. A programming language may further associate an operation with varying concrete algorithms on each type in the case of type polymorphism. Type theory is the study of type systems, although the concrete type systems of programming languages originate from practical issues of computer architecture, compiler implementation, and language design.