4.2: Data Types (and Classes)

All data in the computer is stored as 0’s and 1’s - binary digits. This is most convenient as binary operations are very efficiently effected in terms of the necessary nonlinear circuit elements. The basic unit of memory is the "word-length" of the machine - the number of binary digits, or "bits," which are used to represent data. Most machines these days are based on 32-bit or 64-bit words (which are 4 Bytes and 8 Bytes, respectively); in some cases particular data types might be represented by two words (or more).

But obviously we will need to interpret these 0’s and 1’s in different ways: in some cases the 0’s and 1’s might represent machines codes (instructions) which tell the arithmetic unit what to execute; in other cases, the 0’s and 1’s might represent data on which the the instructions will operate (the "operands"). Furthermore, there are many different type of data: any piece of data is defined not just by the 0’s and 1’s that make up the word, but also by the "data type" which tells the computer how to interpret and operate upon the data. As regards the latter, we note that the same set of 0 ’s and 1’s can mean something very different - and be operated on in very different ways - depending on the data type associated with these 0’s and 1’s. There are several important types within MATLAB (and homologous types within other programming languages). There are logical variables which are either 0 or 1 which correspond respectively to (and in fact the data may be entered as) false or true . There is integer data - a signed whole number. There is character data, in which the 0 ’s and 1’s encode particular characters such as letters in the alphabet or numerals - the famous ASCII code and recent extensions. And particularly important for us, there are floating point numbers, which in MATLAB are 64 bits and are called (for largely historical reasons) simply double. Representation of floating point numbers (FPNs) by a 64 bits is probably less obvious than representation of a whole number, and hence we will discuss representation of FPNs, and also floating point operations, in a separate section. MATLAB also supports a complex floating point type. These types are "atomic" in that they are part of the core MATLAB scripting language.

In some programming languages the user is required upon creation of a variable to specify the data type. (We define variables in the next section - for now, think of a variable as the name of a particular piece of data.) Each variable must be an instance of one of the available (in our case, MATLAB ) data types. MATLAB is much less picky than other programming languages - a blessing and a curse - and typically if no type is specified MATLAB will simply assume a (double) floating point number, which is hence the "default."

It is, however, possible to specify that any particular variable is logical, with the logical function, an integer, with the (say) int32 command, a character, with the char command (or more simply with quotes), and a floating point number, with the double command. We can also determine what type of data a particular variable is with the islogical, isinteger, ischar, and isfloat functions.

We already above and will frequently below refer to functions. We do not fully define functions until a later chapter, in which we learn how to create our own functions. For now, think of a function as a program which takes some (zero, one, two, or many) input arguments and yields some output; we provide illustrations in the next section. All of the functions we describe in the preceding paragraph are "built-in" functions that are part of the core MATLAB scripting language; we shall exercise these functions in the next section once we are armed with the assignment operation. (In fact, false (and true) are also built-in MATLAB functions: false takes no arguments and returns a logical zero.) Note the MATLAB "core" is quite large compared to other languages such as Python, in which most functions must be explicitly brought in as modules. There are, however, official MATLAB extensions to the core, known as "toolkits." In actual practice, functions can yield many outputs, not just a single output; we discuss this extension in a later chapter.

We note that often we might perform operations on data of different types. In that case we might effect "conversion" before proceeding with the operation, or we might let the programming language automatically perform "coercion" - conversion to a common data type based on rules of precedence. For example, in MATLAB , if we attempt to add an integer and a floating point number, MATLAB will (effectively) first convert the integer variable to a floating point variable. (Note that even when we invoke the various round, fix, floor, and ceil MATLAB functions to round a floating point number (the input) to an integer ( the output), the output is of data type double.) In most cases MATLAB makes reasonable choices, though on occasion more direct control is warranted.

Finally we note that there is another term used to describe the proper specification and interpretation of given data: "class." Typically data type is part of the language whereas data classes are created by the user. And typically data type would refer to a word or maybe two words whereas class would refer to a compound type of many words (each of which might be specified as a different data type). Class also has a special significance in object-oriented programming: a class defines not just a compound data type (an instance of which is known as an "object"), but also functions or "methods" on members of this class. MATLAB supports object-oriented programming both ex- plicitly and implicitly, however we will only briefly touch on object-oriented programming in this course, and primarily for purposes of interpretation of various operators.

This section is rather abstract simply because we do not yet know how to create data and hence we can not demonstrate any of the concepts. As already indicated, we shall illustrate the notion of data types, the matlab functions used to define variables of a particular data type, and the functions used to query variables as to their data type, once we learn how to create variables - in the next section.