Data Types and Variables

Data Types and Variables
An Introduction with Examples in Java

Prof. David Bernstein
James Madison University

Computer Science Department

bernstdh@jmu.edu

Data and Values

Data:
- A datum (or piece of data) is a thing that is (known and) used for calculation or reasoning
Values:
- A value is the representation of a datum

Variables and Constants

Variable:
- A named space for holding a value
Constant:
- A named space for holding a value that does not change
Atomic Variables/Constants:
- A variable/constant that can hold one value (e.g., a number or character)
Identifiers:
- The name of a variable/constant

A Little Background on Digital Computers

Physical Storage Devices:
- Electronic/Magnetic Systems - usually differentiate between positive and negative, on and off, or clockwise and counterclockwise
- Mechanical Systems - usually differentiate between up and down, pits and lands, holes and solids, or bumps and flats
An Abstraction:
- Consider two possible values, 0 and 1

Data Representation - The Counting Numbers

Data Representation - Negative Integers

An Obvious Place to Start:
- Since there are two signs, use one bit (e.g., the left-most) to represent the sign
A Shortcoming of this Approach:
- It results in both a +0 and a -0

Going Further

: Negative Numbers

Ones Complement:
- Use the leftmost bit to indicate sign
- One byte can be used to represent [-127, 127]
- Results in both +0 and -0
Twos Complement:
- Eliminate the extra 0
- One byte can be used to represent [-128, 127]
- How do you "create" them?

Going Further

: Negative Numbers (cont.)

Going Further

: Negative Numbers (cont.)

http://imgs.xkcd.com/comics/cant_sleep.png

(Courtesy of xkcd)

Data Representation - Real Numbers

Think About Base 10:
- The positions to the left of the decimal point are powers of 10 and the positions to the right of the decimal place are powers of 1/10
An Obvious Place to Start in Binary:
- The positions to the left of the decimal point are powers of 2 and the positions to the right of the decimal place are powers of 1/2

Going Further

: Real Numbers (cont.)

Terms:
- Sign
- Exponent
- Mantissa
Normalization:
- One digit left of the decimal
Example: +1.101101 x 2³
- Sign: +
- Exponent: 3
- Mantissa: 1.101101

Going Further

: Real Numbers (cont.)

IEEE Short Real (Single Precision):
- 1 bit for the sign
- 8 bits for the exponent
- 23 bits for the mantissa
IEEE Long Real (Double Precision):
- 1 bit for the sign
- 11 bits for the exponent
- 52 bits for the mantissa

Data Representation - Characters

An Obvious Place to Start:
- Count the number of characters
- Determine the number of bits needed
- Assign a binary number to each character
An Example:
- There are 26 letters in the alphabet
- 5 bits can represent $2^5$ (i.e., 32) different things
- Assign 00001 to A, 00010 to B, 00011 to C, ...., 11010 to Z

Data Representation - Characters (cont.)

The ASCII (American Standard Code for Information Interchange) Encoding:
Unicode:
- A mapping for every character in every language (including many dead languages)

Some Atomic/Primitive/Fundamental Types in Java

Type	Memory	Range
`byte`	1 byte	-128 to 127
`short`	2 bytes	-32,768 to 32,767
`int`	4 bytes	-2,147,483,648 to 2,147,483,647
`long`	8 bytes	$-2^{63}$ to $2^{63}-1$
`float`	4 bytes
`double`	8 bytes
`char`	2-4 bytes	Unicode
`boolean`		true or false

Data Representation - Some Non-Atomic Types

Text:
- Think of text as consisting of one or more characters
Colors:
- Think of colors as having a red, green and blue component
Images:
- Create a finite grid (called a raster) with equal sized cells (called picture elements or pixels) each of which contains a color

Non-Atomic Types in Java

An Observation:
- The number of components of non-atomic types may be unknown, hence the amount of memory required may be unknown
The Approach in Java:
- Request the amount of memory needed and store the address of that memory
Java Conventions:
- Types of this kind are called reference types
- Types of this kind have names that start with an uppercase letter

Some Non-Atomic Types in Java

String :
- Essentially a collection of char values
Color :
- Essentially a collection of int values
BufferedImage :
- Essentially a collection of Color references

Variables in Java

Name/Identifier Restrictions:
- Must start with a letter
- Can contain letters, digits, and '_'
- Are case-sensitive
Course Style Guide Requirements:
- Must start with a lowercase letter
- Must be descriptive

Variables in Java (cont.)

Nerd Humor

(Courtesy of xkcd)

Variable Declarations

Purposes:
- Set aside enough memory to hold the datum
- Allow the memory that is set aside to be referred to by name elsewhere (with some limitations) in the program
Advantages of Typed Declarations:
- The amount of memory to set aside is known
- It is easy to determine if a variable is being used in a manner that is consistent with its type

Declaration Statements in Java

Syntax:
- type identifier [, identifier]... ;
Examples:
- boolean done;
- double expenses, income;
- int numberOfChecks, styleNumber;
- String name;
Course Style Guide Requirements:
- Each declaration must appear in its own statement (i.e., you can not have multiple identifiers separated by commas)

Declaration Statements in Java (cont.)

Atomic/Primitive/Fundamental Types:
- Enough memory is set aside to hold a value of that type (e.g. 8 bytes for a double)
Reference Types:
- Enough memory is set aside to hold an address (i.e., 4 bytes)

Expressions Revisited

Recall:
- An expression is a syntactically valid construct that can be evaluated (i.e., results in a value)
The Type of an Expression:
- An expression is said to be of the type of the value it evaluates to

There's Always More to Learn