---

Integral numerical information

---

• Previously discussed
  • Recall that:

    A byte is a memory cell consisting of 8 switches and can store a binary number (See: click here ) Although the computer stores binary numbers, we can interpret then as decimal number through a conversion operation: The computer can combine adjacent bytes in the RAM memory to form larger memory cells Although a computer memory can only store numbers, we can use an encoding scheme to represent any kind of information (E.g.: marital status information:   0 = single, 1 = married, and so on...           gender information:              0 = male, 1 = female) We must have context information to interpret a number that is stored in the RAM memory (E.g., we cannot interpret the number 0 stored in RAM memory unless we know kind of information it is.)

  ---

  ---

• Storing information inside a computer
  • A Java computer program uses variables to store information

  • There are different kinds (types) of variables

  • In this webnote, we will study the floating point variables

  ---

  ---

• Variables (in general)
  • Variable in Java

    A variable in a computer program is in fact a memory cell A memory cell can store a number A variable in a computer program stores a number Each variable in Java has a data type The data type allows the computer program to use the appropriate encoding (interpretation) scheme to interpret the number stored in the variable

    ---

  • Analogy of a variable

    A variable (in Computer Science) is like a piece of paper with a tag attached to it. The tag represents the data type of the variable (the value of the tag cannot be changed) You can only write one (binary) number on the piece of paper. You can erase the number and write a new number on the paper; but you can never write more than one number on the paper at any time.

  ---

  ---

• Floating point values
  • A floating point value (in decimal) can be expressed using one of the following form:

    x..x.x..x x..x.x..xex..x

    where x..x represent a sequence of (decimal) digits

    ---

  • Examples:

    3.1415 0.31415e1 (= 0.31415×101 = 3.1415) 31.415e-1 (= 31.415×10-1 = 3.1415)

  ---

  ---

• Floating point variables
  • A double precision floating point variable is a variable that:

    uses 8 consecutive bytes of memory as a single 64 bit memory cell uses a modified binary number system as encoding scheme For more details on the floating point encoding method, please take CS255 It can hold an floating number of about 16 (decimal) digits accuracy

    (I used a double precision floating point variable to avoid explaining casting)

    ---

  • Every variable in Java must be defined
    This rule applies to a floating point variable.

    Also, you must use the correct syntax construct to write a variable definition

    ---

  • Syntax to define an floating point variable:

    double NameOfVariable ;

    Notes:

    The keyword double announces the variable definition clause The NameOfVariable is an identifier which is the name of the variable. The variable definition clause is must be ended with a semi-colon ";"

    ---

    ---

  • Example:

    public class Var01 { public static void main(String[] args) { double x; // Define floating point variable with name "x" System.out.println("Hello Class"); System.out.println(" The variable x contains this number:"); System.out.println(x); // Print variable "x" } }

    Notes:

    The name of the Java program is Var01 Therefore, the UNIX filename that contain this Java program must be: Var01.java The statement "System.out.println(x);" will print the content of the variable x to the terminal

    ---

  • Example Program: (Demo above code)                                                
    • Prog file: click here

    If you compile the program, you will get an error:

    Var01.java:11: variable x might not have been initialized System.out.println(x); // Print the content in variable "x" ^

    This is because the variable x does not have a value yet.

  ---

  ---

• Update the value stored in a variable
  • Assignment statement:

    The assignment statement in the Java programming language instructs the computer to update the value stored in a variable

    ---

  • Syntax of an assignment statement:

    VariableName = Value ;

    Notes:

    The symbol = is used to tell the computer to assign some value to a variable The symbol = is called the assignment operator in Java The item on left-hand-side of the = operator is the receiving variable The item on right-hand-side of the = operator is the value that is assigned to the receiving variable The assignment statement must be ended with a semi-colon ";"

    ---

    ---

  • Example:

    public class Var02 { public static void main(String[] args) { double x; // Define floating point variable with name "x" x = 0.31415e1; // Assign 3.1415 to x System.out.println("Hello Class"); System.out.println(" The variable x contains this number:"); System.out.println(x); // Print variable "x" } }

    Notes:

    The name of the Java program is now Var02 Therefore, the UNIX filename that contain this Java program must be: Var02.java (I will not make this comment anymore from this point on...)

    ---

  • Example Program: (Demo above code)                                                
    • Prog file: click here

    How to run the program:

    Right click on link and save in a scratch directory To compile:   javac Var02.java To run:          java Var02

    Output:

    Hello Class The variable x contains this number: 3.1415

  ---

  ---

• Floating point operators
  • Floating point operators are arithmetic operators that manipulate (operate on) floating point values

    A floating point operator only operates on 2 floating point values The result of an integer operator is always a floating point value

    All of the floating point (arithmetic) operators should look familiar to you...

    ---

  • Floating point arithmetic operators:

    Operator symbol	Operation
    +	addition
    -	subtraction
    *	multiplication
    /	division

    ---

  • Example:

    Result of the integer operation 5.0 + 3.0 is 8.0 Result of the integer operation 5.0 - 3.0 is 2.0 Result of the integer operation 5.0 * 3.0 is 15.0 Result of the integer operation 5.0 / 3.0 is 1.666666666666...

  ---

  ---

• Floating point expressions
  • An Floating point expression is a (legal) combination of

    Floating point values Floating point variables and Floating point operators

  ---

  ---

• Section

  ---

  ---

• Section

  ---

  • Locations in a Java program where you can define variables:

    Variables can be defined inside a method Variables can be defined outside any method

    Schematically:

    ---

  • Warning:

    Where you define a variable will affect where you can access the information stored in that variable !!!

  ---

  ---

• Data types built into a computer
  • Types of data:

    Each type of data is given a unique type name Different types of data are represented in different ways inside a computer

    ---

  • Built-in data types

    Every computer has 2 built-in types: Integer number type Floating point number type In other words: A computer contain built-in circuitry that can manipulate representations of integer numbers and of floating point numbers

    ---

  • Examples:

    The integer number 1 is represented inside the computer by the byte (= 8 bits) 00000001 The integer number 2 is represented inside the computer by the byte (= 8 bits) 00000010 The computer also knows how to add, subtract, multiply and divide binary numbers.

  • We don't need to learn about how the computer does it in this course. It will be explained in other courses.

  ---

  ---

• Integers and floating point numbers of different lengths
  • Recall that:

    The smallest memory element in a computer RAM memory is a byte (= 8 bits) The computer can combine adjacent bytes (memory cells) and use it as a larger memory cell

    ---

  • Practically speaking, the integer value 1 can be represented inside the computer using:

  • There is a trade-off between

  ---

  ---

• Data types in a programming language
  • Although the computer can only work with 2 data types (integers and floating numbers), a programming language can uses these two data types to represent any number of data types

    All it takes is a bit of imagination

    ---

  • The way a programming language represents a new data type is as follows:

    Define a new context Define an encoding for the new context

    (Context: remember the example of "you is a word" and "you are a student" ?)

    ---

  • The context information is called type information in Computer Science

    ---

    ---

  • Very important facts:

    Every value stored used inside a program is a (binary) number Every value stored used inside a program has a type The type information provides the context to interpret the given value

    Example:

    We will write the type next to the value in the examples 0 (integer) represents 0 (numeric) 1 (integer) represents 1 (numeric) 0 (logical) represents false 1 (logical) represents true

  ---

  ---

• The Java programming language
  • In this course, we will be studying the programming language named Java

  • It is important to understand

  ---

  ---

• Common data types that are pre-defined in a programming language
  • Every modern programming language provides the following pre-defined data types

  • The names of the built-in data types as usually:

    int:           Integer type float:       Floating point number type char:         Alpha-numeric (characters) type boolean:   Logic value type

  ---

  ---

• The int data type
  • Recall that a computer can process 2 types of data representations:

    integer numbers floating point numbers

  • The int data type in a programming language uses the same representation as the integers in

  ---

  ---

• The int data type
  • Example: how a programming language represent logic information

    Logic value	Value used to encode the logic value
    true	1 (integer)
    false	0 (integer)

    In other words:

    The computer has the built-in integer type The programming language uses the integer value 1 to represent the