Floating point numerical information

Previously discussed

• Recall that:

• A byte is a memory cell consisting of 8 switches and can store a binary number

(See:http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/01/binary.html)

Previously discussed (cont.)

• Although the computer stores binary numbers, we can interpret then as decimal number through a conversion operation:

Previously discussed (cont.)

• The computer can combine adjacent bytes in the RAM memory to form larger memory cells

Previously discussed (cont.)

• 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

Variables (in general) (cont.)

• 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 numbers

• A floating point number is a number where the number of decimal digits before and after the decimal point is not fixed (i.e., it "floats")

• Examples:

1234.5 1 decimal digits after the decimal point

0.087 3 decimal digits after the decimal point

3.1415 5 decimal digits after the decimal point

Floating point numbers (cont.)

• Floating point numbers can also be written in the exponent form:

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

Floating point variables (cont.)

• A double precision floating point variable can represent a floating point number:

• in range of from −10308 to 10308

• and with about 15 decimal digits accuracy

This kind of variable is commonly used in scientific computations.

A calculator uses double precision floating point variables.

(I used a double precision floating point variable to avoid using the casting operation - casting will be explained later)

Floating point variables (cont.)

• Important fact:

• A floating point variable behaves like a piece of paper where you can record (exactly) one floating point number

Floating point variables (cont.)

• BTW, that's how you perceive a double typed variable. Inside the computer, the number is represented with bits. It looks something like this:

The encoding method used is called the IEEE 754 Standard - See: http://en.wikipedia.org/wiki/Double_precision_floating-point_format

Defining floating point variables

• 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

Defining floating point variables (cont.)

• Syntax to define an floating point variable:

• Notes:

• double NameOfVariable ;

• 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 ";"

Defining floating point variables (cont.)

• 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“

}

}

Defining floating point variables (cont.)

• 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

• Notice that the statement "System.out.println(x);" does not uses quotes ".." around the variable x

• The statement "System.out.println("x");" (with quotes ".." around x) will print the text x

Effect of a variable definition clause

• When a Java program starts to run inside the computer, it will use up a portion of the RAM memory to store various things

A (large) portion of the RAM memory will remain unused

Effect of a variable definition clause (cont.)

• The effect of the definition:

is the following:

double x;

• The computer will find 8 consecutive bytes of RAM memory that is unused

• The computer will then reserve these memory bytes

Effect of a variable definition clause (cont.)

• It also associate the name x with the (8 bytes of) reserved memory

• Whenever the Java program uses the name x, the computer will translate that into read/write operations to these (8 bytes of) reserved memory

Effect of a variable definition clause (cont.)

• The computer can store (exactly) one floating point number in the reserved memory bytes.

That is why:

• A floating point variable behaves like a piece of paper where you write down (exactly) one floating point number

Effect of a variable definition clause (cont.)

• When the Java program is run, it starts with the main() method:

• Example

Effect of a variable definition clause (cont.)

A portion of the RAM memory is used.

But a large portion will be unused

Effect of a variable definition clause (cont.)

• When the variable definition "double x" is processed, it causes the computer to reserve consecutive 8 bytes of RAM memory:

Effect of a variable definition clause (cont.)

These 8 bytes of reserved memory can now be referred to by the name x !!!

(How this is done exactly will be explained in CS255)

Update the value stored in a variable

• Assignment statement:

• Syntax of an assignment statement:

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

VariableName = Value ;

Update the value stored in a variable (cont.)

• Notes:

• The symbol "=" is called the assignment operator in Java

• The variable on left-hand-side of the "=" operator is the receiving variable

• The expression 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 ";"

Update the value stored in a variable (cont.)

• Meaning of the assignment statement:

• The expression on the RHS of the "=" operator is first computed

• The computed value is then assigned to the receiving variable

Update the value stored in a variable (cont.)

• 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"

}

}

Update the value stored in a variable (cont.)

• 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...)

Update the value stored in a variable (cont.)

• Example:

When the variable definition "double x" is processed, it causes the computer to reserve consecutive 8 bytes of RAM memory:

Update the value stored in a variable (cont.)

• These 8 bytes of reserved memory can now be referred to by the name x !!!

Update the value stored in a variable (cont.)

• The assignment statement x=0.31415e1 will store the value 3.1415 into the memory cell identified by the name x:

Update the value stored in a variable (cont.)

• The Print statement System.out.println(x) will read the value stored at the memory cell identified by the name x and print it to the terminal:

Update the value stored in a variable (cont.)

• Example Program: (Demo above code)   – Prog file:

http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/04/Progs/Var02.java       

• How to run the program:

Right click on link and save in a scratch directory

• To compile:   javac Var02.java

• To run:          java Var02

Update the value stored in a variable (cont.)

Hello Class

The variable x contains this number:

3.1415

Output:

Defining and initializing a variable at the same time

• When a variable is defined, it does not contain a legitimate value

• You can give an initial value to a variable when you define the variable

• Syntax to define an initialized double precision floating point variable:

double varName = initialValue ;

Defining and initializing a variable at the same time (cont.)

• Example:

public class Var03 { public static void main(String[] args) { double x = 0.31415e1; // Define an initialized variable

System.out.println("Hello Class"); System.out.println(" The variable x contains this number:"); System.out.println(x); // Print variable "x" } }

Defining multiple variables of the same type

• You can define multiple variables of the same type with multiple clauses

Defining multiple variables of the same type (cont.)

• Example: defining 3 variables

public class Var04 { public static void main(String[] args) { double x = 0.31415e1; // <----- Focus here double y; double z = 2.71828;

y = 1.0;

System.out.println(x); // Print variable "x" System.out.println(y); // Print variable "y" System.out.println(z); // Print variable "z" } }

Defining multiple variables of the same type

• You can also define multiple variables of the same type with one clauses by separating the different variable names with a comma.

Example: defines that same 3 variables with 1 clause

Notice the comma (,) separating the variable names.

double x = 0.31415e1, y, z = 2.71828;

Defining multiple variables of the same type (cont.)

Example: defines that same 3 variables with 1 clause

public class Var04 { public static void main(String[] args) { double x = 0.31415e1, y, z = 2.71828; // <----- Focus here

y = 1.0;

System.out.println(x); // Print variable "x" System.out.println(y); // Print variable "y" System.out.println(z); // Print variable "z" } }

Notice the comma (,) separating the variable names.