CSE 135:

Numerical Data
Week 3

By
Javed Siddique
Objectives

After this week you should be understand

 Numeric data types
 Arithmetic operators and expressions
 Standard classes
 Math
 GregorianCalendar
 DecimalFormat
 Input and output classes
Primitive Data Types
 Although the primary type of data in OOP is
objects, there is another important data type.
 These are called primitive types.
 In contrast, objects are reference data types.
 There is no class for primitive data.
 Data in an object must be either another object,
or primitive data.
 There are three main primitive types:
 Numeric This week.
 Character
 Logic
Declaration
 As with objects, primitive data values are
accessed using identifiers.
 The declaration specifies the type of the identifier
 The type of an object is given by its class
 Primitive data have one of the following types:
 Numeric: by te, s hort, int, long , flo at,
doubl e
 Character: ch ar
 Logic: bo olean
 Unlike objects, primitive data items are created
upon declaration
 No need to call new in order to allocate the space.
Variables
 Data items are also called variables.
 A variable has three properties:
 A memory location to store the value,
 The type of data stored in the memory location, and
 The name used to refer to the memory location.
 Sample declaration:
in t x;
 When the declaration is made, memory space is
allocated to store integer values; x is a reference
for this space.
 It is a “variable” since its value can be changed
during program execution. Similarly, object
identifiers are also variables.
Assignment Statements
 We assign a value to a variable using an
assignment statement.
 The syntax is
<variable> = <expression> ;
 We will discuss expressions later. For now, they
can be numeric values or numeric variables.
 Examples:
in t i,j ;
i = 5;
j = i;
 This assignment is different than the assignment
to object identifiers.
Primitive Data Declaration and Assignments

int fir stNumb er, s econdN umbe r;

fir stNu mber = 234 ;
sec ondN umber = 87; A. Variables are
allocated in memory.

A firstNumber 234

int firs tNumbe r, se condN umbe r;

secondNumber 87
fir stNu mber = 234 ;
sec ondN umber = 87; B
B. Values are assigned
to variables.

Code State of Memory

Assigning Numerical Data

int num ber;

num ber = 237 ;
num ber = 35; number 35
237

A. The variable
is allocated in
int numb er; A memory.
num ber = 237; B B. The value 237
is assigned to
num ber = 35; C number.
number

C. The value 35
overwrites the
previous value 237.

Code State of Memory

Assigning Objects

Customer customer; customer

customer = new Customer( );
customer = new Customer( );

: Customer : Customer
A
B A. The variable is
Customer customer; allocated in memory.
customer
customer =
= new
new Customer(
Customer( );
);
B. The reference to the
customer = new Customer( ); new object is assigned
to customer.
customer

C C. The reference to
another object overwrites
the reference in customer.

Code State of Memory

Two References to a Single Object

Customer clemens, twain; clemens

clemens = new Customer( );
twain = clemens; twain

A : Customer

twain;
Customer clemens, twain,
B A. Variables are
allocated in memory.
clemens
clemens =
= new
new Customer(
Customer( );
);
B. The reference to the
twain = clemens; new object is assigned
to clemens.
clemens

C C. The reference in
clemens is assigned to
twain.

Code State of Memory

Assigning a primitive to a primitive

int first, second; first 5

first = 5;
second = first; second 5

A
B A. Variables are
int first, second;
allocated in memory.
first = 5;
second = first;
B. 5 is stored in first.

C
A. Value in first is
copied to second.

Code State of Memory

Actually, this is the same!

Customer clemens, twain; clemens

clemens = new Customer( );
twain = clemens; twain
C. The value in : Customer
clemens is copied to
twain.

Customer clemens, twain,

This value happens to be a
clemens = new Customer( ); reference to an object.
twain = clemens;
Hence: reference data type
C vs. primitive data types.

Code State of Memory

Numerical Data Types
 There are six numerical data types: byte ,
shor t, in t, lo ng, f loat , and double .
 Sample variable declarations:
int i, j, k;
float numberOne, numberTwo;
long bigInteger;
double bigNumber;
 At the time a variable is declared, it also can be
initialized. For example,
int count = 10, height = 34;
 Otherwise, it MAY be given a default value.
 Try it out!
Numeric Data Types
The six data types differ in the precision of
values they can store in memory.
Type Content Default Size Minimum Value Maximum Value
Value

byte 1 byte -128 127

short 2 bytes -32768 32767

Integer 0
int 4 bytes -2147483648 2147483647

long 8 bytes -9223372036854775808 9223372036854775807

float 4 bytes -3.40282347E+38 3.40282347E+38

Real 0.0
doubl 8 bytes -1.79769313486231570E+308 1.79769313486231570E+308

e
Arithmetic Operators
 The following table summarizes the
arithmetic operators available in Java.
Operation Java Example Value
Operator (x=10, y=7, z=2.5)

Addition x+y 17
+
Subtraction x-y 3
-
Multiplication x*y 70
*
Division x/y 1
/ 4.0
x/z
Modulo x%y 3
division
%
(remainder)

This is integer division

where the fractional part
is truncated.
Arithmetic expressions
 An arithmetic expression is composed of numeric
values, numeric variables, and operators.
 For example, given: in t i,j ;
i + 3
(i + 2*( j-i ))
-i + j
 Expressions can be used to assign values:
i = j + 3;
Take the value of j, add 3 to it and assign that value
to i.
Arithmetic Expression
 How is the following expression evaluated?
x + 3 * y
Answer: x is added to 3*y .
 We determine the order of evaluation by
following precedence rules.
 Evaluation is in order of precedence.
 Operators at same level are evaluated left
to right for most operators.
Precedence Rules

Order Group Operator Rule

High Subexpression () Starting with innermost ()

Unary -, + Left to right.
operators
Multiplicative *, /, % Left to right.
operators
Additive +, - Left to right.
operators
Low
Precedence Examples
4 5 6
x + 4*y - x/z + 2/x = ?
1 2 3
x + (4*y) - (x/z) + (2/x)

6 4 7 5
(x + y * (4 - x) / z + 2 / -x ) =?
3 1 2

(x + ((y * (4-x)) / z) + (2 / (-x)))

To be safe, use parentheses!

Expression Types
 What is the data type of
i + j;
 Depends upon the types of i and j.
 If they are both
 in t then the result is also an int
 do uble then the result is also a do uble
 lo ng … long
 Etc.
 Similarly for the other operators: -,*, …
Type Casting
 If x is a float and y is an int, what is the data type
of
x * y ?
The answer is float.
 The above expression is called a mixed
expression.
 Operands in mixed expressions are converted to
a common type based on promotion rules.
 All are converted to the type with the highest
precision in the expression.
 The entire expression is of this type too.
Implicit Type Casting
 Consider the following expression:
double x = 3 + 5;
 The result of 3 + 5 is of type int. However,
since the variable x is double, the value 8
(type int) is promoted to 8.0 (type double)
before being assigned to x.
 byte short int long float double
 Notice that it is a promotion. Demotion is not
allowed.
A higher precision value
int x = 3.5; cannot be assigned to a
lower precision variable.
Explicit Type Casting
 Instead of relying on the promotion rules,
we can make an explicit type cast:
( <data type> ) <expression>
 Example
Type cast x to float and
(float) x / 3 then divide it by 3.

Type cast the result of

(int) (x / y * 3.0) the expression x / y * 3.0
to int.

 NOTE: Only the type of the return values is

changed -- not the data itself.
Explicit demotion
 Promotion is automatically done whenever
necessary.
 Demotion is not automatic, but can be
forced:
int x;
double y;
y = 3.5;
x = (int)y;
 Assigning double ( or float) to integer types
results in truncation (not rounding).
Constants

 We can change the value of a variable. If

we want the value to remain the same,
we use a constant.
final double PI = 3.14159;
final int MONTH_IN_YEAR = 12;
final short FARADAY_CONSTANT = 23060;
final float CARBON_MASS = 12.034F;

The reserved word These are constants,

These are called
final is used to also called named
literal constant.
declare constants. constant.
Why use Constants?
 Consistent value
 No errors due to mistyping.
 Easy to manage
 If we need to change the precision of PI, then
we change it only once in the program.
 Programs are more readable.
Operators
 Some assignments and operators are
combined into one operator to ease
programming.
Operator Usage Meaning

+= a+=b; a=a+b;
-= a-=b; a=a-b;
*= a*=b; a=a*b;
/= a/=b; a=a/b;
%= a%=b; a=a%b;
Type Mismatch

 Suppose we want to input an age. Will this

work?

int age;

age = JOptionPane.showInputDialog(null, “Enter your age”);

• No.
A string value cannot be assigned directly to
an int variable.
Type Conversion

 Wrapper classes are used to perform

necessary type conversions, such as
converting a String object to a numerical
value.
int age;
String inputStr;

inputStr = JOptionPane.showInputDialog(
null, “Enter your age”);

age = Integer.parseInt(inputStr);
Other Conversion Methods

Class Method Example

Integer parseInt Integer.parseInt(“25”) 25

Integer.parseInt(“25.3”) error

Long parseLong Long.parseLong(“25”) 25L

Long.parseLong(“25.3”) error
Float parseFloat Float.parseFloat(“25.3”) 25.3F
Float.parseFloat(“ab3”) error

Double parseDouble Double.parseDouble(“25”) 25.0

Integer.parseInt(“ab3”) error
CAUTION: Imprecision
 It is not possible to exactly represent every
possible float (double) point number
 Fixed number of bits
 Float: 4 bytes -- 32 bits:232 (~1 billion) values
 double: 8 bytes -- 64 bits: 264 (~1 million trillion) values
 Infinite numbers (e.g. between 1.0 and 2.0)!
 Floats and doubles may only store an
approximation of the actual number!!!!
 Do not rely on exact values!
 Integers are stored precisely though!
Sample Code Fragment

//code fragment to input radius and output

//area and circumference
double radius, area, circumference;

radiusStr = JOptionPane.showInputDialog(
null, "Enter radius: " );

radius = Double.parseDouble(radiusStr);

//compute area and circumference

area = PI * radius * radius;
circumference = 2.0 * PI * radius;

JOptionPane.showMessageDialog(null,
"Given Radius: " + radius + "\n" +
"Area: " + area + "\n" +
"Circumference: " + circumference);
Overloaded Operator +
 The plus operator + can mean two different
operations, depending on the context.
 <val1> + <val2> is an addition if both are
numbers. If either one of them is a String, then it
is a concatenation.
 Evaluation goes from left to right.
output = “test” + 1 + 2; output = 1 + 2 + “test”;
The DecimalFormat Class
 Use a DecimalFormat object to format the
numerical output.
double num = 123.45789345;

DecimalFormat df = new DecimalFormat(“0.000”);

//three decimal places

System.out.print(num); 123.45789345

System.out.print(df.format(num));
123.458
Standard Output

 The showMessageDialog method is

intended for displaying short one-line
messages, not for a general-purpose
output mechanism.

 Using System.out, we can output multiple

lines of text to the standard output window.
Standard Output Window
 A sample standard output window for
displaying multiple lines of text.

• The exact style of standard output window

depends on the Java tool you use.
The print Method
 We use the print method to output a value to the
standard output window.
 The print method will continue printing from the
end of the currently displayed output.
 Example
System.out.print( “Hello, Dr. Caffeine.” );
The println Method
 We use println instead of print to skip a line.
int x = 123, y = x + x;
System.out.println( "Hello, Dr. Caffeine.“ );
System.out.print( " x = “ );
System.out.println( x );
System.out.print( " x + x = “ );
System.out.println( y );
System.out.println( " THE END“ );
Standard Input
 The technique of using System.in to input
data is called standard input.
 We can only input a single byte using
System.in directly.
 To input primitive data values, we use the
Scanner class (from Java 5.0).
Scanner scanner;

scanner = Scanner.create(System.in);

int num = scanner.nextInt();

Common Scanner Methods:

Method Example

nextByte( ) byte b = scanner.nextByte( );

nextDouble( )double d = scanner.nextDouble( );
nextFloat( ) float f = scanner.nextFloat( );
nextInt( ) int i = scanner.nextInt( );
nextLong( ) long l = scanner.nextLong( );
nextShort( ) short s = scanner.nextShort( );
next() String str = scanner.next();
The Math class
 The Math class in the java.lang package
contains class methods for commonly used
mathematical functions.
double num, x, y;

x = …;
y = …;

num = Math.sqrt(Math.max(x, y) + 12.4);

• Table 3.8 in the textbook contains a list of class

methods defined in the Math class.
Some Math Class Methods
Method Input Output Description
type type

exp(a) Return e raised to power a.

double double
log(a) Return natural log of a.
double double
floor(a) Return largest whole number
double double smaller than a.
max(a,b) Return larger of a or b.
int int
double double
… …
pow(a,b) Return a raised to power b.
double double
sqrt(a) Return square root of a.
double double
sin(a) Return sine of a(in radians).
double double
Table 3.8 page 113 in the textbook contains a list of
class methods defined in the Math class.
Computing the Height of a Pole

alphaRad = Math.toRadians(alpha);
betaRad = Math.toRadians(beta);

height = ( distance * Math.sin(alphaRad) * Math.sin(betaRad) )

/
Math.sqrt( Math.sin(alphaRad + betaRad) *
Math.sin(alphaRad - betaRad) );
The GregorianCalendar Class
 Use a GregorianCalendar object to manipulate
calendar information

GregorianCalendar today, independenceDay;

today = new GregorianCalendar();

independenceDay
= new GregorianCalendar(1776, 6, 4);
//month 6 means July; 0 means January
Retrieving Calendar Information
 This table shows the class constants for
retrieving different pieces of calendar information
from Date.
Constant Description
YEAR The year portion of the calendar date
MONTH The month portion of the calendar date
DATE The day of the month
DAY_OF_MONTH Same as DATE
DAY_OF_YEAR The day number within the year
DAY_OF_MONTH The day number within the month
DAY_OF_WEEK The day number within the week (Sun --1, Mon -- 2, etc.)
WEEK_OF_YEAR The week number within the year
WEEK_OF_MONTH The week number within the month
AM_PM The indicator for AM or PM (AM -- 0, PM -- 1)
HOUR The hour in the 12-hour notation
HOUR_OF_DAY The hour in 24-hour notation
MINUTE The minute within the hour
Sample Calendar Retrieval

GregorianCalendar cal = new GregorianCalendar();

//Assume today is Nov 9, 2003

System.out.print(“Today is ” +
(cal.get(Calendar.MONTH)+1) + “/” +
cal.get(Calendar.DATE) + “/” +
cal.get(Calendar.YEAR));

Output Today is 11/9/2003