chapter 4 numeric types

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Chapter 4

Numeric Types

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Knowledge Goals

• Discover why different numeric types have different ranges of values

• Understand the differences between integral and floating-point types

• See how precedence rules affect the order of evaluation in an expression

• Understand implicit type conversion and explicit type casting

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Knowledge Goals

• Be able to use additional operations associated with the String class

• Understand how value-return methods work with numeric types

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Skill Goals

• Declare named constants and variables of types int and double

• Construct simple arithmetic expressions• Evaluate simple arithmetic expressions• Construct and evaluate expressions that

include multiple arithmetic operations• Read numeric values using the methods

in class Scanner

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Skill Goals

• Use java math methods in expressions• Format the statements in a class in a

clear and readable fashion

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Numeric Data Types

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Numeric Data Types

Integral Types can represent whole numbers and their negatives

when declared as byte, short, int, or long can represent single characters when declared as

char

Floating-Point Types represent real numbers with a decimal point declared as float or double

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Numeric Data Types

byte 8 bits

short 16 bits

int 32 bits

long 64 bits

Sizes of Integral Types

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Numeric Data Types

Type Size in Bits Minimum Value to Maximum Value

byte 8 -128 127

short 16 -32,768 32,767

int 32 -2,147,483,648 2,147,483,647

long 64 -9,223,372,036,854,775,808 to

+9,223,372,036,854,775,807

Range of Integral Types

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Numeric Data Types

How many different numbers can be represented in one byte using 0’s and 1’s?

Each bit can hold either a 0 or a 1. So there are just two choices for each bit, and there are 8 bits.

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 28 = 256

0 1 1 0 0 0 1 1

1 byte = 8 bits

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Numeric Data Types

216 = 65536

If we have only one number representing the integer zero, and half of the remaining numbers positive, and half negative, we can obtain the 65,536 numbers in the range

-32768 . . . . 0 . . . . 32767

0 1 0 0 1 0 1 00 1 1 0 0 0 1 1

How many numbers can be represented in 2 bytes?

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Numeric Data Types

2.7E4 means 2.7 x 10 4 =

2.7000 =

27000.0

2.7E-4 means 2.7 x 10 - 4 =

0002.7 =

0.00027

Scientific Notation

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Numeric Data Types

Floating-point Types

Numbers with an integer part and a fractional part, with a decimal point in between; either the integer part or the fractional part may be missing but not both

18.4 500. .8 -127.358

Scientific notation is also ok

1.84E1 5E2 8E-1 -.127358E3

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Type Size in Bits Range of Values

float 32 +1.4E - 45 to

+3.4028235E+38

double 64 +4.9E - 324 to

+1.7976931348623157E+308

Numeric Data Types

Floating-point size and range

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Numeric Data Types

Literal numeric values in JavaLiteral Type0 int0L long2007 int18005551212L long18005551212 invalid (too long)0.0 double0.0f float2.001E3 double2.001E3F float1.8E225F invalid (exponent too large)

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Numeric Declarations

Named constant declaration

final double PI = 3.14159;

final String HOME = “Texas”;

final int TEXAS_TEMP = 95;

Variable declaration

double taxIncreae;

char initial;

int dailyTemp;

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Arithmetic Expressions

Arithmetic expression A valid arrangement of variables, constants, operators and parentheses

An expression can be evaluated to compute a value of a given type

The value of the expression

9.3 * 4.5 is 41.85

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Arithmetic Expressions

Arithmetic Operators

+ Unary plus

- Unary minus

+ Addition

- Subtraction

* Multiplication

/ Division

% Modulus

Divisionand

Modulusneed moreexplanation

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Arithmetic Expressions

Division (/)The result of the division operator depends on the type of its operands

If one or both operands has a floating type, the result is a floating-point type (float or double); otherwise, the result is an integral type

11 / 4 has value 2

11.0 / 4.0 has value 2.75

11 / 4.0 has value 2.75

11 / 0 invalid (cannot divide by 0)

11.0 / 0 has value infinity

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Arithmetic ExpressionsModulus (%)When used with integer type operands, the % operator returns the remainder from integer division; with floating-point operands, it returns the remainder after dividing the dividend by the divisor a whole number of times

11 % 4 has value 3

9 % 3 has value 0

3 % 5 has value 3

5 % 0 invalid (cannot divide by 0)

6.0%4.2 has value 0.12

6.0%0.0 has value not a number (NaN)

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Arithmetic Expressions

Remember the Scanner class?

Scanner in = new Scanner(System.in);

String line = in.nextLine();

int nextInt() Returns next token as an int

long nextLong() Returns next token as a long

float nextFloat() Returns next token as a float

String next() Returns next token as a string

Inputs next line

What happens if the next token is not a number?

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Arithmetic Expressions

Exception

An unusual condition in execution of Java code

control is transferred to statements designed to handle the condition

exception is thrown when the condition is detected

exception is caught by the handling code

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Arithmetic Exceptions

Checked exceptions

An exception in Java that must either be caught with a catch statement or explicitly thrown to the next level

Unchecked exception

An exception in Java that can optionally be caught or allowed to propagate automatically to the next level

InputMismatchException is unchecked

More on exceptions in Chapter 6

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Arithmetic Expressions

int number = in.nextInt();

float real = in.nextFloat();

long number2 = in.nextLong();

double real2 = in.nextDouble();

String string = in.next();

String string2 = in.next();

Data

33 12

333

44.22 End

3.13158

What isstored innumber,real,

number2,real2,string,string2

?

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Arithmetic Expressions

int number = in.nextInt();

float real = in.nextFloat();

long number2 = in.nextLong();

double real2 = in.nextDouble();

String string = in.nextLine();

String string2 = in.nextLine();

Data

33 12

333

44.22 End

3.13158

Now,what is

stored innumber,real,

number2,real2,string,string2

?

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Arithmetic Expressions

String string = in.nextLine();

nextLine() returns the rest of the line

Arithmetic reads do not consume the separator

Thus, nextLine() following an arithmetic read returns the separator, the empty string if the arithmetic value was the last value on a line

How can you solve the problem?

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Arithmetic Expressions

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int age;

age = 8;

++age;

age

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age

Java prefix increment operator: ++

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Arithmetic Expressions

8

int age;

age = 8;

age++;

age

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age

Java postfix increment operator: ++

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Arithmetic Expressions

100

int dogs;

dogs = 100;

--dogs;

dogs

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dogs

Java prefix decrement operator: --

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Arithmetic Expressions

100

int dogs;

dogs = 100;

dogs--;

dogs

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dogs

Java postfix decrement operator: --

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Arithmetic Expressions

Which form to use?

When the increment (or decrement) operator is used in a “stand alone” statement solely to add one (or subtract one) from a variable’s value, it can be used in either prefix or postfix form

dogs--; --dogs;

USE EITHER

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Compound Arithmetic Expressions

Precedence

Rules that determine which operator is

applied first in an expression having several

operators

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Compound Arithmetic Expressions

Operator Precedence

Highest ( ) (operations within parentheses)

++ -- (postfix increment and decrement)

++ -- (prefix increment and decrement)

+ - (unary plus and minus)

* / % (multiplication, division, modulus)

Lowest + - (addition and subtraction)

Can you see why increment and decrementoperators might be problems in compound expressions?

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Compound Arithmetic ExpressionsLeft-to-right associativity

In an expression having two operators with the same priority, the left operator is applied first

In Java, the binary operators

* , / , % , + , - are all left associative

Expression 9 - 5 - 1 means (9 - 5) - 1

4 - 1

3

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7 * 10 - 5 % 3 * 4 + 9

(7 * 10) - 5 % 3 * 4 + 9

70 - 5 % 3 * 4 + 9

70 - (5 % 3) * 4 + 9

70 - 2 * 4 + 9

70 - (2 * 4) + 9

70 - 8 + 9 (70 - 8) + 9

62 + 9

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Evaluate the Expression

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Parentheses

Use parentheses to change the usual order

Parts in () are evaluated first

Evaluate (7 * (10 - 5) % 3) * 4 + 9

(7 * 5 % 3) * 4 + 9

(35 % 3) * 4 + 9

2 * 4 + 9

8 + 9

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Compound Arithmetic Expressions

But…

When the increment (or decrement) operator is used in a statement with other operators, the prefix and postfix forms can yield different results

Prefix Increment (or decrement) then use

Postfix Use then increment (or decrement)

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Compound Arithmetic Expressions

int alpha;int num;num = 13;alpha = ++num * 3;

What is alpha?

alphs = num++ * 3;What is alpha?

Did youforesee

thisproblemfrom the

precedencetable

?

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Compound Arithmetic Expressions

Type conversion

The implicit (automatic) conversion of a value from one data type to another

Widening conversion

One that does not result in a loss of information

Narrowing conversion

One that may result in a loss of information

How do type conversions happen?

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Compound Arithmetic Expressions

Given

int someInt;

double someDouble;

float someFloat;

What happens in these cases?

someDouble = 12;

someInt = 4.5;

someFloat = someDouble;

someFloat = someInt * 3.5 + 4;

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Compound Arithmetic Expressions

Type casting

The explicit conversion of a value from one data type to another

(data type name) ExpressionsomeDouble = (double)12;

someInt = (int)4.5;

someFloat = (float)someDouble;

someFloat = (float)someInt * 3.5 + (float)4;

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Compound Arithmetic Expressions

What values are stored?double loCost;

double hiCost;

loCost = 12.342;

hiCost = 12.348;

loCost = (double) ((int) (loCost * 100.0 + 0.5))

/ 100.0;

hiCost = (double) ((int) (hiCost * 100.0 + 0.5))

/ 100.0;

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Compound Arithmetic Expressions

What is the difference between these statements?String answer = "The results are: " + 27 + 9;

and

String answer = 27 + 9 + " The results are:";

Conversion from number to string occurs only with the concatenation operator

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Compound Arithmetic Expressions

What about converting from string to a numeric value?

We instantiate a Scanner object with the string and use the Scanner input methodsScanner in = new Scanner("43 55.0");

int one = in.nextInt();

float two = in.nextFloat();

Scanner in = new Scanner(in.nextLine())

…

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Value-Returning Methods

Additional methods of class StringMethod length returns an int value that is the number

of characters in the string String name = “Donald Duck”;

numChars;

numChars = name.length();

instance method

Whatis

returned ?

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Value-Returning Methods

Method indexOf searches a string to find a particular substring, and returns an int value that is the beginning position for the first occurrence of that substring within the stringString stateName = “Mississippi”;

int index;

index = stateName.indexOf("is");

What is returned? (Remember the firstposition is 0 not 1)

What is returned if the substring isn't there?

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Value-Returning Methods

Method charAt returns the character at a specified position within the stringString stateName = “Mississippi”;

char letter;

letter = stateName.charAt(5);

What is returned?

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Value-Returning Methods

Method substring returns a substring of a string, but does not change the string itself

The first parameter specifies a starting position within the string

The second parameter specifies the last position plus one

String stateName = “Mississippi”;

String substring;

substring = stateName.substring(9, 11);

What is returned?

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Value-Returning Methods

Method trim returns a copy of a string with all whitespace characters removed from either end

String myString = " Good morning Susy Sunshine ";

System.out.println(myString.length());

System.out.println(myString.trim().length());

What is printed?

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Value-Returning Methods

Class Math provides a collection of useful value-returning methods for common numeric functions

Math.abs(x) returns the absolute value of X

Math.cos(x) returns the cosine of X

Math.sqrt(x) returns the square root of X

Math.random()returns a random number

between 0 and 1

…

Why is Math uppercase?

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Class Time

Designing a class to represent timeImmediately we have an ambiguous situation:

Time of day with hours, minutes, and seconds

Elapsed time where seconds only is appropriate

Here we mean elapsed time, so

our only attribute is seconds of type double

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Class Time

Constructorspublic Time() // default

{ seconds = 0.0; }

public Time(double newSeconds)

{ seconds = newSeconds; }

public Time(int hours, int minutes,

double new Seconds)

{

seonds = (double)(hours*3600 + minutes * 60)

+ newSeconds;

}

}

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Class Time

Observerspublic double getTime()

{ return seconds; }

public int getHours()

{ return (int) seconds/3600; }

public int getSeconds()

{ return seconds % 60.0) }

getMinutes is more difficult…

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Class Time

We must remove hours before we can calculate minutes

public int getMinutes()

{

int remainingSeconds = (int) seconds % 3600;

return remainingSeconds/60;

}

5463 seconds is 1 hours, 31 minutes, and 3 second

Prove it to yourself

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Class Time

Other operationspublic String toString()

{

int hours = (int) sconds / 3600;

int minutes = (int) seconds % 3600 / 60;

return hours + ":" + minutes + ":" + seconds%60;

}

Why is a toString method useful?

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Class Time

Binary operationTime myTime(300);

Time yourTime(200);

Time ourTime = myTime.plus(yourTime);

public Time plus(Time otherTime)

{

return (new Time(seconds + otherTime.seconds);)

}

300 200

What are seconds and otherTime.seconds here? Time ourTime = yourTime.plus(myTime);

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Class Time

No class is complete until it is tested

Test plan

A document that specifies how a class is to be tested

Test plan implementation

Writing and running a driver that implements the test cases specified in a test plan to verify that the class methods produce the predicted results

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Class Time

Test Plan

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Class Time

Implemented test plan

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Extras

I designed boththe Difference

Engine andthe Analytical

Engine inthe 1800s

Who am I?

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Extras - GUI Track

Dialog box

A small temporary panel that appears on the screen, with which user can interact