Numerical Data

1
Chapter 3

• Numerical Data

2
Topics

• Variables
• Numeric data types
• Assignment
• Expressions

3
Numeric Data and Operations

• So far, our programs have used only String data
• It is common to use computers for numeric
  calculations
• We can write literal numbers into our programs -
  just write the number
• We need a way to store numeric data - variables

4
Variables

• In mathematical expressions, we often use x and y
  to represent unknown values and to make a
  placeholder for many different values
• y x2 5
• A variable is used in a similar way in a program
• A variables has a Java identifier for a name.

5
Variables

• In the last chapter, we declared variables whose
  location stored the address of an object
• Now we need to learn to declare variables to
  store numeric data.
• A declaration sets aside memory locations to
  store data values.
• These memory locations are called variables, and
  x and y are the names we associate with the
  memory locations.
• As before, we need to say what kind of data the
  variable represents.

6
Variables

• A variable has three properties
• A memory location to store the value.
• The type of data stored in the memory location.
• The name used to refer to the memory location.

7
Variable Declarations

• The syntax for declaring variables is
• ltdata typegt ltvariablesgt
• where ltvariablesgt is a sequence of identifiers
  separated by commas.
• Every variable we use in a program must be
  declared.

8
Numeric Types

• There are six numeric data types in Java
• We nee to be able to use two basic kinds of
  numbers.
• We have several types for each kind of number to
  allow for different ranges of values.
• Integers have discrete values (whole numbers).
• byte
• short
• int
• long
• Real numbers are needed for values that have
  fractional parts.
• float
• double

9
Assignment

• First we need to declare a variable.
• int a
• We assign a value to a variable by using an
  assignment statement.
• a 5
• At the time a variable is declared, it can also
  be initialized.
• int count 10, height 34
• Do not confuse mathematical equality and
  assignment. The following is not valid Java code
• 4 5 x

10
Varaibles for Objects and Numbers

• The only difference between a variable for
  numbers and a variable for objects is the
  contents in the memory locations.
• For numbers, a variable contains the numeric
  value itself.
• For objects, a variable contains an address where
  the object is stored.

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Memory diagram for numeric data

• For numeric data, the actual value is stored in
  the memory location associated with the variable

12
Object Variables

• For objects, the location (memory address) for
  the object is stored in the memory location
  associated with the variable

13
Comparison
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Variables

• We use the new command to create an object.
• Objects are called reference data types, because
  the contents are addresses that refer to memory
  locations where the objects are actually stored.
• Numerical data are called primitive data types.
• We don't need to use new with primitive types.
• You do have to give the primitive variable a
  value.

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Assignment

• Numeric Data

• Objects

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Arithmetic Expressions
Assume x10, y7, z2.5
Operation Operator Expression Result
Addition x y 17
Subtraction - y - z 4.5
Multiplication x y 70
Division / y / x 0.7
Modulo (remainder) x y 3
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Division and Modulo

• Division works differently for integer and
  floating point types
• for floating point types you get a floating point
  result (what your calculator would give you)
• for integers, you get an integer result
• integer division and modulo together are what you
  first learned when you learned division in grade
  school
• 27 divided by 6 is 4 with a remainder of 3
• so 27 / 6 gives a result of 4
• and 27 6 gives a result of 3

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Evaluation order

• In an expression with more than one binary
  operator, we need rules to tell us what order to
  do them in
• What is 5 x 16 / y 5 ?
• Precedence rules tell us which of two different
  operations should get done first
• What is 5 4 3 ?
• Associativity rules tell us which order
  operations of the same type get done in
• What is 16 / 2 / 2 ?

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Precedence rules

• for arithmetic operators and parentheses

Order Group Operator Rule
first Subexpression () innermost first left to right
Unary operation , - single operand
multiplicative operators , /, left to right
last additive operators , - left to right
20
Evaluation of Expressions

• Subexpression evaluation
• x 3 y

21
Mixed-mode Arithmetic

• What happens when the operands in your expression
  have different types?
• x 3.45 / 2
• The hardware supports only single-type operations
• The value of a variable has to be stored in the
  appropriate format.
• Type conversions are used to convert mixed-type
  expressions to single type expressions

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Type Conversions

• Widening conversions happen automatically
• promote a value from one type into another which
  can represent a larger range of values
• converting an int to a double
• Narrowing conversions have to be programmed
  explicitly
• information will be lost
• converting a double to an int
• cast operator is the name of the type of the
  result enclosed in parentheses
• (int)2.34
• fractional part will be truncated

23
Rules for arithmetic promotion

• Unary Operators
• byte and short operands are converted to int
• Binary Operators
• If either operand has type double, the other will
  be converted to a double
• Otherwise, if either operand has type float, the
  other will be converted to a float
• Otherwise, if either operand has type long, the
  other will be converted to a long
• Otherwise, both operands are converted to int
  will be converted to an int

24
Constants

• If we want a variable to remain fixed, we use a
  constant.
• A constant is declared in a manner similar to a
  variable, but with the additional reserved word
  final.
• final double PI 3.14159
• final int MONTHS_IN_YEAR 12

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Literal Constants

• If a literal constant contains a decimal point,
  it is of type double by default.
• To designate a literal constant of type float,
  append a letter f or F to the number
• 2 PI 345.79F

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Scientific Notation

• Numbers in scientific notation, such as
• Number x 10exponent
• are expressed in Java using the syntax
• ltnumbergt E ltexponentgt
• 12.40e209
• 29.009E-102

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Getting Numerical Input Values

• Wrapper classes are used to perform necessary
  type conversions, such as converting a String
  object to a numerical value.

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Getting Numerical Input Values

• radiusStr
• JOptionPane.showInputDialog(null,
• "Enter radius")
• radius Double.parseDouble(radiusStr)

29
The Math Class

• The Math class in the java.lang package contains
  class methods for commonly used mathematical
  functions.
• Some methods available in the Math class
• sqrt, abs, round
• sin, cos, asin,
• Math has the constant Math.PI in it