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MODULE 1-05: Compact Course Programming Lesson 4 - Data Types and Operators -

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Content Simple Data Types, their Values and Operators Expressions Type Conversions

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Try out / Answer: Overflow and Precision Go to the following link to check your answer:

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Simple Data Types, their Values and Operators Simple Data Types in Java

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Simple Data Types, their Values and Operators Simple Data Types in Java In difference to some other programming languages, all simple data types in Java have an agreed fixed size in memory For every simple data type a default value is defined, which is of importance with the initialisation of object and class variables (note: local variables are not automatically initialised with the default value)

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Simple Data Types, their Values and Operators Operators Are special symbols that are used to link operands to determine a new value According to their number of operands we can distinguish three types of operators Single digit (monadic oder unary) operators example: the negative sign - Two digit (dyadic oder binary) operators example: the addition sign + Three digit (triadic oder ternary) operatores example: conditional operator ? :

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Simple Data Types, their Values and Operators Logic Values (boolean) Unary Operator (Operator Operand) Operator Description ! logische Negation Binary Operator (Operand1 Operator Operand2) Operator Description Example == Equality false == true  results in false != Inequality false != true  results in true & logic AND | logic OR ^ logic XOR

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Simple Data Types, their Values and Operators Logic Value (boolean) Notation Properties of the Operators (truth table)

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Simple Data Types, their Values and Operators Truth Table (boolean) Boolean Expressions with & and | evaluate both terms completely In practise complete evaluation is often not required & - operation: is one expression false, then the overall result is false | - operation: is one expression true, then the overall result is true The operators && and || ensure a shortened evaluation Example int m = 3; int n = 5; boolean b = (m < 5) || (n > 3); The shortened evaluation is important to reduce the computation time for example with large arrays

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Try out / Answer: use boolean operators! What is the value of the following expressions? (true & true) | false !!true true & !true (true || false) && true

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Simple Data Types, their Values and Operators Binary Operators (char, byte, short, int, long) Operator Description Example + Addition 5 + 6 yields 11 - Subtraction 9 - 3 yields 6 * Multiplication 10 * 15 yields 150 / Whole Number Division 13 / 3 yields 4 % Modulo (remainder of 20 % 7 yields 6 a whole number division) = bigger equal 5 >= 6 yields false == equal 3 == 3 yields true != not equal 5 != 5 yields false

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Try out / Answer: use boolean operators! What is the value of the following expressions? 7 / 5 7 % 5 5 / 7 5 % 7

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Simple Data Types, their Values and Operators Unary Operators (char, byte, short, int, long) Operator Description Example - Unary Negation -i ++ Increment ++i is the same as i = i+1 -- Decrement --i is the same as i = i-1 Note the difference: Pre-increment vs. Post-increment a = ++b; // is the same as: // b = b+1; a = b; a = b++; // is the same as: // a = b; b = b+1;

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Simple Data Types, their Values and Operators Bitwise - Operators (char, byte, short, int, long) Access to binary representation of whole number data types Numbers are viewed as a set of consecutive bits, which may be manipulated Unary Operator (Operator Operand) Operator Description ~ Complement (bitwise negation) Binary Operators (Operand1 Operator Operand2) Operator Description & bitwise AND | bitwise OR ^ bitwise XOR  The operators >>, >>> and

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Simple Data Types, their Values and Operators Bitwise - Operators (char, byte, short, int, long) Example for shift operator Left-Shift-Operator

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Simple Data Types, their Values and Operators Floating-Point-Numbers (float, double) Unary Operators (analog to whole-number types) - ++ -- Binary Operators (analog to whole-number types) + - * / % (arithmetic operators) < >= == != (comparison operators) Note: whole-number division: 45 / 20 Result: 2 floating-point division: 45.0 / 20.0 Result: 2.25

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Simple Data Types, their Values and Operators Floating-Point-Numbers (float, double) Arithmetic Operators Both operands of type float Result type float In all other cases Result type double Attention with equality checks (x == y) // possible rounding errors !

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Simple Data Types, their Values and Operators Composite Operators E1 op= E2 is the same as E1 = E1 op (E2) Example counter = counter + 1; // abbreviated: counter += 1; counter = counter – 1; // abbreviated: counter –= 1; analog: *=, /=, %=, &=, |=, ^=, =, >>>=

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Content Simple Data Types, their Values and Operators Expressions Type Conversions

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Expressions Expressions: Definition and Features Expression: Processing specification, that delivers a value after execution In the simplest case a variable or a constant Through combination of operands, operations and round brackets we get complex expressions Examples radius = 5.5; area = PI * radius * radius; counter = counter + 1;

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Expressions Brackets The evaluation of expressions in brackets always takes place first Just like the rules in mathematics Expressions may be arbitrarily nested Notation of the nested structure is done with round brackets All expressions are provided in linear notation  Expression are provided in line format

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Expressions Example Mathematic format Line format

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Expressions Operator Priority Rules Well-known from mathematics: „Point before Line“ example 6 + 7 * 3 equals 27 and not 39 In Java: Linking of operators is governed by priorities: An operator with high priority links stronger than an operator with a lower priority If the priority is the same than then the associativity of the operators is evaluated op is is left associative: X op Y op Z equals (X op Y) op Z op ist right associative: X op Y op Z equals X op (Y op Z) Obviously, brackets do control the evaluation order example (6 + 7) * 3 ist 39

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Expressions Priority and Associativity

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Expressions Priority and Associativity

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Try out / Answer: use priority and associativity! For the following expressions, set brackets such that they yield the same result as the expressions without brackets 1. e = --c - d / a; 2. f = b 16; 3. h = a < 5 || b > 10 && d - c >= 0;

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Expressions Mathematical Constants and Functions The class Math provides important mathematical constants and functions (see online documentation) Constants public static final double E (basis e of nat. logarithm) public static final double PI () Usage: Math.E and Math.PI Methods (Selection) public static double abs(double x) |x| public static double cos(double x) cos(x) public static double sin(double x) sin(x) public static double tan(double x) tan(x) public static double sqrt(double x) √x public static double exp(double x) ex public static double pow(double x, double y) xy Usage: for example result = Math.pow(a,b);

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Definition of Constants Constants in Java Constants are defined and initialised like variables with the keyword „final“ their names are typically written in capital letters they can not be changed Example: Statement and definition of constants: Statement rewritten with constants: red = Math.min(red + ADDED_RED, MAX_RED)

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Content Simple Data Types, their Values and Operators Expressions Type Conversions

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Type Conversion Type Conflict Values can only be assigned to variables, if their type is compatible with the type of the variable! Example int a; float b = 10.5f; a = b; // Error because of incompatible types

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Type Conversion Automatic (implicit) type extension Rules An automatic type extension is happening in the direction of the arrows Example double a, b; float c; a = b + c + 2.785f;

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Type Conversion Type extension and selection of operators in expressions Each expression is evaluated step by step according to the priorities and associativity of its operators The operators choosen are the operators that fit to the type of the operands (example: whole number division OR division for floating point numbers) Are the types of operands different, than the „smaller“ operand will receive an automatic type conversion Are both operands of an operation, expressions themselves, then the left operand is calculated before the right operand

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Type Conversion Type Extension and Selection of Operators in Expressions Example double a; int b, c; a = 3.0 + 2.785f + b / c; Evaluation: Addition from left to right, point before line a = ((3.0 + 2.785f) + (b / c));

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Type Conversion Explicit Type Conversion: Type Casting Explicit type conversion happens when the desired type is explicitly requested Example int a; float b = 10.25f; a = (int) b; float-value 10.25f is converted in the int-value 10 a = (int)(b / 3.3f + 5.73f); Note: Type casting takes place AFTER the calculation of the entire term b / 3.3f + 5.73f