Storing and manipulation Floating point information

1. Storing and manipulation Floating point information

2. Recall (1) • Although the computer stores binary numbers, we can interpret then as decimal number through a conversion operation:

3. Recall (2) • The computer can combine adjacent bytes in the RAM memory to form larger memory cells:

4. Variables (in general) • A variable in a computer program is in fact a memory cell • A variable in a computer program stores a number • The tag represents the data type of the variable (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;

5. 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., the decimal point "floats")

6. Floating Variable (1) • A floating point variable behaves like a piece of paper where you can record (exactly) one floating point number:

7. Floating Variable (2) • encoding method used is called the IEEE 754 Standard • Floating point numbers can also be written in the exponent form:

8. Floating Variable (3) • There are 2 kinds of floating point variables in Java • A double precisionfloating point variable is a variable that uses 8 consecutive bytes of memory as a single 64 bit memory cell • This kind of variable is commonly used in scientific computations.

9. Defining Floating Point Variable (1) • Every variable in Java must be defined, and you must use the correct syntax construct to write a variable definition • The keyworddouble 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 ";"

10. Defining Floating Point Variable (2) • The effect of the definition: • The computer will find8 consecutive bytes of RAM memory that is unused • The computer will then reserve these memory bytes • It alsoassociate the name x with the (8 bytes of) reserved memory

11. Update the value stored in a variable (1) • The assignment statement in the Java programming language instructs the computer to update the value stored in a variable • 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 • This statementmust be ended with a semi-colon ";"

12. Update the value stored in a variable (2) • The assignment statementx=0.31415e1 will store the value 3.1415 into the memory cellidentified by the name x:

13. Update the value stored in a variable (3) • System.out.println(x) will read the value stored at the memory cellidentified by the name x and print it to the terminal:

14. 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.

15. Floating point operators • Floating point operators are arithmetic operators that  manipulate floating point values

16. Priority of the floating point arithmetic operators

17. Java Library

18. Mathematical functions (1) • Scientific calculations often involve Mathematical functions, such as sin, cos, tan, log, and so on. • Examples:sin and ln functions on a calculator

19. Mathematical functions (2) • Programming languages allow you to embedMathematical functions within a arithmetic expression.

20. Class and Method • Method = a collection of statements that performs a complex (useful) task • Class = a container for methods

21. Organization of the Java library (1) • To find "things" more easily, humans usually organize (= group) the "things" in a hierarchical manner

22. Organization of the Java library (2) • Each class inside the Java library has a unique class path name in the form: java.PackageName.ClassName

23. Using classes in the Java library (1) • One way is : use the class path • we can refer to the sin() method stored in the Math class (inside the package lang) as:

24. Using classes in the Java library (2) • The other way is: • firstimport the class (with an import clause)

25. Input parameters and output values of a method (1) • Consider a Mathematical function: • A Mathematical function has a unique name • A Mathematical function has a number of function arguments (x, y and z). (Input) • A Mathematical function will produce an answer. (Output)

26. Input parameters and output values of a method (2) • A method resembles a Mathematical function: • A method has a unique "signature" (will learn more about "signatures" later in the course) • A method has a number of input parameters • A methodmayreturnone output value (some methods do not return any output values) • you must store the return value in some variable (using an assignment statement) or else, the returned value will be lost !

27. How to invoke a method (1) 1. Syntax to invoke a method that does not return any value: You can recognize such methods by the return type void.

28. How to invoke a method (2) • 2. Syntax to invoke a method that returns a value: You can recognize such methods by their return type which is not equal to void.

29. Meaning of the method header: • Parameters: You must pass the correct number of parameter of the correct data type to a method • Return: If the methodreturns a value, you must assign it to a variable of the correct type

30. What happens when a method is invoked (1) • The following figure shows the situationjust before the program executes b = Math.sqrt(a);:

31. What happens when a method is invoked (2) • Pass the value of the variablea as parameter to the sqrt method:

32. What happens when a method is invoked (3) • Execute the statements in the method body of sqrt:

33. What happens when a method is invoked (4) • When it completes, the executionreturns to the location of the method call • The return valuereplaces the method call in the expression:

34. What happens when a method is invoked (5) • After the assigning the value to variable b, we have: