1. Numeric Data Types There are six numeric data types: byte, short, int, long, float, and double. Sample variable declarations: int i, j, k; float numberOne, numberTwo; long bigInteger; double bigNumber;

2. Data Type Precisions The six data types differ in the precision of values they can store in memory.

3. Primitive Data Declaration and Assignments Code State of Memory int firstNumber, secondNumber; firstNumber = 234; secondNumber = 87; A A int firstNumber, secondNumber; B B firstNumber = 234; secondNumber = 87; int firstNumber, secondNumber; firstNumber = 234; secondNumber = 87; firstNumber secondNumber A. A. Variables are allocated in memory. B. B. Values are assigned to variables. 234 87

4. Assigning Numeric Data Code State of Memory int number; number = 237; number = 35; number A. A. The variable is allocated in memory. B. 237 number B. The value 237 is assigned to number. 237 int number; number = 237; number = 35; A A int number; B B number = 237; C C number = 35; C. 35 237. C. The value 35 overwrites the previous value 237. 35

5. Numeric Data Types At the time a variable is declared, it also can be initialized. For example, we may initialize the integer variables count and height to 10 and 34 as int count = 10, height = 34; Ping … out to reality … NumericVariables.java

6. Numeric Literal Values Integer types can be Positive or negative Decimal, e.g., -5653 Octal, e.g., 05653 (but not 09876) Hexidecimal, e.g., 0x5A1 Long, e.g., 14084591234L Real types can be Float, e.g., 1.23f Double, e.g., -2.34 Scientific, e.g., 2.17e-27f or -456.2345e19

7. Arithmetic Operators The following table summarizes the arithmetic operators available in Java. ++ and -- for integer type variables This is an integer division where the fractional part is truncated.

8. Arithmetic Expressions Examples: sum = firstNumber + secondNumber; avg = (one + two + three) / 3.0; total++; Assignment operators Tral-la-la, out to reality … NumericOperators.java

9. Arithmetic Expressions How does the expression x + 3 * y get evaluated? Answer: x is added to 3*y. We determine the order of evaluation by following the precedence rules. A higher precedence operator is evaluated before the lower one. If two operators are the same precedence, then they are evaluated left to right for most operators.

10. Precedence Rules

11. Example a * (b + -(c / d) / e) * (f - g % h) a * -b - (d + e * f) * (-g + h) a = 10; b = 5; c = 23; d = 4; e = 2; f = 5; g = 8; h = 3;

12. Example Program Flonk … out to reality … NumericPrecedence.java

13. Type Casting If x is a float and y is an int, what will be the data type of the following expression? x * y The answer is float. The above expression is called a mixed expression. The data types of the operands in mixed expressions are converted based on the promotion rules. The promotion rules ensure that the data type of the expression will be the same as the data type of an operand whose type has the highest precision.

14. Promotion Rules

15. Assignment Conversion If a lower precision value is assigned to a higher precision variable, type casting occurs Example double number; number = 25; is legal but int number; number = 23.45; is not

16. Explicit Type Casting Instead of relying on the promotion rules, we can make an explicit type cast by prefixing the operand with the data type using the following syntax: ( ) Example (float) x / 3 (int) (x / y * 3.0) Type case x to float and then divide it by 3. Type cast the result of the expression x / y * 3.0 to int.

17. Example Program Fuuuurtang … out to reality … NumericCasting.java

18. 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; These are constants, also called named constant. The reserved word final is used to declare constants. These are called literal constant.

19. Use of Constants Very often class variables that are initialized May be private or public Local and instance variables may be declared final so they can be assigned a value only once Yabbadabba … out to reality … FinalVariables.java

20. The Math Class The Math class in the java.lang package includes many common and useful mathematical functions such sin, cos, tan, square root, exponentiation, and others. The mathematical formula is expressed in Java as Math.abs( Math.sin( Math.PI / 4.0) * x ) Splodge … out to reality … MathFunctions.java