Chapter 3

1. Chapter 3 Math Operations

2. Objectives • Use the assignment and arithmetic operators. • Use operators in output statements. • Explain the problem with division by zero. • Increment and decrement variables. • Explain the order of operations. • Properly mix data types in calculations. • Avoid overflow and underflow in calculations. • Explain floating-point rounding errors.

3. Assignment Operator • Recall, the assignment operator changes the value to the left of the variable. • Several variables can be declared in one statement: int i,j,k; • Several variables may also be initialized in one statement: i=j=k=25; • Variables can be declared and initialized in one statement: float n = 4.5;

4. Arithmetic Operators • Arithmetic operators are used to perform calculations in C++. • The arithmetic operators available in C++: • + Addition • - Subtraction • * Multiplication • / Division • % Modulus

5. Using Arithmetic Operators • Arithmetic operators are used with two operands. • The minus sign can be used alone to change the sign of a value. • The portion to the right of the operator is the expression. • The assignment operator is different than the equals sign in algebra: x = x + 10;

6. Example Statements What does each one mean? • cost = price + tax; • owed = total - discount; • area = l * w; • one_eighth = 1 / 8; • r = 5 % 2; • x = -y;

7. The Modulus Operator • The modulus operator (%) returns the remainder rather than the result of division. • Examples: • 9 % 2 would result in 3. • 10 % 2 would result in 0. • 20 % 6 would result in 2.

8. Incrementing and Decrementing • Adding one to a variable is called incrementing. • In C++ you increment with the ++ operator. • Subtracting one from a variable is called decrementing. • In C++ you decrement with the -- operator.

9. Variations of Increment and Decrement k = j++; • In the case of the statement above, k is assigned the value of the variable j before j is incremented. k = ++j; • In this second example, k is assigned the value of j after j is incremented.

10. Order of Operations 1. Minus sign used to change sign (-) 2. Multiplication and division (* / %) 3. Addition and subtraction (+ -) You can use parentheses to override the order of operations.

11. Mixing Data Types • C++ allows you to mix data types in calculations. • C++ can automatically handle the mixing of data types (called promotion), or you can direct the compiler on how to handle the data (called typecasting).

12. Overflow and Underflow • Overflow is the condition where a value becomes too large for its data type. • Underflow occurs with floating-point numbers when a number is too small for the data type.

13. Summary • The assignment operator (=) changes the value of the variable to the left of the operator to the result of the expression to the right of the operator. • You can initialize multiple variables to the same value in a single statement. • The arithmetic operators are used to create expressions. • The modulus operator (%) returns the remainder of integer division.

14. Summary • The ++ and -- operators increment and decrement arithmetic variables respectively. • The placement of the ++ and -- operators becomes important when the operators are used as part of a larger expression or in an output statement. • C++ calculations follow an order of operations. • C++ allows data types to be mixed in calculations.

15. Summary • Overflow is a condition where an integer becomes too large for its data type. • Underflow occurs when a floating-point number is so small that a data type interprets it as zero.