Most programs perform arithmetic calculations. Figure 2.9 summarizes the C++ arithmetic operators. Note the use of various special symbols not used in algebra. The asterisk (*) indicates multiplication and the percent sign (%) is the modulus operator that will be discussed shortly. The arithmetic operators in Fig. 2.9 are all binary operators, i.e., operators that take two operands. For example, the expression number1 + number2 contains the binary operator + and the two operands number1 and number2.
C++ operation 
C++ arithmetic operator 
Algebraic expression 
C++ expression 

Addition 
+ 
f + 7 
f + 7 
Subtraction 
 
p c 
p c 
Multiplication 
* 
bm or b · m 
b * m 
Division 
/ 
x / y 

Modulus 
% 
r mod s 
r % s 
Integer division (i.e., where both the numerator and the denominator are integers) yields an integer quotient; for example, the expression 7 / 4 evaluates to 1 and the expression 17 / 5 evaluates to 3. Note that any fractional part in integer division is discarded (i.e., truncated)no rounding occurs.
C++ provides the modulus operator, %, that yields the remainder after integer division. The modulus operator can be used only with integer operands. The expression x % y yields the remainder after x is divided by y. Thus, 7 % 4 yields 3 and 17 % 5 yields 2. In later chapters, we discuss many interesting applications of the modulus operator, such as determining whether one number is a multiple of another (a special case of this is determining whether a number is odd or even).
Common Programming Error 2.3
Attempting to use the modulus operator (%) with noninteger operands is a compilation error. 
Arithmetic Expressions in StraightLine Form
Arithmetic expressions in C++ must be entered into the computer in straightline form. Thus, expressions such as "a divided by b" must be written as a / b, so that all constants, variables and operators appear in a straight line. The algebraic notation
is generally not acceptable to compilers, although some specialpurpose software packages do exist that support more natural notation for complex mathematical expressions.
Parentheses for Grouping Subexpressions
Parentheses are used in C++ expressions in the same manner as in algebraic expressions. For example, to multiply a times the quantity b + c we write a * (b + c).
Rules of Operator Precedence
C++ applies the operators in arithmetic expressions in a precise sequence determined by the following rules of operator precedence, which are generally the same as those followed in algebra:
( ( a + b ) + c )
the operators in the innermost pair of parentheses are applied first.
The set of rules of operator precedence defines the order in which C++ applies operators. When we say that certain operators are applied from left to right, we are referring to the associativity of the operators. For example, in the expression
a + b + c
the addition operators (+) associate from left to right, so a + b is calculated first, then c is added to that sum to determine the value of the whole expression. We will see that some operators associate from right to left. Figure 2.10 summarizes these rules of operator precedence. This table will be expanded as additional C++ operators are introduced. A complete precedence chart is included in Appendix A.
Operator(s) 
Operation(s) 
Order of evaluation (precedence) 

( ) 
Parentheses 
Evaluated first. If the parentheses are nested, the expression in the innermost pair is evaluated first. If there are several pairs of parentheses "on the same level" (i.e., not nested), they are evaluated left to right. 
* 
Multiplication 
Evaluated second. If there are several, they are evaluated left to right. 
+ 
Addition 
Evaluated last. If there are several, they are evaluated left to right. 
Sample Algebraic and C++ Expressions
Now consider several expressions in light of the rules of operator precedence. Each example lists an algebraic expression and its C++ equivalent. The following is an example of an arithmetic mean (average) of five terms:
The parentheses are required because division has higher precedence than addition. The entire quantity ( a + b + c + d + e ) is to be divided by 5. If the parentheses are erroneously omitted, we obtain a + b + c + d + e / 5, which evaluates incorrectly as
The following is an example of the equation of a straight line:
No parentheses are required. The multiplication is applied first because multiplication has a higher precedence than addition.
The following example contains modulus (%), multiplication, division, addition, subtraction and assignment operations:
The circled numbers under the statement indicate the order in which C++ applies the operators. The multiplication, modulus and division are evaluated first in lefttoright order (i.e., they associate from left to right) because they have higher precedence than addition and subtraction. The addition and subtraction are applied next. These are also applied left to right. Then the assignment operator is applied.
Evaluation of a SecondDegree Polynomial
To develop a better understanding of the rules of operator precedence, consider the evaluation of a seconddegree polynomial (y = ax2 + bx + c):
The circled numbers under the statement indicate the order in which C++ applies the operators. There is no arithmetic operator for exponentiation in C++, so we have represented x2 as x * x. We will soon discuss the standard library function pow ("power") that performs exponentiation. Because of some subtle issues related to the data types required by pow, we defer a detailed explanation of pow until Chapter 6.
Common Programming Error 2.4
Some programming languages use operators ** or ^ to represent exponentiation. C++ does not support these exponentiation operators; using them for exponentiation results in errors. 
Suppose variables a, b, c and x in the preceding seconddegree polynomial are initialized as follows: a = 2, b = 3, c = 7 and x = 5. Figure 2.11 illustrates the order in which the operators are applied.
Figure 2.11. Order in which a seconddegree polynomial is evaluated.
As in algebra, it is acceptable to place unnecessary parentheses in an expression to make the expression clearer. These are called redundant parentheses. For example, the preceding assignment statement could be parenthesized as follows:
y = ( a * x * x ) + ( b * x ) + c;
Good Programming Practice 2.14
Using redundant parentheses in complex arithmetic expressions can make the expressions clearer. 
Introduction to Computers, the Internet and World Wide Web
Introduction to C++ Programming
Introduction to Classes and Objects
Control Statements: Part 1
Control Statements: Part 2
Functions and an Introduction to Recursion
Arrays and Vectors
Pointers and PointerBased Strings
Classes: A Deeper Look, Part 1
Classes: A Deeper Look, Part 2
Operator Overloading; String and Array Objects
ObjectOriented Programming: Inheritance
ObjectOriented Programming: Polymorphism
Templates
Stream Input/Output
Exception Handling
File Processing
Class string and String Stream Processing
Web Programming
Searching and Sorting
Data Structures
Bits, Characters, CStrings and structs
Standard Template Library (STL)
Other Topics
Appendix A. Operator Precedence and Associativity Chart
Appendix B. ASCII Character Set
Appendix C. Fundamental Types
Appendix D. Number Systems
Appendix E. C Legacy Code Topics
Appendix F. Preprocessor
Appendix G. ATM Case Study Code
Appendix H. UML 2: Additional Diagram Types
Appendix I. C++ Internet and Web Resources
Appendix J. Introduction to XHTML
Appendix K. XHTML Special Characters
Appendix L. Using the Visual Studio .NET Debugger
Appendix M. Using the GNU C++ Debugger
Bibliography