1. Expressions
An expression is a portion of a C++ statement that performs an evaluation of some kind
Generally requires that a computation or data manipulation be performed to produce a result of a specified type
Arithmetic expression
Performs a numeric computation producing a numerical result
Logical expression
Produces a Boolean result evaluating to true or false
String expression
Produces a result of type string
Expressions may contain other expressions which are evaluated in order producing an overall result
Ex: (2+5) * (7+3)

2. Arithmetic Expressions
Basic arithmetic operations
+ - * /
int data type includes % (modulus)
Integer division - result is integer
15 / 3 = 5
15 / 2 = 7
0 / 15 = 0
15 / 0 undefined
Float results includes decimal portion
15.0 / 2.0 = 7.5

3. Modulus for Integers Used only with integers
Get a compiler error if used with a float
Yields remainder - the result is integer
Examples:
7 % 2 = 1
299 % 100 = 99
49 % 5 = 4
15 % 0 undefined
15 % -7 system dependent

4. Mixed-type Expressions
Example: / 2 evaluates to 2.3
Rule: when an integer and a floating point operand are combined by an operator, the integer gets converted to the floating point type
Caveat: this rule is dependent on operator precedence rules

5. Mixed-type Assignments
If the variable on left side of assignment is of different type than the type of the evaluated expression on the right side of =, the result of the expression must be converted to the appropriate type
Conversion from a float to an int involves dropping (truncating, not rounding!) the decimal part
Example:
int n;
float x=2.7;
n= x; // n will be assigned the value 2
(trick: to round, add 0.5 first!)

6. Mixed-type Assignment Examples
float a, b, x; int m, n; a=10; // result is 10.0 stored in a b = 3.5; m=5; n = 10; x = m / n; // result is 0 assigned to x m = b * 3; // result is 10 assigned to m

7. Order of Operator Precedence
Highest
( ) nested expressions evaluated
inside out
unary +, -
*, /, %
binary +, -
Associativity
Lowest
Warning: watch out for the types of operands and the type of the result from evaluating each operand!

8. Step-by-Step Expression Evaluation

9. Figure 2.10 Evaluation for z - (a +b / 2) + w * -y;

10. Figure 2.11 Evaluation tree for m = x + k / 2:

11. Mathematical Formulas in C++
a = bc not valid C++ syntax
Must use * operator
a = b * c;
m= y − b x − a
Must use ( ) and /
m = (y - b) / (x - a);