This lesson builds on top of the concepts from lesson %Failed lesson reference, id 7899%. A quick review follows:
In mathematics, an operation is a mathematical calculation involving zero or more input values (called operands) that produces a new value (called an output value). The specific operation to be performed is denoted by a construct (typically a symbol or pair of symbols) called an operator.
For example, as children we all learn that 2 + 3 equals 5. In this case, the literals 2 and 3 are the operands, and the symbol + is the operator that tells us to apply mathematical addition on the operands to produce the new value 5.
In this chapter, we’ll discuss topics related to operators, and explore many of the common operators that C++ supports.
Now, let’s consider a more complicated expression, such as 4 + 2 * 3. In order to evaluate this expression, we must understand both what the operators do, and the correct order to apply them. The order in which operators are evaluated in a compound expression is determined by an operator’s precedence. Using normal mathematical precedence rules (which state that multiplication is resolved before addition), we know that the above expression should evaluate as 4 + (2 * 3) to produce the value 10.
In C++, when the compiler encounters an expression, it must similarly analyze the expression and determine how it should be evaluated. To assist with this, all operators are assigned a level of precedence. Operators with the highest level of precedence are evaluated first.
You can see in the table below that multiplication and division (precedence level 5) have more precedence than addition and subtraction (precedence level 6). Thus, 4 + 2 * 3 evaluates as 4 + (2 * 3) because multiplication has a higher level of precedence than addition.
What happens if two operators in the same expression have the same precedence level? For example, in the expression 3 * 4 / 2, the multiplication and division operators are both precedence level 5. In this case, the compiler can’t rely upon precedence alone to determine how to evaluate the result.
If two operators with the same precedence level are adjacent to each other in an expression, the operator’s associativity tells the compiler whether to evaluate the operators from left to right or from right to left. The operators in precedence level 5 have an associativity of left to right, so the expression is resolved from left to right: (3 * 4) / 2 = 6.
Table of operators
The below table is primarily meant to be a reference chart that you can refer back to in the future to resolve any precedence or associativity questions you have.
- Precedence level 1 is the highest precedence level, and level 17 is the lowest. Operators with a higher precedence level get evaluated first.
- L->R means left to right associativity.
- R->L means right to left associativity.
Global scope (unary)
Namespace scope (binary)
Uniform initialization (C++11)
Functional cast (C++11)
Member access from object
Member access from object ptr
Run-time type information
Cast away const
Run-time type-checked cast
Cast one type to another
Compile-time type-checked cast
typeid(type) or typeid(expression)
Size in bytes
Dynamic memory allocation
Dynamic array allocation
Dynamic memory deletion
Dynamic array deletion
sizeof(type) or sizeof(expression)
Member pointer selector
Member object selector
expression * expression
expression / expression
expression % expression
expression + expression
expression - expression
Bitwise shift left
Bitwise shift right
expression << expression
expression >> expression
Comparison less than
Comparison less than or equals
Comparison greater than
Comparison greater than or equals
expression < expression
expression <= expression
expression > expression
expression >= expression
expression == expression
expression != expression
|10 L->R||&||Bitwise AND||expression & expression|
|11 L->R||^||Bitwise XOR||expression ^ expression|
|12 L->R|||||Bitwise OR||expression | expression|
|13 L->R||&&||Logical AND||expression && expression|
|14 L->R||||||Logical OR||expression || expression|
Conditional (see note below)
Bitwise shift left assignment
Bitwise shift right assignment
Bitwise AND assignment
Bitwise OR assignment
Bitwise XOR assignment
expression ? expression : expression
lvalue = expression
lvalue *= expression
lvalue /= expression
lvalue %= expression
lvalue += expression
lvalue -= expression
lvalue <<= expression
lvalue >>= expression
lvalue &= expression
lvalue |= expression
lvalue ^= expression
|16 R->L||throw||Throw expression||throw expression|
|17 L->R||,||Comma operator||expression, expression|
You should already recognize a few of these operators, such as +, -, *, /, (), and sizeof. However, unless you have experience with another programming language, the majority of the operators in this table will probably be incomprehensible to you right now. That’s expected at this point. We’ll cover many of them in this chapter, and the rest will be introduced as there is a need for them.
C++ doesn’t include an operator to do exponentiation (operator^ has a different function in C++). We discuss exponentiation more in lesson %Failed lesson reference, id 8734%.
In normal arithmetic, you learned that you can use parenthesis to change the order of application of operations. For example, we know that 4 + 2 * 3 evaluates as 4 + (2 * 3), but if you want it to evaluate as (4 + 2) * 3 instead, you can explicitly parenthesize the expression to make it evaluate the way you want. This works in C++ because parenthesis have one of the highest precedence levels, so parenthesis generally evaluate before whatever is inside them.
Now consider an expression like x && y || z. Does this evaluate as (x && y) || z or x && (y || z)? You could look up in the table and see that && takes precedence over ||. But there are so many operators and precedence levels that it’s hard to remember them all. In order to reduce mistakes and make your code easier to understand without referencing a precedence table, it’s a good idea to parenthesize any non-trivial compound expression, so it’s clear what your intent is.
Use parenthesis to make it clear how an expression should evaluate, even if they are technically unnecessary.
You know from everyday mathematics that expressions inside of parentheses get evaluated first. For example, in the expression
(2 + 3) * 4, the
(2 + 3) part is evaluated first.
For this exercise, you are given a set of expressions that have no parentheses. Using the operator precedence and associativity rules in the table above, add parentheses to each expression to make it clear how the compiler will evaluate the expression.
Show Hint 
Sample problem: x = 2 + 3 % 4
Binary operator % has higher precedence than operator + or operator =, so it gets evaluated first:
x = 2 + (3 % 4)
Binary operator + has a higher precedence than operator =, so it gets evaluated next:
Final answer: x = (2 + (3 % 4))
We now no longer need the table above to understand how this expression will evaluate.
a) x = 3 + 4 + 5;
Show Solution 
b) x = y = z;
Show Solution 
c) z *= ++y + 5;
Show Solution 
d) a || b && c || d;
Show Solution 
|5.2 -- Arithmetic operators |
|4.x -- Chapter 4 summary and quiz |