# 6.5 Binary Operators

The binary operators are categorized as follows:

• Multiplicative operators: multiplication (*), remainder (%), and division (/) (see Section 6.5.1)

• Shift operators: left shift (<<) and right shift (>>) (see Section 6.5.3)

• Relational operators: less than (<), less than or equal to (<=), greater than (>), and greater than or equal to (>=) (see Section 6.5.4)

• Equality operators: equality (==) and inequality (!=) (see Section 6.5.5)

• Bitwise operators: AND (&), OR (|), and XOR (^) (see Section 6.5.6)

• Logical operators: AND (&&) and OR (||) (see Section 6.5.7)

The following sections describe these binary operators.

## 6.5.1 Multiplicative Operators

The multiplicative operators are *, /, and %. Operands must have arithmetic type. Operands are converted, if necessary, according to the usual arithmetic conversion rules (see Section 6.10.1).

The * operator performs multiplication.

The / operator performs division. When integers are divided, truncation is toward zero. If either operand is negative, the result is truncated toward zero (the largest integer of lesser magnitude than the algebraic quotient).

The % operator divides the first operand by the second and yields the remainder. Both operands must be integral. When both operands are unsigned or positive, the result is positive. If either operand is negative, the sign of the result is the same as the sign of the left operand.

The following statement is true if `b` is not zero:

```(a/b)*b + a%b == a;
```

The DEC C compiler, with the check option enabled, issues warnings for these undefined behaviors:

• Integer overflow occurs

• Division by zero is attempted

• Remainder by zero is attempted

The additive operators + and - perform addition and subtraction. Operands are converted, if necessary, according to the usual arithmetic conversion rules (see Section 6.10.1).

When two `enum` constants or variables are added or subtracted, the type of the result is `int` .

When an integer is added to or subtracted from a pointer expression, the integer is scaled by the size of the object being pointed to. The result has the pointer's type. For example:

```int arr;
int *p = arr;
p = p + 1;  /* Increments by sizeof(int) */
```

An array pointer can be decremented by subtracting an integral value from a pointer or address; the same conversions apply as for addition. Pointer arithmetic also applies one element beyond the end of the array. For example, the following code works because the pointer arithmetic is limited to the elements of the array and to only one element beyond:

```int i = 0;
int x = {0,1,2,3,4};
int y;
int *ptr = x;
while (&y[i] != (ptr + 5)) { /*  ptr + 5 marks one beyond the end of the array */
y[i] = x[i];
i++;
}
```

When two pointers to elements of the same array are subtracted, the result (calculated by dividing the difference between the two addresses by the length of one element) is of type `ptrdiff_t` , which in DEC C is `int` , and represents the number of elements between the two addressed elements. If the two elements are not in the same array, the result of this operation is undefined.

## 6.5.3 Shift Operators

The shift operators << and >> shift their left operand to the left or to the right, respectively, by the number of bits specified by the right operand. Both operands must be integral. The compiler performs integral promotions on each of the operands (see Section 6.10.1.1). The type of the result is the type of the promoted left operand. Consider the following expression:

```E1 << E2
```

The result is the value of expression E1 shifted to the left by E2 bits. Bits shifted off the end are lost. Vacated bits are filled with zeros. The effect of shifting left is to multiply the left operand by 2 for each bit shifted. In the following example, the value of `i` is 100:

```int n = 25;
int m = 2;
int i;

i = n << m;
```

Consider the following expression:

```E1 >> E2
```

The result is the value of expression E1 shifted to the right by E2 bits. Bits shifted off the end are lost. If E1 is `unsigned` or if E1 has a signed type but nonnegative value, vacated bits are filled with zeros. If E1 has a signed type and negative value, vacated bits are filled with ones.

The result of the shift operation is undefined if the right operand is negative or if its value is greater than the number of bits in an `int` .

For a nonnegative left operand, the effect of shifting right is to divide the left operand by 2 for each bit shifted. In the following example, the value of `i` is 12:

```int n = 100;
int m = 3;
int i;

i = n >> m;
```

## 6.5.4 Relational Operators

The relational operators compare two operands and produce a result of type `int` . The result is 0 if the relation is false, and 1 if it is true. The operators are: less than (<), greater than (>), less than or equal (<=), and greater than or equal (>=). Both operands must have an arithmetic type or must be pointers to compatible types. The compiler performs the necessary arithmetic conversions before the comparison (see Section 6.10.1).

When two pointers are compared, the result depends on the relative locations of the two addressed objects. Pointers to objects at lower addresses are less than pointers to objects at higher addresses. If two addresses indicate elements in the same array, the address of an element with a lower subscript is less than the address of an element with a higher subscript.

The relational operators associate from left to right. Therefore, the following statement relates `a` to `b` , and if `a` is less than `b` , the result is 1 (true). If `a` is greater than or equal to `b` , the result is 0 (false). Then, 0 or 1 is compared with `c` for the expression result. This statement does not determine "if `b` is between `a` and `c` ".

```if ( a < b < c )
statement;
```

To check if `b` is between `a` and `c` , use the following code:

```if ( a < b && b < c )
statement;
```

## 6.5.5 Equality Operators

The equality operators, equal (==) and not-equal (!=), produce a result of type `int` , so that the result of the following statement is 1 if both operands have the same value, and 0 if they do not:

```a == b
```

Operands must have one of the following type combinations:

• Both operands have an arithmetic type.

• Both operands are pointers to qualified or unqualified versions of compatible types.

• One operand is a pointer to an object or incomplete type and the other is a pointer to a qualified or unqualified version of `void` .

• One operand is a pointer and the other is a null pointer constant.

Operands are converted, if necessary, according to the usual arithmetic conversion rules (see Section 6.10.1).

Two pointers or addresses are equal if they identify the same storage location.

Note
Although different symbols are used for assignment (=) and equality (==), C allows either operator in all contexts, so be careful not to confuse them. Consider the following example:
```if ( x = 1 )
statement_1;
else
statement_2;
```
In this example, `statement_1` always executes, because the result of the assignment `x = 1` is equivalent to the value of `x` , which equals 1 (or true).

## 6.5.6 Bitwise Operators

The bitwise operators require integral operands. The usual arithmetic conversions are performed (see Section 6.10.1). The result of the expression is the bitwise AND (&), inclusive OR (|), or exclusive OR (^), of the two operands. The order of evaluation of their operands is not guaranteed.

The operands are evaluated bit by bit. The result of the & operator is 0 if one bit value is 0 and the other is 1, or if both bit values are 0. The result is 1 if both bit values are 1.

The result of the | operator is 0 if both bit values are 0. The result for each bit is 1 if either bit value is 1, or both bit values are 1.

The result of the ^ operator is 0 if both bit values are 0, or if both bit values are 1. The result for each bit is 1 if either bit value is 1 and the other is 0.

## 6.5.7 Logical Operators

The logical operators are AND (&&) and OR (||). These operators guarantee left-to-right evaluation. The result of the expression (of type `int` ) is either 0 (false) or 1 (true). The operands need not have the same type, but both types must be scalar. If the compiler can make an evaluation by examining only the left operand, the right operand is not evaluated. Consider the following expression:

```E1 && E2
```

The result of this expression is 1 if both operands are nonzero, or 0 if one operand is 0. If expression E1 is 0, expression E2 is not evaluated because the result is the same regardless of E2's value.

Similarly, the following expression is 1 if either operand is nonzero, and 0 otherwise. If expression E1 is nonzero, expression E2 is not evaluated, because the result is the same regardless of E2's value.

```E1 || E2
```