Bitwise operators in C

We use Bitwise operators to manipulate data at its lowest level (bit level). Bitwise operators works on each bit of the data.

Data in the memory (RAM) is organized as a sequence of bytes. Each byte is a group of eight consecutive bits. Bitwise operators are useful when we need to perform actions on bits of the data.

Bitwise operators work with integer type. They do not support float or real types.

C has six Bitwise operators.

Operator Description
& Bitwise AND
| Bitwise OR
^ Bitwise XOR
~ Bitwise complement
<< Bitwise left shift
>> Bitwise right shift

Bitwise AND & operator

Bitwise AND is a binary operator. It sets each bit of the resultant value as 1 if corresponding bit in both operands is 1.

Suppose a and b are two integer variables with initial value
int a=10, b=11;

Let us re-write integers in 8-bit binary representation

a = 0000 1010
b = 0000 1011

c = a & b
The above expression a & b will evaluate to 0000 1010 which is 10 in decimal.

a       0000 1010
b       0000 1011
-----------------
a & b   0000 1010

Bitwise AND operator is used extensively to check whether a particular bit of data is on (1) or off (0).

Important Note: As a beginner do not get confused with bitwise AND & with logical AND &&.

Bitwise OR | operator

Bitwise OR is a binary operator. It sets each bit of the resultant value as 1 if corresponding bit of any of its two operand is 1.

Bitwise OR operator is commonly used to set flag bit values.

Suppose a and b are two integer variables with initial value as.
int a=2, b=13;

Let us re-write the integer in 8-bit binary representation.

a = 0000 0010
b = 0000 1101

c = a | b

The above expression a|b will evaluate to 0000 1111 which is 15 in decimal.

a       0000 0010
b       0000 1101
-----------------
a | b   0000 1111

Important note: Do not confuse between bitwise OR | and logical OR || operator.

Bitwise XOR ^ operator

Bitwise XOR operator is also binary operator. It sets each bit of the resultant value to 1 whenever the corresponding bits of the two operands differ.

Suppose a and b are two integer variables with initial value as.
int a=6, b=13;

Let us re-write the integers in 8-bit binary representation:

a = 0000 0110
b = 0000 1101

c = a ^ b

The above expression a^b will evaluate to 0000 1011 which is 11 in decimal.

a       0000 0110
b       0000 1101
-----------------
a ^ b	0000 1011

Important note: Do not confuse bitwise XOR ^ operator as exponential operator. There is no exponential operator supported by C.

Bitwise complement ~ operator

Bitwise complement is a unary operator. It sets each bit of the resultant value to 1 if corresponding bit of the operand is 0 and vice versa. In other words, it flips all bit values.

Suppose a is an integer variable with initial value as.
int a=2;

In 8-bit binary representation:

a = 0000 0010

c = ~a
The above expression ~a will evaluate to 1111 1101 which is -3 (2’s complement) in decimal.

a       0000 0010
-----------------
~a      1111 1101

Bitwise left shift << operator

Bitwise left shift is a binary operator. It is used to shift bits to left n times. Consider the below example:

int a=15;

Which in 8-bit binary will be represented as:

a = 0000 1111

c = a << 3;
The above expression a << 3; shifts bits of a three times to left and evaluates to 0111 1000 which is 120 in decimal.

a       0000 1111
a << 1  0001 1110
a << 2  0011 1100
a << 3  0111 1000

Shifting bits to left causes insertion of zero from right and shifting each bit to one position left from its current position. The most significant bit (the left most bit) is dropped off on every left shift.

Important note: Shifting bits to left is also equivalent to multiplying value by 2. You can use bitwise left shift operator if you need to multiply a variable by a power of two.

Bitwise right shift >> operator

Bitwise right shift is binary operator used to shift bits to right. Consider the below example:
int a=15;

Which in 8-bit binary will be represented as:

a = 0000 1111

c = a >> 3
The above expression a >> 3 shifts bits of variable a three times right and will evaluate to 0000 0001 which is 1 in decimal

a       0000 1111
a >> 1  0000 0111
a >> 2  0000 0011
a >> 3  0000 0001

Shifting bits to right causes insertion of 0 or 1 depending on the value of Most Significant Bit (the left most bit). Shifts each bit to one position right from its current position. After each right shift, the least significant bit (left most bit) is dropped off.

Important note: Shifting bits to right is equivalent to dividing by 2. We can use bitwise right shift operator in case we need to divide by power of 2.

In bitwise right shift 1 is inserted from right if the MSB is 1; otherwise 0 is inserted from right. However, in case of bitwise left shift always 0 is inserted from left.

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