In C, bitwise operators are used to perform operations directly on the binary representations of numbers. These operators work by manipulating individual bits (0s and 1s) in a number.
The following 6 operators are bitwise operators (also known as bit operators as they work at the bit-level). They are used to perform bitwise operations in C.
- The & (bitwise AND) in C takes two numbers as operands and does AND on every bit of two numbers. The result of AND is 1 only if both bits are 1.
- The | (bitwise OR) in C takes two numbers as operands and does OR on every bit of two numbers. The result of OR is 1 if any of the two bits is 1.
- The ^ (bitwise XOR) in C takes two numbers as operands and does XOR on every bit of two numbers. The result of XOR is 1 if the two bits are different.
- The << (left shift) in C takes two numbers, the left shifts the bits of the first operand, and the second operand decides the number of places to shift.
- The >> (right shift) in C takes two numbers, right shifts the bits of the first operand, and the second operand decides the number of places to shift.
- The ~ (bitwise NOT) in C takes one number and inverts all bits of it.
Let’s look at the truth table of the bitwise operators.
X | Y | X & Y | X | Y | X ^ Y |
|---|
0 | 0 | 0 | 0 | 0 |
|---|
0 | 1 | 0 | 1 | 1 |
|---|
1 | 0 | 0 | 1 | 1 |
|---|
1 | 1 | 1 | 1 | 0 |
|---|
Outputa&b = 1
a|b = 13
a^b = 12
~a = 4294967290
b<<1 = 18
b>>1 = 4
Interesting Facts About Bitwise Operators
- Shift Operators: Left-shift (<<) and right-shift (>>) should not be used with negative numbers. Shifting by a negative number or more than the size of the integer leads to undefined behavior. No shift occurs if the number of shifts is 0.
- Bitwise OR (|): The OR of two numbers is like adding them if no carry occurs. If there is a carry, the sum is calculated as a | b + a & b.
- Bitwise XOR (^): Very useful in programming problems. For example, finding the odd occurring number in a set where all other numbers occur even times can be done efficiently using XOR.
- Logical vs Bitwise: Bitwise operators should not replace logical operators. Logical operators (&&, ||, !) return 0 or 1, while bitwise operators return an integer value.
- Shift and Arithmetic: Left-shift (<<) is equivalent to multiplication by 2, and right-shift (>>) is equivalent to division by 2 for positive numbers.
Outputx << 1 = 38
x >> 1 = 9
- Check Odd/Even: The AND operator (&) can quickly check if a number is odd or even. (x & 1) is non-zero if x is odd, and 0 if even.
Time Complexity: O(1)
Auxiliary Space: O(1)
- Bitwise NOT (~): Should be used carefully. Applying ~ can produce large numbers for unsigned variables or negative numbers for signed variables due to 2’s complement representation.
