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In the arithmetic-logic unit (which is within the CPU), mathematical operations like: addition, subtraction, multiplication and division are done in bit-level. To perform bit-level operations in C programming, bitwise operators are used.

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Bitwise AND Operator &

The output of bitwise AND is 1 if the corresponding bits of two operands is 1. If either bit of an operand is 0, the result of corresponding bit is evaluated to 0.

In C Programming, the bitwise AND operator is denoted by &.

Let us suppose the bitwise AND operation of two integers 12 and 25.

12 = 00001100 (In Binary)
25 = 00011001 (In Binary)

Bit Operation of 12 and 25
  00001100
& 00011001
  ________
  00001000  = 8 (In decimal)

Example 1: Bitwise AND

#include 

int main() {

    int a = 12, b = 25;
    printf("Output = %d", a & b)
;

    return 0;
}

Output

Output = 8

---

Bitwise OR Operator |

The output of bitwise OR is 1 if at least one corresponding bit of two operands is 1. In C Programming, bitwise OR operator is denoted by |.

12 = 00001100 (In Binary)
25 = 00011001 (In Binary)

Bitwise OR Operation of 12 and 25
  00001100
| 00011001
  ________
  00011101  = 29 (In decimal)

Example 2: Bitwise OR

#include 

int main()  b);


    return 0;

Output

Output = 29

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Bitwise XOR (exclusive OR) Operator ^

The result of bitwise XOR operator is 1 if the corresponding bits of two operands are opposite. It is denoted by ^.

12 = 00001100 (In Binary)
25 = 00011001 (In Binary)

Bitwise XOR Operation of 12 and 25
  00001100
^ 00011001
  ________
  00010101  = 21 (In decimal)

Example 3: Bitwise XOR

#include 

int main() {

    int a = 12, b = 25;
    printf("Output = %d", a ^ b);

    return 0;
}

Output

Output = 21

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Bitwise Complement Operator ~

Bitwise complement operator is a unary operator (works on only one operand). It changes 1 to 0 and 0 to 1. It is denoted by ~.

35 = 00100011 (In Binary)

Bitwise complement Operation of 35
~ 00100011 
  ________
  11011100  = 220 (In decimal)

Twist in Bitwise Complement Operator in C Programming

The bitwise complement of 35 (~35) is -36 instead of 220, but why?

For any integer n, bitwise complement of n will be -(n + 1). To understand this, you should have the knowledge of 2’s complement.

2’s Complement

Two’s complement is an operation on binary numbers. The 2’s complement of a number is equal to the complement of that number plus 1. For example:

 Decimal         Binary           2's complement 
   0            00000000           -(11111111+1) = -00000000 = -0(decimal)
   1            00000001           -(11111110+1) = -11111111 = -256(decimal)
   12           00001100           -(11110011+1) = -11110100 = -244(decimal)
   220          11011100           -(00100011+1) = -00100100 = -36(decimal)

Note: Overflow is ignored while computing 2's complement.

The bitwise complement of 35 is 220 (in decimal). The 2’s complement of 220 is -36. Hence, the output is -36 instead of 220.

Bitwise Complement of Any Number N is -(N+1). Here’s how:

bitwise complement of N = ~N (represented in 2's complement form)
2'complement of ~N= -(~(~N)+1) = -(N+1)

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Example 4: Bitwise complement

#include 

int main() {

    printf("Output = %d\n", ~35);
    printf("Output = %d\n", ~-12);

    return 0;
}

Output

Output = -36
Output = 11

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Shift Operators in C programming

There are two shift operators in C programming:

• Right shift operator
• Left shift operator.

Right Shift Operator

Right shift operator shifts all bits towards right by certain number of specified bits. It is denoted by >>.

212 = 11010100 (In binary)
212 >> 2 = 00110101 (In binary) [Right shift by two bits]
212 >> 7 = 00000001 (In binary)
212 >> 8 = 00000000 
212 >> 0 = 11010100 (No Shift)

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Left Shift Operator

Left shift operator shifts all bits towards left by a certain number of specified bits. The bit positions that have been vacated by the left shift operator are filled with 0. The symbol of the left shift operator is <<<>.

212 = 11010100 (In binary)
212<<1>

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Example #5: Shift Operators

#include 

int main() {

    int num=212, i;

    for (i = 0; i <=>        printf("Right shift by %d: %d\n", i, num >> i);

}