AND, OR, XOR, Complement and Shift Operations (2024)

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.

OperatorsMeaning of operators
&Bitwise AND
|Bitwise OR
^Bitwise XOR
~Bitwise complement
Shift left
>>Shift right

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 <stdio.h>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 <stdio.h>int main() { int a = 12, b = 25;

printf("Output = %d", a | b);

return 0;}

Output

Output = 29

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 <stdio.h>int main() { int a = 12, b = 25;

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

return 0;}

Output

Output = 21

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)

Example 4: Bitwise complement

#include <stdio.h>int main() {

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

return 0;}

Output

Output = -36Output = 11

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)

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 = 110101000 (In binary) [Left shift by one bit]212<<0 = 11010100 (Shift by 0)212<<4 = 110101000000 (In binary) =3392(In decimal)

Example #5: Shift Operators

#include <stdio.h>int main() { int num=212, i; for (i = 0; i <= 2; ++i) {

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

} printf("\n"); for (i = 0; i <= 2; ++i) {

printf("Left shift by %d: %d\n", i, num << i);

} return 0;}
Right Shift by 0: 212Right Shift by 1: 106Right Shift by 2: 53Left Shift by 0: 212Left Shift by 1: 424Left Shift by 2: 848
AND, OR, XOR, Complement and Shift Operations (2024)

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