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.
| Operators | Meaning 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 = -36 Output = 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: 212 Right Shift by 1: 106 Right Shift by 2: 53 Left Shift by 0: 212 Left Shift by 1: 424 Left Shift by 2: 848