Sometimes, it is more feasible to perform bit by bit operations, especially for performance boost in graphics rendering, in machine level communication, and even in communication via network. Recall that 0 signifies false and 1 signifies true, therefore, 0 and 1 are called truth values. Practically, at machine level, 0 is represented by low voltage and 1 is represented by high voltage. Let us see what happens when we apply bitwise operators on these truth values.
This table illustrates bit wise operation at a single bit level. At a higher level (8-bit, 16-bit etc. ), bitwise operations are as follows:
35 in 8-bit representation - 0010 0011
18 in 8-bit representation - 0001 0010
35 & 18 - 0000 0010 (i.e, 2)
Here is a code example that illustrates all the Bitwise operators.
Output:
>> and << were not mentioned before, because their operation is a bit different from &, | and ^. However, they are quite simple. These operators are called Shift operators. << for Left Shift and >> for Right Shift.
35 << 1 tells the compiler to shift all the bits (in bit-level representation of 35) towards the left by 1 step. So 0010 0011 << 1 returns 0100 0110 which is 70
Similarly, 0010 0011 >> 1 returns 0001 0001 which is 17 (By shifting all bits of 35 towards right by 1 step). You can experiment by using some other number instead of 1.
During shifting, the spaces are filled by zeroes.
An interesting thing to note here is, Left shift by 1 step Multiplies the number by 2 and Right shift by 1 step Divides the number by 2.
Therefore, result of 35 << 1 is same as 35 * 2 i.e 70, and result of 35 >> 1 is same as 35 / 2 i.e, 17 (integer division).
Generalized formulae:
A
|
B
|
A&B
(A AND B)
|
A|B (A OR B)
|
A^B (A XOR B)
|
~A (NOT A)
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
This table illustrates bit wise operation at a single bit level. At a higher level (8-bit, 16-bit etc. ), bitwise operations are as follows:
35 in 8-bit representation - 0010 0011
18 in 8-bit representation - 0001 0010
35 & 18 - 0000 0010 (i.e, 2)
Here is a code example that illustrates all the Bitwise operators.
#include <stdio.h> int main() { int a = 35; int b = 18; printf (" a & b = %d\n", a & b ); printf (" a | b = %d\n", a | b ); printf (" a ^ b = %d\n", a ^ b ); printf (" ~a = %d\n", ~a ); printf (" a << 1 = %d\n", a << 1); printf (" a >> 1 = %d\n", a >> 1); }
Output:
>> and << were not mentioned before, because their operation is a bit different from &, | and ^. However, they are quite simple. These operators are called Shift operators. << for Left Shift and >> for Right Shift.
35 << 1 tells the compiler to shift all the bits (in bit-level representation of 35) towards the left by 1 step. So 0010 0011 << 1 returns 0100 0110 which is 70
Similarly, 0010 0011 >> 1 returns 0001 0001 which is 17 (By shifting all bits of 35 towards right by 1 step). You can experiment by using some other number instead of 1.
During shifting, the spaces are filled by zeroes.
An interesting thing to note here is, Left shift by 1 step Multiplies the number by 2 and Right shift by 1 step Divides the number by 2.
Therefore, result of 35 << 1 is same as 35 * 2 i.e 70, and result of 35 >> 1 is same as 35 / 2 i.e, 17 (integer division).
Generalized formulae:
- For Left shift - a << b = a * pow (2, b)
- For Right shift - a >> b = a / pow (2, b)
Here, pow(); is an inbuilt function available in header file <math.h>, which results '2 raised to power b'
The next Section will discuss about reaming operators.
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