Bitwise operations tend to be confusing because it uses some of the more cryptic symbols on the keyboard and what they do is less clear.
Code:
& - AND
| - inclusive OR (This is a pipe, SHIFT-\)
^ - exclusive OR (XOR)
~ - one's complement
<< - left shift
>> - right shift
AND:
Input 1 |
Input 2 |
Output |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
Usage:
x = x & 0177;
This will set every bit above the bottom 7 to 0, then save the lower 7 to their original state.
INCLUSIVE OR:
Input 1 |
Input 2 |
Output |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
Usage:
x = x | 0177;
This will set the bottom 7 bits to 1, and retain the rest from x.
EXCLUSIVE OR (XOR):
Input 1 |
Input 2 |
Output |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
Note the difference from inclusive OR by its behavior with two 1 inputs.
Usage:
x = x ^ 0177;
This will reverse the bottom 7 bits of x.
The advantage of ^ versus | is that you can get the original input again by XORing with the same number.
x == ( (x ^ 0177) ^ 0177)
This property means that XOR is used extensively in encryption applications.
ONE'S COMPLIMENT:
This is like XOR, but with only one number. It reverses every bit, so 0110 would become 1001.
Usage:
x = ~077;
This will set every bit in x to 1 except the bottom 6. This is an advantage because it doesn't matter what the word size of x is.
x = 0177700; Assumes x is a 16 bit value, if x is changed to a 32 or 64 bit value, you would have to go through and change every piece of code making assumptions about word size.
LEFT AND RIGHT SHIFT:
These two commands are probably the one's I use the most of any on this page. They shift the bits either left or right by the number given to it, then usually fills the rest with 0s.
Usage:
x = x<<2;
This would be equivalent to multiplying x by 4.
Note:
When you're right shifting an unsigned interger, the empty bits will be filled with 0s. When you're right shifting a signed interger, the results are less predictable and, depending on the machine, will either fill it with 0s or 1s.
For a huge list of possible uses for bitwise operations, see http://graphics.stanford.edu/~seander/bithacks.html
Sources:
The C Programming Language 2nd Ed., Kernighan & Ritchie, pg. 48-49.
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