The Basics
At the heart of bit manipulation are the bit-wise operators&(and),|(or),~(not) and^(xor). The first three you should already be familiar with in their boolean forms (&&,||and!). As a reminder, here are the truth tables:
| A | B | !A | A && B | A \ | \ | B | A ^ B |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 | 0 | ||
| 0 | 1 | 1 | 0 | 1 | 1 | ||
| 1 | 0 | 0 | 0 | 1 | 1 | ||
| 1 | 1 | 0 | 1 | 1 | 0 |
The bit-wise versions of the operations are the same, except that instead of interpreting their arguments as true or false, they operate on each bit of the arguments.
Thus, if A is 1010 and B is 1100, then
- A & B = 1000
- A | B = 1110
- A ^ B = 0110
- ~A = 11110101 (the number of 1′s depends on the type of A).
The other two operators we will need are the shift operators
a << b and a>> b. The former shifts all the bits in a to the left by b positions; the latter does the same but shifts right.