Binary and
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If two conditions are combined by and, they must both be true for the compound condition to be true as well.
Likewise, two bits may be combined with and:
| x | y | x AND y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
I.e. the result is 1, if both x and y are 1, and 0 otherwise. If 0 is equated with false, and 1 with true the bit and operation works like our logical and.
Binary and can work on binary numbers of any size, the numbers are simply anded digit by digit. For example:
x: 10001101
y: 01010111
x AND y: 00000101
(Only in the first, and third column from the right, both operands had 1 digits.)
and is often called masking, because y can be seen as a mask which is transparent (1) in some places (x will shine through), and black (0) in others (x will be blocked).