AND
A bitwise AND takes two binary representations of equal length and performs the logical AND operation on each pair of corresponding bits. The result in each position is 1 if the first bit is 1 and the second bit is 1; otherwise, the result is 0. In this, we perform the multiplication of two bits; i.e., 1 × 0 = 0 and 1 × 1 = 1. For example:
0101 (decimal 5)
AND 0011 (decimal 3)
= 0001 (decimal 1)
This may be used to determine whether a particular bit is set (1) or clear (0). For example, given a bit pattern 0011 (decimal 3), to determine whether the second bit is set we use a bitwise AND with a bit pattern containing 1 only in the second bit:
0011 (decimal 3)
AND 0010 (decimal 2)
= 0010 (decimal 2)
Because the result 0010 is non-zero, we know the second bit in the original pattern was set. This is often called bit masking. (By analogy, the use of masking tape covers, or masks, portions that should not be altered or portions that are not of interest. In this case, the 0 values mask the bits that are not of interest.)
If we store the result, this may be used to clear selected bits in a register. Given the example 0110 (decimal 6), the second bit may be cleared by using a bitwise AND with the pattern that has a zero only in the second bit:
0110 (decimal 6)
AND 1101 (decimal 13)
= 0100 (decimal 4)
Because of this property, it becomes easy to check the parity of a binary number by checking the value of the lowest valued bit. Using the example above:
0110 (decimal 6)
AND 0001 (decimal 1)
= 0000 (decimal 0)
Therefore 6 is divisible by two and even.