Editing Bitwise operation (section)

===AND===
[[File:0...15 AND.svg|thumb|Bitwise AND of [[4-bit computing|4-bit]] integers]]
A '''bitwise AND''' is a [[binary operation]] that takes two equal-length binary representations and performs the [[logical AND]] operation on each pair of the corresponding bits. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1&nbsp;× 1&nbsp;= 1); otherwise, the result is 0 (1&nbsp;× 0&nbsp;= 0 and 0&nbsp;× 0&nbsp;= 0). For example:

     010'''1''' (decimal 5)
 AND 001'''1''' (decimal 3)
   = 000'''1''' (decimal 1)

The operation may be used to determine whether a particular bit is ''set'' (1) or ''cleared'' (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:

     00'''1'''1 (decimal 3)
 AND 00'''1'''0 (decimal 2)
   = 00'''1'''0 (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.)

The bitwise AND may be used to clear selected bits (or [[Flag word|flags]]) of a [[Processor register|register]] in which each bit represents an individual [[Boolean data type|Boolean state]]. This technique is an efficient way to store a number of Boolean values using as little memory as possible.

For example, 0110 (decimal 6) can be considered a set of four flags numbered from right to left, where the first and fourth flags are clear (0), and the second and third flags are set (1). The third flag may be cleared by using a bitwise AND with the pattern that has a zero only in the third bit:

     0'''1'''10 (decimal 6)
 AND 1'''0'''11 (decimal 11)
   = 0'''0'''10 (decimal 2)

Because of this property, it becomes easy to check the [[Parity (mathematics)|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)

Because 6 AND 1 is zero, 6 is divisible by two and therefore even.