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A bitwise operator treats its operands as a vector of bits rather than a single number. Boolean bitwise operators combine bit N of each operand using a Boolean function (NOT, AND, OR, XOR) to produce bit N of the result.

For example, a bitwise AND operator ("&" in C) would evaluate 13 & 9 as (binary) 1101 & 1001 = 1001 = 9, whereas, the logical AND, (C "&&") would evaluate 13 && 9 as TRUE && TRUE = TRUE = 1.

In some languages, e.g. Acorn's BASIC V, the same operators are used for both bitwise and logical operations. This usually works except when applying NOT to a value x which is neither 0 (false) nor -1 (true), in which case both x and (NOT x) will be non-zero and thus treated as TRUE.

Other operations at the bit level, which are not normally described as "bitwise" include shift and rotate.
This article is provided by FOLDOC - Free Online Dictionary of Computing (


Dealing with bits rather than larger structures such as a byte. For example, each of the eight bits in a byte can be used as an individual flag to signal yes/no, on/off (1 or 0) about some condition. The Boolean operators AND, OR and NOT also deal with individual bits rather than bytes.

Bitwise operators are programming commands that work with individual bits. The primary ones are:

Symbol   Function

    <<     Shift left 4 bits
    >>     Shift right 4 bits
    &      AND
    |      OR
    ^      XOR (Exclusive OR)
    ~      NOT (0 to 1; 1 to 0)
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We compute the bitwise exclusive-OR of the zero-watermark [W.sub.a] with [A'.sub.i] and we get the detected copyright watermark W':
(4) For the range associated with each chunk, apply a bitwise logical OR operation of all bit vectors in this range with [2.sup.RuleID].
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Significance checks are always done with bitwise AND operation.
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Feistel ciphers have a repetitive structure where each stage or round of calculations involves splitting the input into two halves ([L.sub.i-1], [R.sub.i-1]), passing the right input [R.sub.i-1] to the left output [L.sub.i], and computing the right output Ri by taking the bitwise exclusive-or of the left input [L.sub.i-1] with a function of the right input [R.sub.i-1] and subkey [K.sub.i] denoted by F([R.sub.i-1], [K.sub.i]).
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The [P'.sub.train] is subjected to a bitwise XOR operation with the plaintext [P.sub.train] of the training set, and the error percentage is calculated, which is called the training error.
where XOR denotes the bitwise operations with exclusive-OR (XOR).
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