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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
bitwise
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.
(1995-05-12)