# Logical Operations

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## Abstract

In this chapter, we define and analyze the four basic logical operations: the unary “not”, or complement, and the binary “and”, “inclusive or” and “exclusive or”. These are commonly known as *bit-wise* operations, as each one may be computed by performing a certain operation on each bit of its argument (in the unary case) or each pair of corresponding bits of its arguments (for binary operations). For example, the logical “and” Open image in new window of two bit vectors may be specified in a bit-wise manner as the bit vector *z* such that for all \(k \in \mathbb {N}\), *z*[*k*] = 1 iff *x*[*k*] = *y*[*k*] = 1.

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