Template:LogicalTruthPlugin: Difference between revisions

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   The results of the bitwise logical operations, where '''A''' and '''B''' are operands,
              Table 4: The logical operations and its results.
        and '''true''' or '''false''' indicate whether a bit is set or not set:
 
   ┌───────────────┬────────────────────────────────────────────────────────┐
   The results of the logical operations, where '''A''' and '''B''' are the [[Expressions]]
   │   '''Operands'''    │                  '''Logical operations'''                   │
  to invert or combine. Both may be results of former [[Boolean]] evaluations.
   ├───────┬───────┼───────┬─────────┬────────┬─────────┬─────────┬─────────┤
   ┌────────────────────────────────────────────────────────────────────────┐
   │  '''A'''   │  '''B'''   │ [[NOT]] B │ A [[AND]] B │ A [[OR]] B │ A [[XOR]] B │ A [[EQV]] B │ A [[IMP]] B │
   │                           '''[[Logical operations]]'''                           │
   ├───────┬───────┬───────┬─────────┬────────┬─────────┬─────────┬─────────┤
   │  A  │  B  │ [[NOT]] B │ A [[AND]] B │ A [[OR]] B │ A [[XOR]] B │ A [[EQV]] B │ A [[IMP]] B │
   ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤
   ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤
   │ '''true'''  │ '''true'''  │ false │  true  │ true  │  false  │  true  │  true  │
   │ '''true'''  │ '''true'''  │ false │  true  │ true  │  false  │  true  │  true  │
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   │ '''false''' │ '''false''' │ true  │  false  │ false  │  false  │  true  │  true  │
   │ '''false''' │ '''false''' │ true  │  false  │ false  │  false  │  true  │  true  │
   └───────┴───────┴───────┴─────────┴────────┴─────────┴─────────┴─────────┘
   └───────┴───────┴───────┴─────────┴────────┴─────────┴─────────┴─────────┘
    [[Relational Operations]] return '''negative one''' (-1, all bits set) and '''zero'''
  '''Note:''' In most BASIC languages incl. QB64 these are bitwise operations,
  (0, no bits set) for '''true''' and '''false''', respectively. This allows relational
        hence the logic is performed for each corresponding bit in both
  tests to be inverted and combined using the bitwise logical operations.
        operators, where '''true''' or '''false''' indicates whether a bit is set or
        not set. The outcome of each bit is then placed into the respective
        position to build the bit pattern of the final result value.
 
  As all [[Relational Operations]] return '''negative one''' (-1, all bits set) for
    '''true''' and '''zero''' (0, no bits set) for '''false''', this allows us to use these
    bitwise logical operations to invert or combine any relational checks,
    as the outcome is the same for each bit and so always results into a
            '''true''' (-1) or '''false''' (0) again for further evaluations.
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Revision as of 23:58, 14 December 2022

               Table 4: The logical operations and its results.

  The results of the logical operations, where A and B are the Expressions
  to invert or combine. Both may be results of former Boolean evaluations.
  ┌────────────────────────────────────────────────────────────────────────┐
  │                           Logical operations                           │
  ├───────┬───────┬───────┬─────────┬────────┬─────────┬─────────┬─────────┤
  │   A   │   B   │ NOT B │ A AND B │ A OR B │ A XOR B │ A EQV B │ A IMP B │
  ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤
  │ true  │ true  │ false │  true   │ true   │  false  │  true   │  true   │
  ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤
  │ true  │ false │ true  │  false  │ true   │  true   │  false  │  false  │
  ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤
  │ false │ true  │ false │  false  │ true   │  true   │  false  │  true   │
  ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤
  │ false │ false │ true  │  false  │ false  │  false  │  true   │  true   │
  └───────┴───────┴───────┴─────────┴────────┴─────────┴─────────┴─────────┘
  Note: In most BASIC languages incl. QB64 these are bitwise operations,
        hence the logic is performed for each corresponding bit in both
        operators, where true or false indicates whether a bit is set or
        not set. The outcome of each bit is then placed into the respective
        position to build the bit pattern of the final result value.

   As all Relational Operations return negative one (-1, all bits set) for
    true and zero (0, no bits set) for false, this allows us to use these
    bitwise logical operations to invert or combine any relational checks,
    as the outcome is the same for each bit and so always results into a
            true (-1) or false (0) again for further evaluations.
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