Template:LogicalTruthPlugin: Difference between revisions
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│ '''false''' │ '''false''' │ true │ false │ false │ false │ true │ true │ | │ '''false''' │ '''false''' │ true │ false │ false │ false │ true │ true │ | ||
└───────┴───────┴───────┴─────────┴────────┴─────────┴─────────┴─────────┘ | └───────┴───────┴───────┴─────────┴────────┴─────────┴─────────┴─────────┘ | ||
'''Note:''' In most BASIC languages incl. QB64 these are bitwise operations, | '''Note:''' In most BASIC languages incl. QB64 these are '''bitwise''' operations, | ||
hence the logic is performed for each corresponding bit in both | hence the logic is performed for each corresponding bit in both | ||
operators, where '''true''' or '''false''' indicates whether a bit is '''set''' or | operators, where '''true''' or '''false''' indicates whether a bit is '''set''' or | ||
Revision as of 00:26, 15 December 2022
Table 4: The logical operations and its results.
In this table, 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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