Template:LogicalTruthPlugin

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.