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4.2.6 : Xor
The last main boolean operator is XOR. XOR is eXclusive OR. As we know, the OR operator renders true as long as at least one value is true. The XOR operator only renders true as long as only one value is true. This mean if both values are true, the XOR is false. The Digital Logic Workbench refers to XOR as EOR. The name isn't as important as what happens though. It is very important to know the different between OR and XOR.
Notation: x ⊕ y
| x | y | x ⊕ y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
{
"width":312,
"height":108,
"showToolbox":false,
"devices":[
{"type":"Toggle","id":"dev0","x":108,"y":12,"label":"X"},
{"type":"Toggle","id":"dev1","x":108,"y":60,"label":"Y"},
{"type":"DC","id":"dev2","x":52,"y":36,"label":"DC"},
{"type":"EOR","id":"dev3","x":164,"y":36,"label":"EOR"},
{"type":"LED","id":"dev4","x":220,"y":36,"label":"LED"}
],
"connectors":[
{"from":"dev0.in0","to":"dev2.out0"},
{"from":"dev1.in0","to":"dev2.out0"},
{"from":"dev3.in0","to":"dev0.out0"},
{"from":"dev3.in1","to":"dev1.out0"},
{"from":"dev4.in0","to":"dev3.out0"}
]
}
In set theory, XOR is the same thing as the symmetric difference, or disjunctive union of two sets. The disjunctive union (∆) of two sets are the values that are in one set, but not the other.
Practice Problems
Will (x ⊕ x) ever be true?