3-input XOR, A = 1, B = 1, C = 1 — XOR gate
coreodd parity, not exactly-one
Answer
output 1
Why this example is worth doing
All three inputs high gives 1, which surprises anyone carrying the exactly-one reading forward from two inputs. A multi-input XOR is odd-parity: it is 1 when an odd number of inputs are 1, and three is odd. The page makes this the headline caution of the page, since it is also the trap behind the IEC =1 qualifier discussed on the symbols page, where the rectangular symbol genuinely does mean exactly-one.
Try your own input in the XOR gate. Truth table, symbol and algebraic form for A ⊕ B, the difference detector.
How the answer is reached
The probed row
A = 1, B = 1, C = 11— Row 7 of 8.
Truth table
| # | A | B | C | A ⊕ B ⊕ C |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 2 | 0 | 1 | 0 | 1 |
| 3 | 0 | 1 | 1 | 0 |
| 4 | 1 | 0 | 0 | 1 |
| 5 | 1 | 0 | 1 | 0 |
| 6 | 1 | 1 | 0 | 0 |
| 7 | 1 | 1 | 1 | 1 |