A ⊕ B ⊕ C — truth table
coretrue on the 4 odd-parity rows
Answer
8 rows, 4 true (1, 2, 4, 7)
Why this example is worth doing
The output column is 1 exactly when an odd number of inputs is 1, which is the definition of odd parity and the reason this circuit appears at the transmit end of every parity-checked bus. Reading the table as a specification rather than a calculation is the skill being taught: the pattern of 1s tells you the function's name. The page links to the parity and checksum tool, where the same column is generated for eight and sixteen inputs instead of three.
Try your own input in the Truth table generator. Turn an expression into a full truth table, with a column for every sub-expression.
How the answer is reached
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 |