D is 1 when an odd number of inputs are 1, which is the odd-parity function.
| A | B | C | D |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
Sum of products (rows where D = 1):
\(D = \overline{A}\,\overline{B}C + \overline{A}B\overline{C} + A\overline{B}\,\overline{C} + ABC\)
Simplified: \(D = A \oplus B \oplus C\) — two XOR gates.
Applied to the given waveforms, segment by segment between input edges: D = 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0.
— rhs