Circuits / Combinational
XOR Gate & 3-Bit Odd Parity Checker
Cascades two 2-input XOR gates to compute A ⊕ B ⊕ C, outputting 1 whenever an odd number of inputs are 1.
An Exclusive-OR (XOR) gate outputs 1 when its two inputs differ (Y = A ⊕ B = A·~B + ~A·B) and 0 when they are equal.
Because XOR is associative, cascading two 2-input XOR gates computes the 3-bit XOR sum Parity = (A ⊕ B) ⊕ C, which is 1 whenever an odd number of inputs (one or all three) are High (1).
Notice that flipping any single input bit (A, B, or C) always flips the final Parity output—the exact property used by memory buses and serial links to detect single-bit transmission errors.
The same two-stage XOR cascade also computes the Sum bit (A ⊕ B ⊕ Cin) inside every Full Adder.
Tip: Click any row in the truth table to apply that (A, B, C) input combination directly to the schematic and watch the live wire colors update.
| A | B | C | Parity |
|---|---|---|---|
| 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 |