Components / Gates
XNOR Logic Gate in Logisim
Exclusive NOR (logical equivalence) gate (Y = ~(A ⊕ B)) that outputs 1 when two inputs are equal or when an even number of inputs are 1.
| Library | Gates |
|---|---|
| Type name | XNOR Gate |
| Pins and defaults | in0..inN (-50, ±10), out0 (0, 0), width 1..32, inputs 2..8 |
How the XNOR Works in Logisim
The XNOR Gate (Exclusive NOR) is an XOR gate followed by an inversion bubble (Y = ~(A ⊕ B) = A·B + ~A·~B). For two inputs, it functions as a 1-bit equality comparator: it outputs 1 when A and B are identical (0,0 or 1,1) and outputs 0 when they differ.
For three or more inputs (inputs = 3..8), the XNOR Gate evaluates even parity across its active inputs, outputting 1 whenever an even number of inputs (including zero inputs) are High (1). Like XOR, any E input propagates to an E output.
Tip: Combine four 2-input XNOR gates with a 4-input AND gate to build a fast 4-bit equality detector (A = B).
XNOR Pins & Pinout
| Pin | Direction | Width | Location & Role |
|---|---|---|---|
| in0 .. in(N-1) | Input (Left edge) | 1–32 bits | Located at x = -50. Configurable from 2 to 8 inputs. |
| out0 (out) | Output (Right tip) | 1–32 bits | Located at (0, 0). Outputs 1 when an even number of active inputs are 1. |
XNOR Truth Table & Behavior
| A | B | Y = ~(A ⊕ B) | Meaning |
|---|---|---|---|
| 0 | 0 | 1 | Inputs are equal (0 = 0) |
| 0 | 1 | 0 | Inputs differ |
| 1 | 0 | 0 | Inputs differ |
| 1 | 1 | 1 | Inputs are equal (1 = 1) |