XNOR gate in redstone

On when the two inputs match. An XOR with one extra inverter on the output. Footprint 6 wide × 5 deep × 2 tall. Build it block by block in Minecraft.

How to build it

XNOR is "XOR followed by a NOT". Build the four-torch XOR, then tack one more inverter on its output.

  1. Build an XOR as described on the XOR page.
  2. Run the XOR's output dust into a new solid block.
  3. Attach a redstone torch to that block's far side.
  4. The torch's dust is the XNOR output: high when both inputs match, low when they differ.

Why it works

A XNOR B = ¬(A ⊕ B) — just one inversion on the XOR's output flips the truth table, lighting the output when A equals B.

Alternative

If you want XNOR directly without building XOR first, the expression (A ∧ B) ∨ (¬A ∧ ¬B) gives the same result — two ANDs and an OR. Same number of torches as the "XOR + NOT" version, but the wiring is a touch different. Pick whichever fits your space better.

Where you'll use it

Equality checks, parity-error detection, sign-bit comparison in comparators. If you're building a "does X equal Y?" test in a CPU, a row of XNORs is the start.

Gotchas