XNOR gate truth table
The XNOR gate outputs 1 when its two inputs are equal, and 0 when they differ. It is the inverse of XOR. Here is its full truth table, the boolean expression, and how it is actually built.
| A | B | Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Boolean expression: Y = (A ⊕ B)̅. A 1 in the table means a high voltage (logic true) and a 0 means low (false). Read each row as: for these inputs, the output Y is this value.
What the XNOR gate does
XNOR is a 1-bit equality test: its output is 1 exactly when the inputs match. Chain XNORs across two multi-bit numbers and AND the results and you have a comparator that tells you whether the numbers are equal.
Build it yourself
Reading a table is one thing; watching the signals flow is another. Open the logic gate simulator and wire a XNOR gate up from transistors, or read the full lesson on how this gate is designed. You can also generate the table for any expression with the truth table generator.
Other gates:
The XNOR gate is one small step toward a working CPU. Build every gate from CMOS transistors and work up to an 8-bit processor in the free digiwleea lab and course.
Open the gate simulator →Frequently asked
What is the truth table of a XNOR gate?
The XNOR gate outputs 1 when its two inputs are equal, and 0 when they differ. It is the inverse of XOR. For inputs (A,B) the outputs are 0,0→1 0,1→0 1,0→0 1,1→1.
What is the boolean expression for XNOR?
The XNOR gate is written Y = NOT (A XOR B) (symbolically Y = (A ⊕ B)).
How many transistors does a XNOR gate take?
A standard CMOS XNOR gate uses about 10 transistors. In digiwleea you build it from those transistors and the simulator verifies it against this exact truth table.