What does XNOR actually compute?

XNOR is NOT(A XOR B): it produces a 1 when the two input bits match (both 0 or both 1), and a 0 when they differ. It's the exact inverse of XOR at every bit position, and is also called the 'equivalence' gate for this reason.

What happens if my two values have different lengths?

The shorter value is left-padded with leading zero digits until it matches the longer value's digit count, then XNOR runs across every aligned bit position of that shared width, including the complement step.

Why is 1010 XNOR 0110 equal to 0011?

First XOR gives 1100 (the first two bit positions disagree). XNOR then flips every bit of that within the 4-bit width, turning 1100 into 0011.

Why is XNOR called the 'equivalence' gate?

XNOR outputs 1 exactly where the two inputs agree bit-for-bit, which is the logical definition of 'these two values are equal at this position' — that's why it's also known as the equivalence or 'bit match' gate.

Binary XNOR Calculator - Bitwise XNOR of Two Binary Values

Overview

Introduction

XNOR is the logical complement of XOR, and is useful whenever you want to know where two values agree rather than where they disagree.

This tool computes the bitwise XNOR of two binary values, so you can see exactly which bit positions match between the two inputs.

What Is Binary XNOR Calculator?

A calculator for the bitwise XNOR of two binary values: it XORs the two values bit by bit, then flips every bit of that result within the shared width, so matching bit positions end up as 1.

Like the other two-operand binary gate calculators in this category, it automatically left-pads the shorter operand with zero digits so both values line up bit-for-bit before combining them.

How Binary XNOR Calculator Works

Both Value A and Value B are validated as binary strings, then the shorter is left-padded with leading zero digits to match the longer value's digit count.

The padded values are combined bit-by-bit with XOR using BigInt, then the combined result is bitwise-inverted within that same shared width (masked so leading zero bits above the width aren't affected) to produce the final XNOR output.

When To Use Binary XNOR Calculator

Use it whenever you need to test bit-level equivalence between two values, such as counting how many bits two registers have in common.

It's also a useful teaching tool for showing how XNOR relates to XOR by simple inversion.

Often used alongside Binary XOR Calculator, Binary AND Calculator and Binary OR Calculator.

Features

Advantages

Automatically handles operands of different lengths by zero-padding, so you don't have to align widths by hand first.
Works on arbitrarily long binary values via BigInt, not limited to a fixed 8/16/32/64-bit width.
Instant, deterministic, fully client-side.

Limitations

Zero-padding the shorter operand assumes you want it treated as a smaller number within a larger field; pad manually first if your context expects different alignment.
Only combines two operands at a time; chain the tool manually if you need to XNOR together more than two values.

Examples

XNOR of two mixed bit patterns

Input

A: 1010, B: 0110

Output

1010 XOR 0110 = 1100, then inverting within the 4-bit width gives 0011.

XNORing a value with itself always gives all 1s

Input

A: 1010, B: 1010

Output

Every bit position matches, so every position agrees and the result is all 1s.

Best Practices & Notes

Best Practices

Confirm both values are the width you intend before relying on the auto-padding, since a short operand gets left-padded with zeros.
XOR a value with itself as a quick sanity check that XNOR of matching inputs returns all 1s.

Developer Notes

Implemented with JavaScript BigInt: after zero-padding both operands to the same digit width, it computes `~(a ^ b)` masked to that width, avoiding JavaScript's native 32-bit-limited bitwise operators and the infinite leading 1s an unmasked BigInt NOT would otherwise produce.

Binary XNOR Calculator Use Cases

Counting or highlighting matching bit positions between two binary values
Simulating digital logic circuits that use an equivalence/XNOR gate
Teaching or demonstrating the XNOR logic gate using concrete multi-bit binary examples

Common Mistakes

Confusing XNOR with AND; XNOR treats two matching 0 bits as a 1, while AND would treat that same case as a 0.
Forgetting that a short operand gets zero-padded on the left, which can change the intended meaning if it was meant to be right-aligned instead.

Tips

XNOR a value with itself to quickly confirm the tool produces all 1s, a handy sanity check.
Compare the result with the Binary XOR Calculator on the same inputs to see the exact inverse relationship.

Binary XNOR Calculator