Binary Bitwise XNOR

What Is Bitwise XNOR on Binary Numbers?

The bitwise XNOR (Exclusive NOR) operation compares binary numbers bit by bit. It is the logical negation of the bitwise XOR operation. For each bit position, the output bit is 1 if the inputs are identical (both 1 or both 0) and 0 if they differ. Because of this, XNOR is also known as the equivalence gate or comparator in digital logic.

How Bitwise XNOR Works

Align the binary inputs by their least significant bits, pad them to a consistent bit width, perform the XOR operation across all numbers, and invert the final result. In a two-input truth table:

• 1 XNOR 1 = 1
• 1 XNOR 0 = 0
• 0 XNOR 1 = 0
• 0 XNOR 0 = 1

For multiple inputs (more than two), the bitwise XOR returns 1 if an odd number of inputs are 1. The bitwise XNOR negates that result, returning 1 when an even number of inputs (including zero inputs) are 1.

Example: XNOR of 11001100, 10101010, and 11110000:

  11001100
^ 10101010
^ 11110000
----------
  10010110  (Intermediate XOR Result - odd ones count)
  
~ 10010110  (NOT operation)
----------
  01101001  (Final XNOR Result)
    

Result: 01101001 (decimal 105).

Applications of Bitwise XNOR

• Parity Generation: Used in error detection systems to compute and verify even parity across data lines.
• Binary Comparators: XNOR circuits are the fundamental building blocks of digital hardware comparators that test if two binary numbers are equal.
• Cryptographic Algorithms: Frequently combined with XOR for key scheduling, block mixing, and logical hashing.