Binary Bitwise NOR

What Is Bitwise NOR on Binary Numbers?

The bitwise NOR (Not OR) operation compares binary numbers bit by bit. It is the exact logical negation of the bitwise OR operation. An output bit is 1 only if all corresponding input bits are 0; otherwise, the output bit is 0. NOR is a universal logic gate in electronics, meaning any other logic gate (AND, OR, NOT, XOR) can be constructed using only NOR gates.

How Bitwise NOR Works

Align the binary numbers by their least significant bits (padding shorter inputs with leading zeros), apply the OR operation, and then invert (NOT) all the resulting bits. For a direct truth table:

• 1 NOR 1 = 0
• 1 NOR 0 = 0
• 0 NOR 1 = 0
• 0 NOR 0 = 1

Example: NOR of 11001100, 10101010, and 11110000 (with an 8-bit width):

  11001100
| 10101010
| 11110000
----------
  11111110  (Intermediate OR Result)
  
~ 11111110  (NOT operation)
----------
  00000001  (Final NOR Result)
    

Result: 00000001 (decimal 1).

Significance of Bitwise NOR

• Universal Gate: NOR gates can be combined to implement any boolean algebraic function.
• Inverting Logic: Useful for checking if all conditions/flags are completely inactive (all zeros).
• Digital Circuit Design: Hardware engineers use NOR-only structures to optimize silicon space and propagation delays.