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Bit xor

BITXOR Function

The BITXOR function in Excel performs a bitwise XOR (exclusive OR) operation between the binary representations of two numbers. The XOR operation compares each bit in the binary forms of the two numbers, and the result is 1 if the bits are different and 0 if the bits are the same.

In simpler terms:

  • If a bit in one number is 1 and the corresponding bit in the other is 0, the result bit will be 1.
  • If both corresponding bits are the same (both 1 or both 0), the result bit will be 0.

Key Features of BITXOR:

  • Outputs the binary XOR operation between two integers.
  • The result combines binary values from two numbers where differences in their bits determine 1, and similarities determine 0.
  • Useful for cryptography, binary logic, and low-level data manipulation.

Syntax:

BITXOR(number1, number2)
  • number1: A non-negative integer.
  • number2: A non-negative integer.

Examples:

  1. Basic XOR Operation:
    =BITXOR(5, 3)
    Binary representation of 5 is 0101, and 3 is 0011.
    XOR operation: 

    0101
0011
----
0110
    Binary 0110 is 6 in decimal.
    Result: 6

  2. XOR with Zero:
    =BITXOR(7, 0)
    Binary representation of 7 is 0111. XOR with zero leaves the number unchanged.
    Result: 7

  3. XOR of Same Numbers:
    =BITXOR(9, 9)
    Binary representation of 9 is 1001. XOR of any number with itself results in 0 because every bit is the same.
    Result: 0

  4. XOR with Larger Numbers:
    =BITXOR(15, 6)
    Binary representation of 15 is 1111, and 6 is 0110.
    XOR operation: 

    1111
0110
----
1001
    Binary 1001 is 9 in decimal.
    Result: 9

Notes:

  • Non-Negative Numbers Only:

    • The inputs number1 and number2 must be non-negative integers. Negative inputs will result in a #NUM! error.

  • Error for Non-Integers:

    • If either number1 or number2 is not an integer, Excel returns a #VALUE! error.

  • Behavior with XOR:

    • XOR always clears (results in 0) when both bits are the same.
    • XOR is commutative: BITXOR(a, b) equals BITXOR(b, a).

Applications:

  • Use Case:

    • Useful for toggling bits or performing simple cryptographic operations.
    • Ensures differentiation between changes in binary data.

  • Complementary Functions:

    • BITAND: Performs a bitwise AND operation.
    • BITOR: Performs a bitwise OR operation.
    • BITLSHIFT: Shifts bits to the left by a specified number.
    • BITRSHIFT: Shifts bits to the right by a specified number.