xor_without_operator

The xor_without_operator function computes the XOR (exclusive OR) of two 8-bit unsigned integers without directly using the ^ operator. It achieves this by using bitwise OR (|) and bitwise NOT (~) operations.

Function Code

uint8_t xor_without_operator(uint8_t x, uint8_t y)
{
    return (x | y) & (~x | ~y);
}

How It Works

To understand how this function works, let's break it down step-by-step:

1. Bitwise OR: (x | y)

   • This operation sets a bit to 1 if the corresponding bit in either x or y is 1.

2. Bitwise NOT: (~x | ~y)

   • This operation first inverts the bits of x and y, then performs a bitwise OR. This sets a bit to 1 if the corresponding bit in either ~x or ~y is 1.

3. Bitwise AND: (x | y) & (~x | ~y)

   • This final step performs a bitwise AND between the results of the previous two operations. This sets a bit to 1 only if the corresponding bit in both (x | y) and (~x | ~y) is 1.

The final result of these operations gives the same result as x ^ y.

Example

Let's consider an example where x = 5 and y = 3.

1. Binary Representation:

   • x = 5 (binary 00000101)
   • y = 3 (binary 00000011)

2. Step-by-Step Execution:

• Initial Values:
  • x = 5 (binary 00000101)
  • y = 3 (binary 00000011)

return (x | y) & (~x | ~y);

• Bitwise OR:

  • x | y = 00000101 | 00000011 = 00000111

• Bitwise NOT:

  • ~x = 11111010
  • ~y = 11111100
  • ~x | ~y = 11111010 | 11111100 = 11111110

• Bitwise AND:

  • (x | y) & (~x | ~y) = 00000111 & 11111110 = 00000110

• Result:

  • The function returns 00000110 (binary), which is 6 in decimal.

Textual Diagram

Initial Values:
x =  5 (binary 00000101)
y =  3 (binary 00000011)

Bitwise OR:
x | y       : 00000101 | 00000011 = 00000111

Bitwise NOT:
~x          : 11111010
~y          : 11111100
~x | ~y     : 11111010 | 11111100 = 11111110

Bitwise AND:
(x | y) & (~x | ~y) : 00000111 & 11111110 = 00000110

Result: 6

Use Cases

When to Use

• Hardware Constraints: When the XOR operation is not directly supported by the hardware but OR and NOT operations are available.
• Educational Purposes: To understand the fundamental relationships between different bitwise operations.
• Algorithm Optimization: In certain algorithms, using different combinations of bitwise operations can optimize performance or achieve specific requirements.

Use Cases in Embedded Systems

• Bit Manipulation: Implementing bit manipulation functions where direct XOR operations are not feasible.
• Custom Logic Circuits: In hardware design, sometimes specific logic gate combinations are used to achieve desired results.