XOR using mathematical operators

Question

How can I implement XOR using basic mathematical operators like +,-,*,/ Update: Actually, I need to track change in two matrix having Boolean values. This can be done using XORing each value with corresponding value in other matrix. But, Lp_Solve library doesn't support XOR operation. Also, it accepts only linear equations.

Accepted Answer

(a − b)²

This works because:

```
(a − b)² = a * (a − b) + b * (b − a)
```

Since multiplication in ℤ₂ is conjuction (`&`), and `1 - a` is negation (`!`), the above formula is equivalent to XOR for `a, b ∈ {0, 1}`:

```
(a & !b) | (b & !a)
```

See the comment below by Pascal Cuoq explaining why this cannot be a linear equation.

XOR using mathematical operators

Solution

Problem