# Inverse operation of xor

If x = a xor b, given the values of x and a can we find b? In other words, which function can be applied on both sides in the equation to get the value of b?

XOR is its own inverse and it's commutative, so $$x = a \oplus b \implies x\oplus a = a \oplus b \oplus a = 0 \oplus b = b$$
For any $$b$$ and $$a$$, it is true that $$b = (\underbrace{a \operatorname{XOR} b}_{\textrm{your }x}) \operatorname{XOR}a$$.