I have a given equation, and there is one calculation step, that I don't understand.
I thought, I have to xor the $0$ with $\bar{k}_1 \oplus k_2 \oplus \bar{k}_3$, and that I have to xor the $1$ with $k_1 \bar{k}_2 \oplus \bar{k}_1 \bar{k}_3$.
So I understand the second term, since xor is commutative, that it gives simply $k_1 \bar{k}_2 \oplus \bar{k}_1 \bar{k}_3 \oplus 1$.
But I don't understand the first term. Why is $\bar{k}_1 \oplus k_2 \oplus \bar{k}_3 \oplus 0$ equal to $k_1 \oplus k_2 \oplus k_3$?
Notice that $$\overline a=a\oplus 1$$ Thus $$ \overline{k_1}\oplus \overline{k_3}=k_1\oplus1\oplus k_3\oplus 1=k_1\oplus k_3$$ since the 1s cancel.