How do you perform XOR on binary numbers? Calculate: $1010\,0111 \oplus 0011\,1100$

Apply XOR bit by bit — where bits differ you get 1, where they match you get 0. Result: $1001\,1011$.

Step by step:

$$\begin{array}{r} 1010\,0111 \\ \oplus\; 0011\,1100 \\ \hline 1001\,1011 \end{array}$$

Each column is independent — just compare the two bits:

• $1 \oplus 0 = 1$, $0 \oplus 0 = 0$, $1 \oplus 1 = 0$, $0 \oplus 1 = 1$, $0 \oplus 1 = 1$, $1 \oplus 1 = 0$, $1 \oplus 0 = 1$, $1 \oplus 0 = 1$

Tip: "Same = 0, Different = 1" — that's all you need to remember for XOR.