Why does 1 plus 1 equals 0 in binary?

1 + 1 = 0 in binary. Why does this happen?

Note: Adding binary numbers is related to modulo 2 arithmetic.

Let's review mod and modular arithmetic with addition.

modulus 2 is the mathematical term that is the remainder from the quotient of any term and 2. For instance, if we have 3 mod 2, then we have 3 / 2 = 1 + ½. The remainder is 1. So 3 ≡ 1 mod 2.

What if we want to add moduli?

The general form is a mod n + b mod n ≡ (a + b) mod n.

Now, for the given problem, 1 mod 2 + 1 mod 2 ≡ 2 mod 2. Then, 2 mod 2 ≡ 0 mod 2.

Therefore, 1 + 1 = 0 in binary.