What is 1+1?

Let's add two bits. Each one is 0 or 1, so there are only four sums to check:

0 + 0 = 0.
0 + 1 = 1.
1 + 0 = 1.
1 + 1 = ?

Here's the catch. In binary there is no symbol for 2. The only digits are 0 and 1. So the answer to 1 + 1 doesn't fit in a single digit.

You already know the fix, you do it in normal numbers all the time. Add 9 + 1 and you don't cram "10" into one column. You write a 0 and carry the 1 to the next column.

Binary does exactly the same thing. 1 + 1 becomes 1 0: a 0 here, and a 1 carried over.

So every addition gives us two answers:
- the digit that stays in this column (the sum)
- the digit that carries to the next (the carry)

What is 1+1?

Let's add two bits. Each one is 0 or 1, so there are only four sums to check:

0 + 0 = 0.
0 + 1 = 1.
1 + 0 = 1.
1 + 1 = ?

Here's the catch. In binary there is no symbol for 2. The only digits are 0 and 1. So the answer to 1 + 1 doesn't fit in a single digit.

You already know the fix, you do it in normal numbers all the time. Add 9 + 1 and you don't cram "10" into one column. You write a 0 and carry the 1 to the next column.

Binary does exactly the same thing. 1 + 1 becomes 1 0: a 0 here, and a 1 carried over.

So every addition gives us two answers:
- the digit that stays in this column (the sum)
- the digit that carries to the next (the carry)