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Now that we know binary numbers, we will learn how to add them. Binary addition is much like your normal everyday addition (decimal addition), except that it carries on a value of 2 instead of a value of 10.

For example: in decimal addition, if you add 8 + 2 you get ten, which you write as 10; in the sum this gives a digit 0 and a carry of 1. Something similar happens in binary addition when you add 1 and 1; the result is two (as always), but since two is written as 10 in binary, we get, after summing 1 + 1 in binary, a digit 0 and a carry of 1.

Therefore in binary:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (which is 0 carry 1)

Example. Suppose we would like to add two binary numbers 10 and 11. We start from the last digit. Adding 0 and 1, we get 1 (no carry). That means the last digit of the answer will be one. Then we move one digit to the left: adding 1 and 1 we get 10. Hence, the answer is 101. Note that binary 10 and 11 correspond to 2 and 3 respectively. And the binary sum 101 corresponds to decimal 5: is the binary addition corresponds to our regular addition.

More examples:

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