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Binary Addition


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:

Practice
Binary Addition


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