An online calculator that adds two binary numbers is presented along with the steps needed to understand the process included.

Addition of Binary Digits

Additions of Basic Binary
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (answer is 0 and carry 1)

Calculator

Note 1 that before calculations, the two binary numbers are written such that they have the same numbers of digits by filling the number with smaller number of digits with zeros on the left.
Note 2 The steps shows the addition process starting from the righmost digits. If the addition of two digits gives one digit then that is the answer. It it gives two digits, then the digit on the left is carried to the addition of the next digits. At each step, we add three digits: two from the addition and the third (in red at each step) is the carry. In step (1) the carry is zero.;

Enter two binary numbers (using 1's and 0's only) and press ADD

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Note 3 The digit in red, in each step, is the carry digit.