Binary adders are devices used to add binary numbers. They are used in computers. They take two binary numbers and put them together to get a sum. In its most basic form, it uses two XOR gates, two AND gates, and an OR gate. These gates figure out what the numbers being sent in mean and if the digit needs to be turned on or not.
When solving this example: 1001 + 1100 (9 + 12 in decimal form), it would need five single bits to give an answer. The first digits in each number would go to one adder, 1 and 0. It would calculate that 1 + 0 = 1, so that first digit would be 1. The second digits from each are 0 and 0, and 0 + 0 = 0, so the second digit is 0. the third digit from each are 1 and 0, and 1 + 0 = 1, so the third digit is 1. The fourth digit in each are 1 and 1, and 1 + 1 = 10, but because this is a 2 digit number, it holds the first digit (0) and send the second digit to the next adder. The next adder sees 1, and 1 = 1, so the fifth digit is 1. If we take the sum digits in order, they come out as 10101 (21), so 1001 + 1100 = 10101 (9 + 12 = 21).