Binary addition calculator

This binary addition calculator allows you to add two binary numbers and display the result in binary format. It includes a user interface that allows you to input the two binary numbers, and a button or other mechanism to initiate the calculation. The calculator then performs the binary addition algorithm and displays the result.




How to add binary numbers

Adding binary numbers is a simple process that is similar to adding decimal numbers, with the only difference being that the base of the number system is 2 instead of 10. Here are the steps to add binary numbers:

  1. Line up the two binary numbers so that their least significant digits (the right-most digits) are aligned.
  2. Starting from the rightmost digit, add the digits of both numbers together. If the sum is less than 2, simply write the sum as the corresponding digit in the result.
  3. If the sum of two digits is equal to or greater than 2, the leftmost digit of the sum is carried over to the next column. For example, if the sum is 10 (binary), the leftmost digit is 1 and the rightmost digit is 0. The leftmost digit is carried over and added to the next column.
  4. Repeat steps 2 and 3 for each digit in the binary numbers, working from right to left.
  5. If there is a carry left over after adding the last digit, add it to the leftmost position of the result.
  6. The final result is the binary representation of the sum of the two binary numbers.

For example:
Let's add binary numbers 1011 and 1101.

1 0 1 1
+ 1 1 0 1
--------
1 0 0 1 0

The addition is done from right to left, the last digit of both numbers 1+1 = 10 (2 in decimal), the carry is 1 and the result is 0.
The second digit of both numbers is 1+0 = 1.
The third digit of both numbers is 0+1 = 1.
The forth digit of both numbers is 1+1 = 10 (2 in decimal), the carry is 1 and the result is 0.
The sum of the numbers is 10110 which is equal to 22 in decimal.

In this example, the result is the same as if we had added the decimal equivalents of the binary numbers, 11 and 13, and then converted the sum back to binary.

Adding binary numbers is only applicable to positive numbers, for negative numbers there is a different process called two's complement which is used to perform arithmetic operations on negative numbers.