Binary Addititon

Adding binary numbers is similar to adding decimal numbers, but you only have two digits to work with: 0 and 1.

Step 1

Start by aligning the binary numbers you want to add vertically, with the least significant digit (the rightmost digit) aligned at the bottom.

Step 2

Begin adding the digits from the rightmost column (the least significant digit) to the leftmost column. Start with the rightmost digits and move towards the left.

Step 3

Perform the addition for each column:

0 + 0 = 0: If both digits are 0, the sum is 0.

0 + 1 = 1: If one of the digits is 0 and the other is 1, the sum is 1.

1 + 1 = 0 (with carry 1): If both digits are 1, the sum is 0, and you carry over 1 to the next column on the left.

Step 4: Add the carry

If there's a carry from the previous column, add it to the next column's sum.

Step 5: Continue along

Continue adding columns from right to left, taking into account any carries, until you have added all the columns.

Step 6

If you have a carry after adding the leftmost columns, include it in the result.

Binary addition example

Here's an example of adding two binary numbers, 1101 and 1011:

   1101
 + 1011
-------
  11000

So, 1101 + 1011 in binary equals 11000 in binary.

How do computers perform binary addition?

It is the job of the Arithmetic Logic Unit to perform binary addition. It is achieved through the use of two types of circuit:

A half adder

Half adders take 2 binary inputs and produced a sum and a carry. This circuit is used for the right most bit calculation.

A Full adder

Full adders take 3 binary inputs(the addition bits and the carry from the previous column) and produces a sum and a carry.

If the final result of the addition produces a carry that does not fit within the size of the register (for instance a result of an addition is 9 bits long and the register size is 8 bits) then this results in an overflow, which can be handled in multiple ways.