To add binary numbers with fractions, we use exactly the same technique we used to add integer binary values. The only difference is that we need to keep track of the radix point so we can distinguish the fractional part of our answer from the integer part. The example below demonstrates how to add the binary numbers 110.012 and 1.0112.



  1. First, we align the two numbers so that the radix point of each number is located in the same column.
    110.01
  +   1.011
  1. Next, we fill in the blank spaces with 0s and add the two numbers together.
    110.010
  + 001.011
  1. The first column adds to 1.
    110.010
  + 001.011
          1
  1. The second column adds to 102, so we write a 0 below it and carry a 1 to the next column.
        1
    110.010
  + 001.011
         01
  1. All of the remaining columns add to 1, so we write 1 below them.
        1
    110.010
  + 001.011
    111.101
  1. This gives us a final answer of 111.1012.
        1
    110.010
  + 001.011
    111.101