How to Subtract Binary Numbers
Like binary addition, binary subtraction also plays an important role in binary arithmetic as well as in digital electronics system. We have discussed the binary subtraction process briefly in this article on binary arithmetic. But here we will focus on the process of binary subtraction – i.e. how to subtract binary numbers.
When adding binary numbers, there are four points or steps to remember before proceeding through the operation. These are:
As there are only two digits in binary number system 0 and 1 that’s why these four steps are able to describe all the operations of binary subtraction.
Now we will discuss the process elaborately with the help of a few examples.
Suppose, A = 10101100 and B = 1010100 and we want to find out A – B.
Now implementing the rules of binary subtraction
The first step is 0 – 0 = 0 and that’s what is written in the place for result
Similarly again the last step is repeated as here the numbers are both 0 and from the table we know 0 – 0 = 0.
From the table, we can find out that 1 – 1 = 0 and it is written
The table shows that 1 – 0 = 1 and we have written exactly that in result
Here 0 – 1 = 1 with the borrowing of 1 from the next significant bit and that’s what has been done. We will treat the next 1 as 0 in the next step as shown below.
As the 1 was borrowed in the previous step we are treating the 1 as 0 and the result is 0 – 0 = 0 and that is written
Again the last 1 has been borrowed because the operation done was 0 – 1 = 1 with borrow 1 from the next most significant bit and the final result of binary subtraction, we got is written in the place of result in the final step.