Binary Subtraction

Under Digital ElectronicsLike addition, subtractions also plays an important role in binary arithmetic as well as in digital electronics system. We have discussed about the binary subtraction process in brief in the article binary arithmetic. But in this article we will look into the process of binary subtraction only and more elaborately. Coming directly to the topic without wasting any time, first we have to look into the four fundamental steps of binary subtraction. These are

0 – 0 = 0
0 – 1 = 1,
borrow 1 from the next more significant bit
 1 – 0 = 1
 1 – 1 = 0

As there are only two digits in binary number system 0&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 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 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.