- Binary Subtraction Definition: Binary subtraction is the process of subtracting binary numbers, similar to decimal subtraction but using only the digits 0 and 1.
- Basic Rules: Binary subtraction follows simple rules: 0-0=0, 1-0=1, 1-1=0, and 0-1=1 with a borrow.
- Importance in Electronics: Binary subtraction is crucial in digital electronics for various calculations and operations.
- Borrowing in Binary: When subtracting 1 from 0, you need to borrow from the next significant bit, changing the dynamic of the calculation.
- Worked Example: Detailed step-by-step examples, like subtracting 1010100 from 10101100, help illustrate the process.
How to Subtract Binary Numbers
Binary subtraction, like binary addition, is crucial in binary arithmetic and digital electronics. While we have briefly discussed binary subtraction before, this article will focus on how to subtract binary numbers step-by-step.
Binary addition, binary subtraction, binary multiplication and binary division are the four types of arithmetic operations that occur in the binary arithmetic.
When adding binary numbers, there are four points or steps to remember before proceeding through the operation. These are:
Since the binary number system uses only the digits 0 and 1, these four steps cover all possible operations in 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.
