Binary Subtraction

Another basic concept of binary operations in binary subtraction. We all know that the first thing we would learn in Mathematics is addition, subtraction, multiplication, and division. In binary subtraction, you will have only two elements: 0 and 1. In this topic, you will learn about binary subtraction in-depth that includes definition, the method, and binary subtraction examples.


What is Binary Subtraction?

Do you think that binary numbers can be subtracted? Yes, the subtraction of binary numbers is possible. It is very similar to the subtraction of base 10 numbers. If you add 1 + 1 + 1 the end result is 3. But according to a binary number system, the value of 1 + 1 + 1 is going to be 1 1. Here, you have to be careful while subtracting or adding because it might get a little confusing. 


Binary Subtraction Rules

To make the understanding of binary numbers easier, here are a few binary subtraction rules you should remember and apply them accordingly:

  • 1 - 1 = 0

  • 1 - 0 = 1

  • 0 - 1 = 1 ( you can borrow 1 from the next number)

  • 0 - 0 = 0

Here is an Example of Subtraction of Binary Numbers

Question 1: Subtract 1 0 1 from 1 1 1 0

Solution: 1 1 1 0

              (-)   1 1 0

__________

    1 0 0 0 

__________


Now, let’s learn how to subtract binary numbers. 


How do you Subtract Binary Numbers?

Let’s take the same example as the one we used above.

    1 1 1 0

(-)    1 1 0

__________

     1 0 0 0 

________


Step 1: You subtract the numbers in the one’s column and not down the result. In this case, the value of 0 - 1 = 0. We borrow 1 from the number in the ten’s place and continue with the subtraction. 

     1 1 1 0

(-)     1 1 0

__________

               0 

__________


Step 2: Now you subtract the values in the 10’s place. Apply the aforementioned binary subtraction rules.

     1 1 1 0

(-)     1 1 0

__________

             0 0 

__________


Step 3: Subtract the value that is present in the hundreds place value.

     1 1 1 0

(-)     1 1 0

__________

          0 0 0 

__________


Step 4: Since we don’t have anything in the thousand’s place, we retain it as it is.

     1 1 1 0

(-)     1 1 0

__________

      1 0 0 0 

__________


To cross-check if the final result is correct, you need to know the decimal values of the given numbers. 


Therefore, 

1 1 1 0 - 1 1 0 = 1 0 0 0

14 - 6 = 8

Hence Proved.


Binary Subtraction Examples

Example 1: 1 0 1 1 0 1 0 - 0 0 1 0 1 0 


1 0 1 1 0 1 0

           (-) 0 0 1 0 1 0 

___________


1 0 1 0 0 0 0 

___________


Cross-checking using the decimal equivalent of the above decimal numbers: 


1 0 1 1 0 1 0 = 90

 0 0 1 0 1 0  = 10

1 0 1 0 0 0 0 = 80


Subtraction Using 1’s Complement

When you’re subtracting a number from another number using one’s complement, you should remember that 0 is the positive sign and 1 is the negative sign. 

Binary Subtraction Rules by 1’s Complement

Step 1: First note down the 1’s complement of the number that has to be subtracted (subtrahend)


Step 2: Add Step 1’s result with the minuend.


Step 3: In case a carryover exists, you should add it to the least significant bit.


Step 4: If no carryover exists, take the one’s complement of the result. 


Binary Subtraction Examples Using 1’s Complement

Example 1: (1110)₂ - (11)

Step 1: 1’s complement of the subtrahend 


1 1 1 1

       (-) 0 0 1 1

       ------------------

1 1 0 0

       ------------------

Step 2: Adding 1’s complement of subtrahend to minuend


1 1 1 0

     + 1 1 0 0

       ------------------

         1 1 0 1 0

       ------------------

Step 3: Since carry over exists, shifting it to the least significant bit.


1 0 1 0

         +       1 

       ------------------

            1 0 1 1

       ------------------


Therefore, the answer is 1 0 1 1.

FAQ (Frequently Asked Questions)

1. What is the Binary Subtraction Definition?

A. Another basic concept of binary operations in binary subtraction. We all know that the first thing we would learn in Mathematics is addition, subtraction, multiplication, and division. In binary subtraction, you will have only two elements: 0 and 1. It is very similar to the subtraction of base 10 numbers. If you add 1 + 1 + 1 the end result is 3. But according to a binary number system, the value of 1 + 1 + 1 is going to be 1 1. Here, you have to be careful while subtracting or adding because it might get a little confusing.

2. What are the Binary Subtraction Rules?

A. To make the understanding of binary numbers easier, here are a few binary subtraction rules you should remember and apply them accordingly:


  • 1 - 1 = 0

  • 1 - 0 = 1

  • 0 - 1 = 1 ( you can borrow 1 from the next number)

  • 0 - 0 = 0

Here is an example of subtraction of binary numbers -

Question: Subtract 1 0 1 from 1 1 1 0

Solution: 1 1 1 0

              (-)   1 1 0

__________

      1 0 0 0 

__________

3. How to apply 1’s Complement to Binary Subtraction?

Step 1: First note down the 1’s complement of the number that has to be subtracted (subtrahend)


Step 2: Add Step 1’s result with the minuend.


Step 3: In case a carryover exists, you should add it to the least significant bit.


Step 4: If no carryover exists, take the one’s complement of the result.

4. How to Subtract two Binary Numbers?

Step 1: You subtract the numbers in the one’s column and not down the result. In this case, the value of 0 - 1 = 0. We borrow 1 from the number in the ten’s place and continue with the subtraction. 


Step 2: Now you subtract the values in the 10’s place. Apply the aforementioned binary subtraction rules.


Step 3: Subtract the value that is present in the hundreds place value.


Step 4: Since we don’t have anything in the thousand’s place, we retain it as it is.