How to Add Binary Numbers

 

Basic mathematical operations with binary numbers work similarly to the decimal system. However, there are a few rules specific to the binary system. The method you use to add two binary values together is similar to the method used to add two denary numbers together, called column maths.

Using denary, you add the numbers that belong to the same place value column together, if there is a carry, add it to the next. 

To answer the questions 136+98, you would do the following:-

(146)₁₀ ​+ (65)₁₀ ​= (211)₁₀​

 

For binary addition, you will use the same method, but this time as binary values only use either a 1 or 0 and the only value that will be carried is a 1. The four rules that apply when two binary digits are added are given below:-

Now, let us use these binary addition rules to learn the process of adding binary numbers.

How to Add Binary Numbers?

Binary numbers are generally used in computer programming when the data is stored in the form of 0 and 1. When solving binary addition two types of methods are used that are binary addition without regrouping and binary addition with regrouping. Let us learn about each of these methods below:

Binary Addition without Regrouping

When the result for the addition of binary numbers is in the form of 0 and 1, there is no need to regroup the elements. Let us understand this using an example.

Example: Add (101)₂ and (10)₂. 

Following steps followed to solve this binary addition without regrouping:-

Step 1: Write the digits of both numbers in different columns according to their place values.

    1  0  1

+      1  0

Step 2: Add the numbers to the extreme right that is 1 and 0. Apply the rule for binary addition that makes 1 + 0 = 1.

    1  0  1

+      1  0

――――

            1

Step 3: Move to the next column towards the left and add 0 + 1 = 1.

    1 0 1

+     1 0

――――

       1 1

Step 4: Move to the next column towards the left, we have only 1. So we can use 1+0 = 1.

    1 0 1

+     1 0

――――

    1 1 1

Therefore, on adding (101)₂ and (10)₂, we get (111)₂.

Binary Addition with Regrouping

When the result for the addition of a binary number is greater than 1, regrouping of terms is required. Let us understand this using an example.

Example: Add (1001)₂ and (111)₂.

Following steps followed for solving this binary addition with regrouping:

Step 1: Write the digits of both numbers in different columns according to their place values.

    1 0 0 1

+     1 1 1

Step 2: Start the addition of the numbers from the extreme right using the rules of binary addition. We will first add 1 + 1 = 0 gives 1 as carry on the preceding column.

          1

    1 0 0 1

+     1 1 1

――――

             0

Step 3: Now add the terms in the next column that is 1 + 0 + 1 = 0, with 1 carrying on the preceding column.

       1 1

    1 0 0 1

+     1 1 1

――――

          0 0

Step 4: Again following the same step for the third column from the right, 1 + 0 + 1 = 0, with 1 carry on the previous column.

    1 1 1

    1 0 0 1

+     1 1 1

――――

       0 0 0

Step 5: Finally in the first column we have 1 + 1 = 0, with carried 1. We get,

    1 1 1

    1 0 0 1

+     1 1 1

――――

  1 0 0 0 0

Hence, (1001)₂ + (111)₂, gives (10000)₂

Let us take another example with "Logic Kit" app this app is very easy and so good in these subjects of number systems. Download This app from the app store for iOS  devices click here.

1- Open the app 

2- Choose More Arithmetic

3- Select the base 2 

4- write your equation you need to solve

5- You see the solution then click on show steps 

Example: Add (001)₂ with (110)₂