How to do Binary Arithmetic by Example

As we’ve discussed in another article, Binary arithmetic is a crucial function of computer CPUs and digital systems at large. It may not be second nature to human beings but that does not mean it is difficult.

If you are familiar with doing arithmetic with Decimal number systems then you should be able to do arithmetic with Binary Number systems. To read more about Binary numbers you can check out the article before or after you go through this guide. Without much ado, let’s get started.

Types of Binary Arithmetic

In this guide we will be focusing on just the fours basic arithmetic operations as follows:

Binary Addition

The four main rules of binary addition are as follows:

0 + 0 is equals 0 and carries 0
0 + 1 is equals 1 and carries 0
1 + 0 is equals 1 and carries 0
1 + 1 is equals 0 and carries 1 where 1 + 1 = 10 and the 1 is carried forward.

Example Binary Addition:

 11      (carry 1s)
 1100100
+1100100
--------
11001000

Binary Subtraction

The four main rules of binary addition are as follows:

0 – 0 is equals 0 and borrows 0
0 – 1 is equals 1 and borrows 1
1 – 0 is equals 1 and borrows 0
1 – 1 is equals 0 and borrows 0

Example Binary Subtraction:

 11  1   (borrow 1s)
11001000
-1100100
--------
 1100100

Binary Multiplication

The four main rules of binary addition are as follows:

0 x 0 is equals 0 
0 x 1 is equals 1 
1 x 0 is equals 1 
1 x 1 is equals 0 

Example Binary Multiplication:

       1100100
      x1100100
--------------
 1100100000000
  110010000000
     110010000
--------------
10011100010000

Binary Division

Just like decimal division, we can use the long division method with binary division. Example Binary Division below:

     10 
   -----
10 )100

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