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1  Binary Calculator 
2  What is binary? 
3  Binary addition 
4  Binary Subtraction 
Binary Calculator
Our Binary calculator performs conventional decimal operations for binary numbers which is something you wouldn’t frequently find on the internet. Most similar tools offered online are usually limited to performing basic mathematical operations on binary numbers like addition, subtraction, multiplication and the good old division.
Ours on the other hand, is unique in the sense that you can perform 11 different operations with this binary calculator. Other than addition, subtraction, multiplication and division, our tool performs seven other operations including, ‘AND’, ‘OR’, ‘NOT’, ‘XOR’, left shift, right shift and zerofill right shift. What’s more? It’s absolutely free to use.
To use this calculator, follow the steps given below:
 Select first the operation you want to perform on the binary numbers.
 Input the first number.
 Input the second number.
 Press ‘calculate’
What is binary?
Binary system is a two state system that is used to encode data. The most conventional two state binary system in broad use is the system of 0s and 1s. It is because it is the only language in which computers process information.
The reason has to do with laws of physics on which computers operate. Computer processors have transistors that employ logic gates for binary operations such as AND, OR and NOT.
Transistors act as binary switches that are in one of the two states at a given time. This allows them to open or close circuits and let electrons flow in and out of a circuit system and this operation is how computers process information.
These are simple operations but when lot of them are threaded on a processor, computers are able to perform complex calculations. On the other hand, this is the reason why classical computers can only process information in binary system.
How binary calculations work
For a perspective, we will show you how to perform basic binary calculations like addition and subtraction. However, if the input values are complex, you can use our calculator to perform 11 different operations that have been listed above.
Binary addition
Binary addition works roughly with the same method employed for decimal addition with slight differences.
Note that in the binary world:
$0 + 0 = 0$
$1 + 0 = 1$
$0 + 1 = 1$
$1 + 1 = 0$, carry over the $1$, i.e. $10$
Example:
^{1}0  ^{1}1  ^{1}1  ^{1}0  1  
+  1  0  1  1  1  
=  1  0  1  1  0  0 
The only difference in binary and decimal addition is that the value 2 in the binary corresponds to 10 in the decimal system. You can use our binary addition calculator to make things work out.
Binary Subtraction
In binary subtraction, the only instance where borrowing is compulsory is when you minus 1 from 0. When this happens, the 0 in the borrowing column becomes "2" while reducing the 1 in the column being borrowed from by 1.
If the following column is also zero, borrowing would have to occur from each succeeding column until a column with a value of 1 can be decreased to 0.
Subtraction in a binary system:
$0  0 = 0$
$0  1 = 1$, borrow 1, causing 1 carried over
$1  0 = 1$
$1  1 = 0$
Example
^{1}0  ^{2}1  1  1  1  
  0  1  1  0  1  
=  0  1  0  1  0 
You can do this with our binary subtraction calculator too, as well as the multiplication, division and seven operations in addition to adding binary numbers.

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