Binary Calculator

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Binary Calculator

To use Binary Calculator, enter the values in the input boxes below and click on Calculate button.


About Binary Calculator

Our Online binary calculator helps to perform basic arithmetic operations (addition, subtraction, multiplication, division, or, and, nor, nand, xor) on two numbers with base 2, 8, 10, and 16. In this guide, you will learn how to use our binary calculator, the importance of the binary system in IT, and more. So, let us get started!!!

Calculations become very easy with this handy and accurate tool. You just need to stick to the following points:

Input Value of our binary calculator:

  1. Then enter the value of the first operand.

  2. Then select the arithmetic operation you want to perform on the two operands. This can be addition, subtraction, multiplication, division, etc.

  3. Next, enter the value of the second operand.

  4. Finally, press the calculate button of our binary calculator.


After all, fields have been entered, the binary calculator will show:

The Result in:

  • Binary system.

  • Decimal system.

  • Hexadecimal system.

It doesn't matter which system you choose to calculate; our free binary calculator will determine the results according to the selected input.

The binary system (binary numbers) is one of the most important arithmetic systems there is. It consists of only two (02) numbers: 0 and 1. Like the Roman numeral system, it is a way to represent numbers differently. That is, all numbers you know can also be represented in the binary system. Before we dive into the binary calculator, we think it will be great to know how to represent numbers in the binary number system.

The system you know and use at school and at home is called the decimal system. You have 10 different numbers (0-9) that can be connected over and over again to form any number you can think of. About Binary calculator: The binary system can also represent any number, but it doesn't have 10 different numbers available; it has to make do with two different ones, 0 and 1; and our binary calculator can perform the most important mathematical and logical operation used in computer science.

As we all know, a computer is an electronic device, more specifically a digital electronic device. A computer uses billions and billions of transistors that operate digitally. The term digital refers to discrete logic levels. Logic levels are different potential levels like 5V, 0V, 10v, and many more. Xor, And, or are some of the examples of these logics, and's the binary calculator can perform these operations and more. A computer uses two logic levels when it works, so if we want to represent any number that is understandable to a computer, we must write numbers in the binary system.

The two symbols in this number system are analogous to two discrete logic levels. For convenience, we treat these two symbols as 0 and 1, but to a computer, 0 and 1 are different voltage levels computers chips. The interaction between these chips leads to binary operations like addition, multiplication, etc. Thanks to our binary calculator, these complex calculations are done with a few clicks of your mouse.

In general, 0 is considered a lower voltage level, and 1 is considered a higher voltage level. Everything we see on a computer screen or enter with a mouse or keyboard is all 0's and 1's; the only difference is their sequential arrangement-the end result of the operation performed by the computer's binary calculator. Additionally, in a computer, there are circuits (made up of transistors, among other things) that allow all the calculations that the computer is asked to perform- his built-in binary calculator. So, if we want our work done from a computer, we need to know how binary numbers work. In the next section, you will learn more about the binary calculation which can be completed with our binary calculator -addition, subtraction, multiplication, and division.

The simplest operations involving numbers are addition, subtraction, division, multiplication. They cease to be so simple to understand when we do not perform them on the decimal system, and we created this free online binary calculator to simplify your life. After all, the decimal system, unlike others, is used in almost all areas of life - prices in stores, information written in proofs, or anywhere we want to determine the quantity of an item. By the way, our binary calculator doesn't support decimal inputs. To manually perform an operation on any number system, you can usually just change the number to decimal, perform the operation and then change the number back from decimal to the system you are interested in. Keep reading this article about a binary calculator because, in this section, you will discover how to perform these binary numbers mathematical operations.

If you are not an IT savvy, or you forgot how to perform a binary addition, feel free to use our binary calculator. The addition of the binary number system is similar to the decimal system. The only difference is that the decimal system consists of the digit from 0-9, and their base is 10 while the binary number system consists of only two digits (0 and 1) which makes their operation easier. This operation is based on the simple principle of the addition table, which represents four partial sums (metho used by our binary calculator):

  • 0 + 0 = 0

  • 0 + 1 = 1

  • 1 + 0 = 1

  • 1 + 1 = 0 and 1 next

The first three sums are self-explanatory, while the fourth results in 0 for the current column, and a 1 (one) is moved to the next column on the left and is added to the numbers in that column. Pretty difficult, right! Feel free to use our binary calculator to simplify your life. The following example illustrates how to perform 69 (decimal) = 1000101 (binary) + 109 (decimal) = 1101101 (binary) = 10110010 (binary).


+1 (d)



+1 (c)

+1 (b)


+1 (a)




































Explanation: According to the rules above, here is how we performed our addition.

  • 1+1= 0 + 1(remaining). For clarity, we placed it in the line above, and we called it (a).

  • 0+0+1= 1

  • 1+0+1= 0 + 1(remaining). For clarity, we placed it in the line above, and we called it (b).

  • 1+0+1= 0 + 1(remaining). For clarity, we placed it in the line above (c).

  • 1+0+0= 1

  • 1+1=0 + 1(remaining). For clarity, we placed it in the line above, and we called it (d).

You can see that the length of the summed digits is 7 positions, and the result is 8 positions. This situation is called overflow, and our binary calculator takes care of this automatically.

This operation, which you can perform on our binary calculator, is based on the simple principle of the multiplication table, which represents four partial multiplications:

  • 0 * 0 = 0

  • 0 * 1 = 0

  • 1 * 0 = 0

  • 1 * 1 = 1

As with multiplying long sequences of decimal numbers, multiplying binary numbers involves multiplying each multiplicative number by each multiplicative number-it is the logic used by this online binary calculator. The resulting digits then need to be added together. The following example shows how to do this:

Here is an example of multiplication in binary: 11 * 110 (3 * 6)









Note: The addition 1+1= 0 and carry 1 is added in the following calculation. You will need at least 5 minutes to perform this simple operation manually, whereas you can do it in less than a minute with our binary calculator.

Subtraction is performed according to the same rules as in the decimal number system- rules used by this cutting-edge binary calculator. When subtracting from a lower number to a higher number, the higher digit is subtracted.

Binary subtraction is carried out digit by digit, starting with the lowest digit and using binary subtraction rules and tables:

  • 0 - 0 = 0;

  • 1 - 0 = 1;

  • 1 - 1 = 0;

  • 0- 1 = 1 and borrow

The above first three operations are easy to understand because they are identical to decimal subtraction. The fourth results in a 1 for the current column and forces a loaner 1 (one) to the next column on the left and is added to the numbers in that column. The following example illustrates what we mean. As we said earlier, you don't need to know all these complex algorithms when you use this binary calculator.

1100 (12) -1010 (10) = 0010.

The above subtraction is performed by the following steps.

  • 0 - 0 = 0

  • For 0 - 1 = 1, take borrow 1 and then 10 - 1 = 1

  • For 1 - 0, since 1 has already been given, it becomes 0 - 0 = 0

  • 1 - 1 = 0,

  • Therefore, the result is 0010.

We have seen that multiplication is based on a succession of additions, whereas division is based on a succession of subtractions and is used in the same way as ordinary decimal division.