In mathematics, the binary number system is said to be a way that allows you to express any number in the base-2 numeral system or binary numeral system. It uses only two symbols, which are o and 1. The base-2 is a positional notation with a radius of 2, and each digit is referred to as a bit. Modern technology & computers use the binary system because of its easy implementation.

It is easy to design the machines that require detecting two states that are on and off. On the other hand, the decimal number system is difficult and complicated because the required hardware detects ten states for the digits from 0 to 9. For ease, you can use the online binary calculator that helps you to add, subtract, multiply, and divide the two binary numbers along with 8, 10, & 16 base numbers.

## How to Perform the Basic Math Operations With Binary Numbers

The basic math operations like addition, subtraction, multiplication, and division work similar to the decimal number system. However, there are few rules to perform the basic math operation along with binary numbers. You can also try the binary calculator to perform these operations instead of performing manual calculations. Here we’re going to discuss each of them individually.

### Binary Addition

When discussing the binary addition, we see that the addition of binary numbers follows the same rules as the decimal number system’s addition except for carrying a one instead of 10. The carryover occurs when the result of the addition is equal to “2”. You can easily perform additional operations in a binary number system by using the binary addition calculator. Look at the below example for a better understanding.

**Example:**

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0, this is because of the carry over the 1, i.e. 10.

**Solution:**

^{ 1}0 ^{1}1 ^{1}1 ^{1}0 1

+ 1 0 1 1 1

——————

= 1 0 0 1 0 0

### Binary Subtraction

There is a bit of difference between binary & decimal subtraction. Binary numbers are the values that contain only two types of digits that are 0 and 1. Each digit is referred to as the consecutive power of “2”. Whether it should be multiplied by zero or one. The borrowing occurs when the number that is subtracted is larger than the number, which is being subtracted from.

Manual calculations on the paper might be complex, so you can simply give a try to the binary subtraction calculator to help to perform the subtraction operation over the binary numbers.

### Binary Multiplication

Multiplication in a binary number system is simple as compared to the decimal counterpart. In this multiplication, only two values are used, and they’re zero & one. The result must be either as the first digit or zero. The complexity in binary multiplication comes from the tedious binary addition, and it depends on how many bits are there in each term. By using binary multiplication, the calculator performs the multiplication of binary numbers.

### Binary Division

The process of binary division is just like the long division in the decimal system. The dividend number is divided by the divisor in a similar manner along with the significant difference that uses the binary rather than the decimal subtraction. To avoid the complexities of the manual calculations, you can consider the binary calculator that helps to verify the answers to your calculations.

## How Do You Use Binary On a Calculator?

The binary calculation becomes easy with the assistance of an online binary calculator, but all you need is to follow the below instructions:

- Select the number type from the dropdown menu of the tool, and it could be binary, decimal, hexadecimal, & octal numbers.
- Add the value of the first operand.
- After that, add the 2
^{nd}operand. - Now, select the basic math operation that you want to perform on the two operands. It could be addition, multiplication, division, and multiplication.
- Now, press the calculate button to generate the results.

## Understanding Binary Number System

Computer technology is everywhere these days where the most common application of using the binary number system can be seen. The two-digit number system is used to do digital coding, and computer language & programming is based on this number system. Using the data and converting it with the restrained bits of the information and is what makes up the digital encoding process. The converted information consists of the binary number system 0 and 1.

The binary number system is also used in the circuit of networking systems, computers, and smart appliances. The machines and circuits are controlled by using the electric pulse, and they recognize the two types of signals or states that are on & off. When it comes to binary number systems, then calculating these numbers becomes difficult. You can use the decimal to a binary calculator that allows you to convert the number from decimal to the binary number system. You can also use the binary to the decimal calculator to convert the number from binary to decimal.

**Advantages of Using the Binary System**

There are so many advantages of using the binary number system, but it is specifically useful for adding the numbers, computer flips switches. The main advantage is that it is considered as a base that is conveniently represented by electronic devices. The binary number system makes the coding simple and easy. It performs various logical operations, so it is used in the programming of the technology.

**See Also:**

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## Conclusion

In this article, we discussed the binary number system, and its calculation with the basic mathematical operations are taken into account. We also mention how to perform the binary calculation with the assistance of a binary calculator. Converting the decimal to binary number system & binary to decimal on the paper is complex, but you can make it easy by using the binary calculator.