# Binary Calculator - Conversion, Arithmetic, and Representation

Simple Binary calculator for calculation of simple math equations.

 +-*/ Result

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

The binary number system is a base-2 number system, which means it only uses two digits, 0 and 1, to represent numbers. In contrast, the decimal number system, which we commonly use, is a base-10 system that uses ten digits (0-9) to represent numbers. The binary system is widely used in computer science, digital electronics, and other related fields. Our Binary Calculator is a handy tool for performing arithmetic operations, conversion, and representation of binary numbers.

## Binary Representation

In the binary number system, each digit has a weight that is a power of 2. The rightmost digit has a weight of 2^0, the next digit to the left has a weight of 2^1, then 2^2, and so on. The value of a binary number is the sum of the products of the digits and their corresponding weights. For example, the binary number 1101 represents the value 1*2^0 + 0*2^1 + 1*2^2 + 1*2^3 = 1 + 0 + 4 + 8 = 13.

## Binary Conversion

Our Binary Calculator allows you to convert binary numbers to decimal and vice versa. To convert a binary number to decimal, multiply each digit by its weight and add up the products. To convert a decimal number to binary, divide the number by 2 and write down the remainder. Repeat this process until the quotient is 0. The binary representation of the number is the remainder written in reverse order. For example, to convert the decimal number 13 to binary, we divide 13 by 2 and get a quotient of 6 and a remainder of 1. We then divide 6 by 2 and get a quotient of 3 and a remainder of 0. We divide 3 by 2 and get a quotient of 1 and a remainder of 1. Finally, we divide 1 by 2 and get a quotient of 0 and a remainder of 1. The binary representation of 13 is therefore 1101.

## Binary Arithmetic

Our Binary Calculator allows you to perform addition, subtraction, multiplication, and division of binary numbers. Binary addition is similar to decimal addition. To add two binary numbers, start from the rightmost digits and add them up. If the sum is 2 or more, carry over the extra 1 to the next column. For binary subtraction, we use the same borrowing method as in decimal subtraction. For binary multiplication and division, we use the same algorithm as in decimal arithmetic.

Binary Addition: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10
Binary Subtraction: 0 - 0 = 0, 0 - 1 = 1, 1 - 0 = 1, 1 - 1 = 0

## Conclusion

The Binary Calculator is a useful tool for performing binary arithmetic operations and conversion between binary and decimal numbers. It is a must-have for students and professionals in computer science, digital electronics, and related fields. With the help of our Binary Calculator, you can quickly and easily perform binary calculations with confidence.

## Math Calculators

You may also find the following Math calculators useful.