## Binary Number System

Start here to understand the binary number base, and how it compares to decimal numbers.

Binary math is a number system with only two digits: 0 and 1. It is used by computers to store and process information, since it's easier for them to work with binary compared to the decimal system (0-9).

Here's a brief overview of the basics of binary math:

**Converting between binary and decimal:** To convert a binary number to decimal, you can use the following formula: decimal = (1st digit * 2^0) + (2nd digit * 2^1) + (3rd digit * 2^2) + ... + (nth digit * 2^(n-1)). For example, the binary number 1101 represents the decimal number (1 * 2^0) + (1 * 2^1) + (0 * 2^2) + (1 * 2^3) = 1 + 2 + 8 = 11.

To convert a decimal number to binary, you can use repeated division by 2, and keep track of the remainders.

**Binary addition:** Adding binary numbers is very similar to adding decimal numbers. Just remember to carry over to the next digit if the result is greater than 1. For example, the binary addition of 1101 and 101 is 10010.

Learn more about binary math by clicking on the sections below!

Our website was created in 2006 to help students and teachers quickly learn and understand binary numbers, and to explain binary arithmetic with clear examples. We also have free practice exercises, and online binary-to-decimal and decimal-to-binary converters.

Have a question or comment? Contact us here.

Start here to understand the binary number base, and how it compares to decimal numbers.

See how simple it is to add binary numbers.

Subtracting binary numbers is fairly straightfoward.

It's easiser to divide binary numbers than to divide decimal numbers.

Learn how to divide in the binary number system.

Here's how to convert from binary to decimal. Try our free online conversion tool.

Use our online decimal to binary converter, and understand how decimal-to-binary conversion works.

Try these free practice exercises and test your knowledge. Perfect for students and teachers.

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