Last updated: April 2026
The Binary to Decimal Converter translates binary numbers (base 2) into decimal (base 10), octal (base 8), and hexadecimal (base 16) in real time. Type a binary number on the left and see the decimal equivalent on the right, or enter a decimal number and get the binary representation instantly. The tool also shows octal and hexadecimal conversions for every input, giving you four number bases in one view. This is essential for computer science students learning number systems, programmers working with low-level code and bitwise operations, and anyone who needs to quickly convert between binary and decimal for networking, electronics, or digital systems. Every output has a copy button for fast use.
Type a binary number using only 0s and 1s in the Binary Number field. The tool validates your input and shows an error if you include any other digits.
If you already know the decimal value, type it in the Decimal Number field instead. The binary representation generates automatically along with octal and hexadecimal.
The results section shows your number in binary, decimal, octal, and hexadecimal. All four formats update in real time as you change either input field.
Each number base output has its own copy button. Click it to copy that specific value to your clipboard for use in your code, homework, or documentation.
Binary to Decimal Converter is the fastest way to convert between number systems online. Key advantages include bidirectional conversion, four simultaneous number base outputs, and real-time validation.
Each digit in a binary number represents a power of 2, starting from the rightmost digit at 2^0. To convert, multiply each binary digit by its power of 2 and add the results. For example, binary 1011 = (1 x 8) + (0 x 4) + (1 x 2) + (1 x 1) = 8 + 0 + 2 + 1 = 11 in decimal.
Binary (base 2) uses only two digits: 0 and 1. It is the fundamental language of computers because electronic circuits have two states: on and off. Decimal (base 10) uses ten digits: 0 through 9. It is the number system humans use in everyday life. Both systems can represent the same values, just with different notation.
Computers use binary because digital circuits are built with transistors that have two stable states: on (1) and off (0). It is much simpler and more reliable to design electronic components with two states than ten. All the math, logic, and data processing inside a computer ultimately reduces to binary operations.
Hexadecimal (base 16) uses digits 0-9 and letters A-F. Each hex digit represents exactly 4 binary digits (bits), making it a compact way to write binary values. For example, binary 11111111 is FF in hex and 255 in decimal. Programmers use hex extensively for memory addresses, color codes, and data representation because it is shorter than binary but easily convertible.
This tool uses JavaScript's native number handling, which accurately represents integers up to 2^53 - 1 (9,007,199,254,740,991). That is a 53-bit binary number. For most practical purposes including computer science coursework, networking, and programming tasks, this range is more than sufficient.