Enter any binary number (base-2) into the Binary Input field and instantly see its decimal equivalent, along with the hexadecimal and octal representations. The step-by-step calculation breakdown shows exactly how each bit maps to its power of 2 — great for learning or double-checking your work.
Decimal Value
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Hexadecimal Value
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Octal Value
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Signed Decimal (Two's Complement)
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Number of Bits
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To convert binary to decimal, multiply each bit by 2 raised to the power of its position (starting from 0 on the right), then sum all the results. For example, 1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13₁₀.
The binary numeral system is a base-2 number system that uses only two digits: 0 and 1. It is the foundation of all modern computing and digital electronics, where 0 represents 'off' and 1 represents 'on' in electronic circuits.
Two's complement is a method for representing signed (positive and negative) integers in binary. To find the two's complement of a number, invert all bits and add 1. It's the most common way computers store negative integers because it simplifies arithmetic operations in hardware.
Group the binary digits into sets of 4 from the right, then convert each group to its hexadecimal equivalent (0–9 and A–F). For example, 11111111₂ becomes 1111 1111, which is FF in hexadecimal. This tool shows the hex conversion automatically.
This converter can handle binary numbers up to 53 bits accurately using JavaScript's standard number precision. For most practical purposes involving 8-bit, 16-bit, or 32-bit values, the results will be exact.
An unsigned binary number treats all bits as representing a positive value. A signed binary number (using two's complement) uses the most significant bit as a sign bit — if it's 1, the number is negative. For example, 11111111 unsigned is 255, but as a signed 8-bit number it represents -1.
Group the binary digits in sets of 3 from the right, then convert each group to its octal digit (0–7). For instance, 111001₂ becomes 111 001, which equals 71 in octal. Our tool computes this for you alongside the decimal result.
Binary is the native language of computers because transistors in CPUs can only be in two states: on (1) or off (0). All data — text, images, video, code — is ultimately stored and processed as binary numbers at the hardware level.