Enter any binary number (using only 0s and 1s) into the Binary Input field and instantly see its decimal equivalent, along with the hexadecimal and octal representations. The Binary to Decimal Converter also shows you the full step-by-step calculation so you can understand exactly how each binary digit maps to a power of 2.
Decimal Value
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Hexadecimal Value
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Octal Value
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Number of Bits
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To convert binary to decimal, multiply each binary digit by 2 raised to the power of its position (starting at 0 from 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 uses base 2, meaning it only uses two digits: 0 and 1. It is the foundation of modern computers and digital electronics, where 0 represents an 'off' state and 1 represents an 'on' state in electronic circuits.
This converter handles binary numbers of up to 53 bits accurately, which corresponds to decimal values up to approximately 9 quadrillion. For everyday computing purposes, 8-bit (0–255), 16-bit (0–65535), and 32-bit (0–4,294,967,295) conversions are the most common.
A binary number can only contain the digits 0 and 1. Any other character — including spaces, letters, or symbols — makes the input invalid. For example, '1010' is valid but '1210' or '1A10' are not.
Binary and hexadecimal are closely related: every group of 4 binary digits (bits) corresponds to exactly one hexadecimal digit. For example, 1111₂ = F₁₆ and 1010₂ = A₁₆. This makes hex a compact shorthand often used in programming and memory addressing.
Octal uses base 8 (digits 0–7), while binary uses base 2 (digits 0–1). Every group of 3 binary digits maps to one octal digit. For example, 111₂ = 7₈ and 1000₂ = 10₈. Octal was commonly used in older computing systems.
Computers use binary because electronic circuits naturally operate in two states — on (1) and off (0). Representing just two states is far simpler and more reliable in hardware than representing ten decimal digits. Binary logic also maps directly to Boolean algebra, which underpins all digital computation.
Two's complement is a method for representing negative integers in binary. To negate a number, you invert all its bits and add 1. For example, in 8-bit two's complement, −1 is represented as 11111111₂. It is the standard way modern processors handle signed integer arithmetic.