Enter a Binary Number to get its Decimal Number equivalent, or flip it around and convert decimal back to binary — toggle Show Calculation Steps to see a full breakdown of Binary Positions and exactly how each digit adds up to the final Converted Value.
Converted Value
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Calculation Steps
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Binary Positions
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To convert binary to decimal, multiply each digit by its corresponding power of 2 (starting from 2^0 on the right) and sum all results. For example, 1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13₁₀.
To convert decimal to binary, repeatedly divide the number by 2 and record the remainders. The binary result is the remainders read from bottom to top. For example, 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1, giving 1101₂.
The binary number system is a base-2 numeral system using only two digits: 0 and 1. Each position represents a power of 2, making it the fundamental language of computers and digital electronics.
The decimal number system is a base-10 numeral system using digits 0-9. Each position represents a power of 10, and it's the standard number system used in everyday mathematics and counting.
This converter can handle binary numbers up to 63 digits long, allowing you to convert very large binary values to their decimal equivalents and vice versa.
Computers use binary because digital circuits can easily represent two states (on/off, high/low voltage) corresponding to 1 and 0. This makes binary the most efficient and reliable system for electronic processing and storage.
Yes, negative binary numbers can be represented using two's complement notation. However, this converter focuses on unsigned binary numbers for simplicity and clarity in learning the basic conversion process.
Common conversions include: 1₂ = 1₁₀, 10₂ = 2₁₀, 11₂ = 3₁₀, 100₂ = 4₁₀, 1000₂ = 8₁₀, 1111₂ = 15₁₀, and 10000₂ = 16₁₀. Powers of 2 are especially important in computer science.