Binary, decimal, octal and hex — enter one, see them all.
Decimal
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Binary
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Octal
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Hexadecimal
How this works
Each digit's place value is a power of the base, counting from the right starting at 0:
1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 11₁₀
Binary (base 2) uses only 0 and 1 — the native representation inside every computer.
Hexadecimal (base 16) uses 0-9 then A-F, and is popular because each hex digit maps to exactly 4 binary bits, making it a compact way to write binary values.
Octal (base 8) uses 0-7, and was common in older computing for the same reason hex is now — 3 binary bits per octal digit.
How do I convert binary to decimal?
Multiply each binary digit by 2 raised to its position (counting from 0 on the right) and add them up. 1011 in binary is 1×8 + 0×4 + 1×2 + 1×1 = 11 in decimal.
How do I convert decimal to hexadecimal?
Repeatedly divide by 16 and read the remainders from last to first, using A-F for remainders 10-15. This calculator does that instantly — enter the decimal value and read the hex figure.
Why does hex use letters?
Hexadecimal needs 16 distinct digit symbols but the normal number system only has 10 (0-9), so A through F stand in for the values 10 through 15.
How do I convert hex directly to binary without going through decimal?
Replace each hex digit with its 4-bit binary equivalent and join them — hex A is 1010, hex F is 1111, so AF becomes 10101111. This shortcut works because 16 is 2⁴, which is also why hex is popular for writing binary compactly.