Enter a binary string to convert it to decimal, hex, and octal — or select arithmetic mode to add, subtract, multiply, or divide two binary numbers and get the result in binary and decimal.
How to use this calculator
For conversion: enter a binary string of 0s and 1s to get decimal, hexadecimal, and octal equivalents.
For arithmetic: enter two binary numbers and select the operation.
The result is shown in binary, decimal, and hexadecimal simultaneously.
Formula & method
Binary to decimal positional notation
Decimal = Σ bit_i × 2^i (from right, i = 0) · Binary add: treat as base-2, carry when sum ≥ 2
Each bit position represents a power of 2, from right to left: 2⁰=1, 2¹=2, 2²=4, 2³=8, etc.
Bit length
The number of digits in the binary representation. An n-bit number can represent values from 0 to 2ⁿ − 1.
Frequently asked questions
What is a binary number?
A base-2 number using only digits 0 and 1. Each position represents a power of 2.
How do I convert binary to decimal?
Multiply each bit by 2 raised to its position (0 from the right) and sum them. 1011₂ = 8+0+2+1 = 11₁₀.
How does binary addition work?
Like decimal but carry when the sum ≥ 2: 0+0=0, 0+1=1, 1+1=10 (carry), 1+1+1=11 (carry).
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