Convert BINARY to DECIMAL, Free
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How to convert BINARY to DECIMAL
Binary is a base-2 numbering system using only 0 and 1, where each digit position represents a power of 2. Decimal is the base-10 system used in everyday arithmetic. Converting from binary to decimal is a foundational skill in computer science, digital electronics, and networking, because computers store all data in binary while humans typically reason in decimal.
The conversion formula sums each bit multiplied by its positional power of two. For example, binary 1011 equals (1x8) + (0x4) + (1x2) + (1x1) = 11 in decimal. This calculator applies that formula instantly, handling both unsigned integers and, optionally, signed representations.
Enter the binary number
Type or paste your binary string (digits 0 and 1 only) into the input field. Spaces between nibbles, such as 1010 0011, are accepted for readability.
Get the decimal result
The converter calculates the positional sum in real time. The decimal equivalent appears as you type.
Check for errors
If the input contains characters other than 0 and 1, the tool will flag the invalid input. Binary strings contain no 2 through 9 digits.
Copy the result
Click to copy the decimal number for use in code, documentation, or further calculations.
Frequently asked questions
How do I manually convert binary to decimal?
Write out the binary number right to left. Multiply each bit by 2 raised to its position (0-indexed from the right). Sum all the products. For 1101: (1x8) + (1x4) + (0x2) + (1x1) = 13.
What is the largest binary number this tool handles?
The tool uses JavaScript's number handling, which supports integers up to 2^53 - 1 (about 9 quadrillion) reliably. For very long binary strings (over 53 bits), consider using BigInt-based tools to avoid precision loss.
Can I convert a binary fraction to decimal?
Binary fractions (such as 0.101 binary = 0.625 decimal) require a different approach: each bit after the point represents a negative power of 2. Most general-purpose binary converters handle integers only. If you need fraction support, look for a specialized tool.
Why do computers use binary instead of decimal?
Electronic circuits are built around switches with two stable states: on and off. These states map naturally to 1 and 0. Representing ten states reliably per digit would require far more complex and less reliable circuitry.
What is a nibble, byte, and word in binary?
A nibble is 4 bits (one hex digit), a byte is 8 bits (values 0-255 in decimal), and a word varies by architecture (typically 16, 32, or 64 bits). Knowing these groupings helps when reading memory addresses or bitfield documentation.