How do I convert binary to decimal?

To convert binary to decimal, multiply each bit by its positional power of 2 and sum the results. For example, binary 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11. This tool does it instantly and shows each step.

What is the difference between binary, octal, decimal, and hexadecimal?

These are all number systems with different bases. Binary (base 2) uses only 0 and 1. Octal (base 8) uses digits 0–7. Decimal (base 10) is the everyday number system using 0–9. Hexadecimal (base 16) uses 0–9 and A–F, and is widely used in computing for compact representation of binary values.

Why is binary used in computers?

Computers use binary because electronic circuits have two stable states — on and off, which map naturally to 1 and 0. All data, instructions, and memory in a computer are ultimately represented as combinations of these two values.

How do I convert a large binary number to decimal?

For large numbers, the process is the same but tedious to do by hand. This tool uses JavaScript BigInt under the hood, so it handles arbitrarily large numbers accurately without overflow errors.

What are valid hexadecimal digits?

Hexadecimal uses 16 symbols: the digits 0–9 represent values zero to nine, and the letters A–F (or a–f) represent values ten to fifteen. For example, hex FF equals decimal 255, which is binary 11111111.

Binary to Decimal Converter — Free Online Tool

Binary to Decimal Converter

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How to Use

1. Select your input base tab (Binary, Octal, Decimal, or Hex). 2. Type or paste your number into the input field. 3. View all four base representations instantly in the output panel. 4. Click "Show steps" to see the full positional breakdown. 5. Switch to Batch mode to convert multiple numbers at once, one per line.

Features

✓Convert between binary, octal, decimal, and hexadecimal simultaneously
✓Bidirectional — enter any base and see all four outputs at once
✓Step-by-step conversion breakdown showing each positional value
✓Binary output with 4-bit grouping for easy reading
✓Batch conversion mode for processing multiple numbers at once
✓BigInt support for arbitrarily large numbers
✓Instant real-time conversion as you type
✓Copy each base result individually with one click

Frequently Asked Questions

How do I convert binary to decimal?: To convert binary to decimal, multiply each bit by its positional power of 2 and sum the results. For example, binary 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11. This tool does it instantly and shows each step.
What is the difference between binary, octal, decimal, and hexadecimal?: These are all number systems with different bases. Binary (base 2) uses only 0 and 1. Octal (base 8) uses digits 0–7. Decimal (base 10) is the everyday number system using 0–9. Hexadecimal (base 16) uses 0–9 and A–F, and is widely used in computing for compact representation of binary values.
Why is binary used in computers?: Computers use binary because electronic circuits have two stable states — on and off, which map naturally to 1 and 0. All data, instructions, and memory in a computer are ultimately represented as combinations of these two values.
How do I convert a large binary number to decimal?: For large numbers, the process is the same but tedious to do by hand. This tool uses JavaScript BigInt under the hood, so it handles arbitrarily large numbers accurately without overflow errors.
What are valid hexadecimal digits?: Hexadecimal uses 16 symbols: the digits 0–9 represent values zero to nine, and the letters A–F (or a–f) represent values ten to fifteen. For example, hex FF equals decimal 255, which is binary 11111111.

Binary to Decimal Converter

How to Use

Features

Frequently Asked Questions

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