What number bases are supported?

Binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). You can also enter a custom base from 2 to 36.

How does the step-by-step explanation work?

The tool breaks down the conversion into individual steps showing the positional values and multiplication, so you can follow the math behind the conversion.

Can I convert large numbers?

Yes. The tool uses BigInt for arbitrary precision, so it handles numbers well beyond the standard 64-bit integer range.

How do I convert binary to decimal manually?

Multiply each binary digit by 2 raised to its position (right to left, starting at 0), then sum the results. For example: 1101 = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13. Our tool shows this calculation step by step.

What is hexadecimal and why is it used in programming?

Hexadecimal (base 16) uses digits 0-9 and letters A-F. It's used because each hex digit represents exactly 4 binary bits, making it a compact way to express binary data. Common uses include memory addresses, color codes (#FF0000), and byte values.

How do I read hexadecimal numbers?

Hex digits 0-9 have their normal values. A=10, B=11, C=12, D=13, E=14, F=15. To convert to decimal, multiply each digit by 16 raised to its position. For example: 2F = 2×16¹ + 15×16⁰ = 32 + 15 = 47.

Binary to Decimal — Number Base Converter

How to Use the Number Base Converter

Enter a number, select its base (binary, octal, decimal, or hexadecimal), and see the equivalent value in all four bases instantly. The step-by-step explanation below shows the positional arithmetic behind the conversion so you can learn the process and verify the math.

What Are Number Bases?

A number base (or radix) determines how many unique digits a number system uses. Decimal (base 10) uses digits 0-9. Binary (base 2) uses only 0 and 1 — it is the foundation of all computer processing. Octal (base 8) uses digits 0-7 and appears in Unix file permissions. Hexadecimal (base 16) uses 0-9 and A-F and is common in memory addresses, color codes, and low-level programming. Converting between these bases is a fundamental skill in computer science.

Common Use Cases

Convert hex memory addresses to decimal for debugging. Translate binary network masks to decimal notation. Understand Unix file permissions in octal with our chmod calculator. Convert hexadecimal color values to their decimal RGB equivalents. Study positional number systems for computer science courses. Verify data integrity with our hash generator. The tool uses JavaScript BigInt, so it handles arbitrarily large numbers without overflow.

Number Base Converter

How to Use the Number Base Converter

What Are Number Bases?

Common Use Cases

Frequently Asked Questions

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