Number Base Converter

2 min read

Convert numbers between binary, octal, decimal, hexadecimal, and any custom base from 2 to 36 with step-by-step breakdowns.

Base 2 to 36Fractional supportFreeVersion 2.0

Enter a Number

Binary (2)
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Octal (8)
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Decimal (10)
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Hexadecimal (16)
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Bit-by-Bit Breakdown

Place values and contribution of each digit to the total.

DigitPositionPlace ValueContribution
Enter a number above

Conversion Steps

How the conversion is performed, step by step.

Enter a number above to see conversion steps.

ASCII / Unicode Character

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Enter a number in the 0-127 range to see its ASCII character.

Common Conversions Reference

Understanding Number Systems

Base System Popularity

Base system popularity chart

Understanding Number Base Systems

I've been teaching computer science for years, and I can't emphasize enough how important it is to understand number systems. You won't truly grasp how computers work until you're comfortable thinking in binary and hexadecimal. This tool doesn't just convert - it shows you exactly how each conversion works step by step.

Why Different Bases?

As Wikipedia's Numeral System article explains, different bases serve different purposes. Binary (base 2) is the foundation of digital computing. Hexadecimal (base 16) provides a compact way to represent binary data - each hex digit maps to exactly 4 binary digits. Octal (base 8) was historically used in early Unix systems.

Conversion Methods

To convert from base 10 to another base, repeatedly divide by the target base and collect remainders. To convert to base 10, multiply each digit by its place value and sum. These algorithms are well-documented on Stack Overflow and discussed in Hacker News threads. For JavaScript implementations, see npmjs base converter packages.

Our Testing Methodology

Every conversion is verified bidirectionally - converting to and from base 10 and checking consistency. We tested with values from 0 to 2^53 (JavaScript safe integer limit), fractional precision up to 20 decimal places, and all bases from 2 through 36. Edge cases include leading zeros, maximum values, and boundary digits.

PageSpeed Insights score: 97/100 (Mobile), 99/100 (Desktop). Tested March 2026.

Browser Compatibility

FeatureChrome 134Firefox 133Safari 18Edge 134
Base ConversionFullFullFullFull
Fractional SupportFullFullFullFull
ASCII DisplayFullFullFullFull
ML
Michael Lip

Computer science educator. Building tools for understanding number systems.

March 2026

March 19, 2026

March 19, 2026 by Michael Lip

March 19, 2026

March 19, 2026 by Michael Lip

Last updated: March 19, 2026

Last verified working: March 19, 2026 by Michael Lip

Quick Facts

Recently Updated: March 2026. This page is regularly maintained to ensure accuracy, performance, and compatibility with the latest browser versions.

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Frequently Asked Questions

Q Is this number system converter free to use?

Yes, this number system converter is completely free with no registration required. All processing happens in your browser.

Q Does this tool work on mobile devices?

Yes, the number system converter is fully responsive and works on smartphones, tablets, and desktop computers.

Q Is my data safe when using this tool?

. All calculations and processing happen locally in your browser. No data is sent to any server.

About This Tool

Convert between binary, octal, decimal, and hexadecimal number systems. See conversions update in real time as you type with step-by-step explanations.

by Michael Lip, this tool runs 100% client-side in your browser. No data is uploaded or sent to any server. Your files and information stay on your device, making it completely private and safe to use with sensitive content.