Number Base Converter
Convert numbers between binary, octal, decimal, hexadecimal, and any base from 2 to 36 — with step-by-step working shown.
Letters A–Z are valid for bases above 10 (e.g. hex uses A–F).
Invalid input for the selected source base.
Result
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Binary (Base 2)
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Octal (Base 8)
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Decimal (Base 10)
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Hex (Base 16)
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Step-by-Step Working
How to Use the Number Base Converter
- 1 Enter Your NumberType the number you want to convert into the input field.
- 2 Select the Source BaseChoose the base your number is currently in — binary (2), octal (8), decimal (10), hexadecimal (16), or any custom base from 2 to 36.
- 3 Select the Target BaseChoose the base you want to convert your number into.
- 4 Click ConvertPress the Convert button or hit Enter to instantly see the result along with a step-by-step conversion breakdown.
- 5 View All Common ConversionsThe results panel also shows your number converted to all four common bases simultaneously: binary, octal, decimal, and hexadecimal.
- 6 Clear and Start OverUse the Clear button to reset all inputs and results for a fresh conversion.
Key Features
Base 2 to Base 36
Convert between any two bases from binary all the way up to base 36 — covering every standard number system used in computing.
4-Base Simultaneous Output
Every conversion instantly shows binary, octal, decimal, and hexadecimal equivalents in a single panel for quick reference.
Step-by-Step Working
See exactly how the conversion was calculated — useful for students learning number systems and verifying results manually.
Letter Support (A–Z)
Handles hex digits A–F and extended base digits up to Z, accepting both uppercase and lowercase input.
Instant Client-Side Logic
All calculations run entirely in your browser — no server, no delay, no data sent anywhere.
Mobile Ready
Fully responsive layout that works cleanly on phones, tablets, and desktops at any screen size from 320px up.
How Number Base Conversion Works
Every number base conversion follows a two-step process: first convert the source number to decimal (base 10), then convert that decimal value to the target base. This two-step bridge through decimal is the universal approach that works between any pair of bases.
Step 1 — Source Base → Decimal: Multiply each digit by its base raised to the power of its positional index (right to left, starting at 0), then sum all the results.
Decimal = d₀ × b⁰ + d₁ × b¹ + d₂ × b² + ... + dₙ × bⁿ
Where d = digit value, b = source base, n = position from right (zero-indexed)
Step 2 — Decimal → Target Base: Repeatedly divide the decimal number by the target base, recording each remainder. Read the remainders in reverse order to get the result.
N ÷ base = quotient remainder R₀
quotient ÷ base = quotient remainder R₁
... repeat until quotient = 0
Result = Rₙ Rₙ₋₁ ... R₁ R₀ (reversed)
Remainders ≥ 10 are represented as letters: 10=A, 11=B, 12=C, 13=D, 14=E, 15=F, etc.
| Base | Name | Digits Used | Common Use |
|---|---|---|---|
2 | Binary | 0, 1 | Computer hardware, digital circuits |
8 | Octal | 0–7 | Unix permissions, legacy computing |
10 | Decimal | 0–9 | Everyday human counting |
16 | Hexadecimal | 0–9, A–F | Memory addresses, colour codes, bytecode |
36 | Base 36 | 0–9, A–Z | URL shorteners, compact IDs |
Practical Examples
Rahul Verma — Pune, India
Computer Science Student — BCA Second Year
Rahul needs to convert decimal 255 to binary for a digital electronics assignment on 8-bit representation.
Sneha Kulkarni — Bengaluru, India
Web Developer — CSS Colour Codes
Sneha is debugging a CSS stylesheet and needs to know the decimal RGB values for the hex colour code #FF5733.
Klaus Hoffmann — Munich, Germany
Systems Engineer — Unix File Permissions
Klaus needs to interpret a Linux chmod value of 755 and verify what binary pattern it represents for each permission group.
Ananya Sharma — Delhi, India
Class 11 Student — Number Systems Chapter
Ananya's textbook asks her to convert binary 1010 1100 to hexadecimal for a number systems exercise.
What is a Number Base Converter?
A number base converter is a tool that translates a number written in one numeral system (called the source base or radix) into its equivalent representation in another system (the target base). Every digit in a number has a positional value that is a power of the base — this is called a positional numeral system, and virtually every number system in modern computing uses it.
The most commonly used bases in computing are binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Each serves a different purpose: decimal is for human use; binary is how processors think; hexadecimal is a compact shorthand for binary that programmers, hardware engineers, and web developers use daily; octal appears in Unix permission systems and some legacy hardware contexts.
Beyond computing, base conversion has applications in mathematics education, cryptography, data compression, and even URL shortening (base 36 is common for compact alphanumeric IDs). Whether you're a student learning number systems for board exams, a developer debugging memory addresses, or a curious learner exploring how different cultures counted historically — understanding base conversion is a foundational skill.
Number Base Converter in Multiple Languages
Want a complete guide to number systems — how binary works, why hex exists, and real computing use cases explained simply?
Read the Full Blog Post →Frequently Asked Questions
Is this number base converter free to use?
Which number bases does this tool support?
Can I convert hexadecimal numbers that contain letters?
What is the difference between binary and decimal?
How does base conversion work mathematically?
Can I convert negative numbers?
What is hexadecimal used for?
Why do computers use binary?
What is octal and where is it used?
Does the tool show step-by-step working?
Does this tool work on mobile?
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