Number Base Converter
Convert numbers between binary, octal, decimal, hexadecimal, and any base from 2 to 36 instantly. Get a full multi-base table, bit-width analysis showing which integer types your number fits in, and a custom base output — free, private, and no signup required.
Enter a number in any base from 2 to 36 and instantly see it in binary, octal, decimal, hexadecimal, and any custom base. All conversions run locally in your browser — no signup required.
Valid digits: 0123456789
Leave blank to skip
Why Use Our Number Base Converter?
Instant Multi-Base Conversion
Enter any number in any base from 2 to 36 and instantly see it in binary, octal, decimal, hexadecimal, and all bases from 2 to 16 simultaneously. The number base converter uses BigInt arithmetic for exact results on arbitrarily large numbers — no floating-point errors.
Secure Number Base Converter Online
The number base converter runs entirely client-side in your browser. Your input values are never sent to any server, stored, or tracked — complete privacy for programming, cryptography, and academic work.
Number Base Converter — No Installation
Use the number base converter directly in any modern browser with no downloads, apps, or plugins required. Copy any result with one click, convert to a custom base, and see bit-width analysis — 100% free forever.
Full Base Table, Bit-Width Analysis & Custom Base
Every conversion shows a complete table of all bases from 2 to 16, a bit-width analysis showing how many bits and bytes the number requires and which integer types it fits in, plus an optional custom base output for any base from 2 to 36.
Common Use Cases for Number Base Converter
Programming & Software Development
Developers constantly convert between decimal, binary, octal, and hexadecimal when working with bitwise operations, memory addresses, color codes, and file permissions. The number base converter handles all four primary bases simultaneously so you never need to convert twice.
Hexadecimal Color Codes
Web designers and front-end developers convert RGB decimal values (0–255) to hexadecimal for CSS color codes. Use the number base converter to instantly translate any decimal color channel value to its hex equivalent — no mental arithmetic needed.
Unix File Permissions (Octal)
Linux and Unix system administrators work with octal file permissions (chmod 755, 644, etc.). The number base converter lets you instantly see the binary representation of any octal permission value to understand exactly which read/write/execute bits are set.
Computer Science Education
Students learning computer architecture, digital logic, and data representation need to convert between number bases constantly. The number base converter shows all bases at once with bit-width analysis, making it an ideal study and homework tool.
Cryptography & Security
Cryptographers and security researchers work with large numbers in hexadecimal, binary, and decimal representations. The number base converter uses BigInt arithmetic to handle arbitrarily large numbers accurately — essential for key material and hash values.
Embedded Systems & Hardware
Embedded systems engineers work with register values, memory-mapped I/O addresses, and bitmasks in binary and hexadecimal. The number base converter's bit-width analysis shows whether a value fits in 8-bit, 16-bit, or 32-bit registers instantly.
Understanding Number Base Conversion
What is a Number Base (Radix)?
A number base (or radix) defines how many unique digits a positional numeral system uses. In base 10 (decimal) — the system humans use daily — there are 10 digits (0–9). In base 2 (binary), used by computers at the hardware level, there are only 2 digits (0 and 1). In base 16 (hexadecimal), there are 16 digits (0–9 and A–F), making it a compact way to represent binary data. In base 8 (octal), digits 0–7 are used, historically common in Unix file permissions. Our number base converter supports any base from 2 to 36, using digits 0–9 followed by letters A–Z for bases above 10.
How Our Number Base Converter Works
- Select Your Input Base: Choose the base of the number you want to convert from the dropdown — from base 2 (binary) to base 36. The valid digit set updates automatically. Optionally enter a custom output base (2–36) for an additional result.
- Enter Your Number: Type the number in the selected base. The number base converter validates your input in real time — only digits valid for the chosen base are accepted. Click Convert to process. All arithmetic uses JavaScript BigInt for exact results on arbitrarily large numbers.
- View All Results Instantly: The number base converter displays binary, octal, decimal, and hexadecimal results as prominent cards, a full table of all bases from 2 to 16, bit-width analysis, and your custom base result — all with one-click copy buttons. Everything runs locally in your browser.
Key Number Base Relationships
- Binary ↔ Hexadecimal: Every 4 binary digits (bits) correspond to exactly 1 hexadecimal digit. For example, binary 1111 = hex F, binary 1010 = hex A. This makes hex a compact shorthand for binary data.
- Binary ↔ Octal: Every 3 binary digits correspond to exactly 1 octal digit. Binary 111 = octal 7, binary 101 = octal 5. This is why octal was historically used for Unix permissions.
- Decimal ↔ Binary: To convert decimal to binary, repeatedly divide by 2 and record remainders. For example, 42 ÷ 2 = 21 R0, 21 ÷ 2 = 10 R1, 10 ÷ 2 = 5 R0, 5 ÷ 2 = 2 R1, 2 ÷ 2 = 1 R0, 1 ÷ 2 = 0 R1 → binary 101010.
- Bit-width: An n-bit unsigned integer can hold values from 0 to 2ⁿ − 1. An 8-bit byte holds 0–255, a 16-bit word holds 0–65,535, a 32-bit integer holds 0–4,294,967,295, and a 64-bit integer holds 0–18,446,744,073,709,551,615.
Supported Bases and Digit Sets
The number base converter supports all integer bases from 2 to 36. For bases above 10, letters are used as additional digits: A=10, B=11, C=12, D=13, E=14, F=15, G=16, and so on up to Z=35. Input is case-insensitive — you can type ff or FF for hexadecimal 255. Base 36 (using all digits 0–9 and letters A–Z) is the maximum supported base and is sometimes used for compact alphanumeric identifiers and URL shorteners.
Related Tools
Voice Recorder & Audio Extractor
Record high-quality audio from your microphone or extract audio from MP4 and WebM video files offline. 100% secure, browser-based utility.
Audio Slicer & Converter
Trim audio clips and convert between MP3, WAV format client-side - Free online audio cutter
ID3 Tag & Metadata Editor
Read and write ID3 tags, album art, artist, and track details directly to MP3 file headers - Free online ID3 tag editor
MP3 Metadata Viewer
View all ID3 tags — title, artist, album, artwork, BPM, and every embedded frame — from any MP3 file instantly in your browser - Free online MP3 metadata viewer
Frequently Asked Questions About Number Base Converter
A number base converter converts integers between different positional numeral systems — such as binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Our number base converter supports any base from 2 to 36, shows all bases from 2 to 16 simultaneously, and runs entirely in your browser with no signup required.
To convert decimal to binary, select "Base 10 — Decimal" as the input base, enter your decimal number, and click Convert. The number base converter instantly shows the binary (base 2) result. For example, decimal 42 = binary 101010. The binary result is displayed with spaces every 4 bits for readability.
Select "Base 2 — Binary" as the input base, enter your binary number (e.g. 11111111), and click Convert. The hexadecimal result appears immediately — 11111111 binary = FF hexadecimal. Every 4 binary digits correspond to exactly 1 hex digit, so the conversion is always exact.
Select "Base 16 — Hexadecimal" as the input base, enter your hex value (e.g. FF or ff — case-insensitive), and click Convert. The decimal result is shown immediately — FF hex = 255 decimal. The number base converter accepts both uppercase and lowercase hex digits.
The number base converter supports all integer bases from 2 to 36. For bases above 10, letters A–Z are used as additional digits (A=10, B=11, ... Z=35). The four primary bases (binary, octal, decimal, hexadecimal) are shown as prominent cards; all bases from 2 to 16 are shown in a full table; and you can specify any custom base from 2 to 36 for an additional result.
Yes. The number base converter uses JavaScript BigInt arithmetic, which supports arbitrarily large integers with exact results — no floating-point rounding errors. This makes it suitable for cryptographic values, hash outputs, and any large number that exceeds the 64-bit integer range.
The bit-width analysis shows how many bits and bytes are required to represent the number, and which standard integer types it fits in (8-bit, 16-bit, 32-bit, 64-bit, 128-bit). This is useful for embedded systems programming, choosing the right data type, and understanding memory requirements.
Yes. The number base converter runs 100% locally in your browser. Your input values are never sent to any server, stored in a database, or tracked in any way. Everything stays completely private on your device.
Yes — the number base converter is 100% free with no signup, no account, and no usage limits. Convert number bases as many times as you need, completely free forever. There are no ads, no premium tiers, and no data collection.