Which bases are supported?

Binary (2), octal (8), decimal (10), hex (16), and arbitrary bases from 2 to 36.

Can I convert negative numbers?

Yes — negative numbers are represented with a leading minus sign, consistent with how most programming languages display them.

Does it support floating-point conversion?

Yes, within JavaScript's double-precision float range — though floating-point representation in bases other than 10 can produce repeating fractions.

What about two's complement?

The converter displays signed values with a minus sign. For bit-level two's complement representation (e.g. 8-bit), enable the 'show binary as two's complement' option.

Why are file permissions in Linux written as 755 or 644?

Octal (base 8) representation of the 9 permission bits (rwx for owner, group, other). Each digit represents 3 bits: 7 = 111 (read+write+execute), 6 = 110 (read+write), 5 = 101 (read+execute), 4 = 100 (read), 0 = 000 (none). 755 means owner has all permissions, group and others can read+execute (typical for executables and directories). 644 means owner can read+write, others can read (typical for files). 600 means owner-only access (sensitive files). Octal is just easier to type than 'rwxr-xr-x' or 'rw-r--r--' — same information, fewer keystrokes.

Why are colors in CSS / web written in hex?

Hex (base 16) compactly represents 8-bit color channels. Each pair of hex digits is one byte (0-255 in decimal, 00-FF in hex). #FF0000 = R=255, G=0, B=0 = pure red. The format matches how memory stores 24-bit colors (3 bytes). Decimal would be 'rgb(255, 0, 0)' — same color, more verbose. Hex is also easier to glance at and identify (FF = max, 00 = min, 80 = mid). Modern CSS supports both; designers prefer hex for compactness, programmers sometimes prefer rgb()/hsl() for arithmetic.

File & Format Converters · Free tool

Number Base Converter

Convert numbers between binary, octal, decimal, and hexadecimal all at once. A clean, ad-free, instant online converter for developers and students alike.

Updated June 2026

Binary (0-1)

Octal (0-7)

Decimal (0-9)

Hex (0-9 a-f)

Type in any field — the others update live. Supports arbitrarily large numbers via BigInt.

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What it does

A free number base converter with binary, octal, decimal, and hexadecimal on screen at the same time. Type in any one field — the others update instantly. Uses BigInt, so arbitrarily large numbers work without precision loss.

Useful for low-level debugging (memory addresses in hex, bitmasks in binary), CSS color math (hex ↔ decimal channels), permissions (octal file modes like 755), and CTF/puzzle work. Prefixes like 0x, 0b, and 0o are accepted in the matching field.

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Paste this snippet into any page. Loads on-demand (lazy), no tracking scripts, and sized to most dashboards. Replace the height to fit your layout.

<iframe src="https://freetoolarena.com/embed/number-base-converter" width="100%" height="720" frameborder="0" loading="lazy" title="Number Base Converter" style="border:1px solid #e2e8f0;border-radius:12px;max-width:720px;"></iframe>

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How to use it

Type a number in any field — binary, octal, decimal, or hex.
Watch the other three update live.
Tap Copy next to any field to grab that representation.
Negative numbers and BigInt-sized values are supported.

When to use this tool

Reading hex memory addresses and converting to decimal for documentation.
Setting Linux file permissions (translating rwx flags to octal 755 / 644).
Bit-level debugging — converting binary masks to decimal or hex for register values.
CTF (capture-the-flag) puzzles where ciphers use base conversions.

When not to use it

Performance-critical conversions in production code — use the language’s native parseInt / toString.
Floating-point binary representation analysis — use IEEE 754 visualizers instead.
Cryptographic operations — use a proper crypto library, not casual base conversions.

Common use cases

Decoding error code 0xFFFFE001 (4294959105 decimal) from a Windows event log.
Converting Linux file mode 0755 (octal) to its binary 111 101 101 representation.
Reading network mask 11111111.11111111.11111111.00000000 = 255.255.255.0 = /24 prefix.
Converting RGB hex #FFD700 to decimal 16766720 for a programming exercise.

Frequently asked questions

Which bases are supported?: Binary (2), octal (8), decimal (10), hex (16), and arbitrary bases from 2 to 36.
Can I convert negative numbers?: Yes — negative numbers are represented with a leading minus sign, consistent with how most programming languages display them.
Does it support floating-point conversion?: Yes, within JavaScript's double-precision float range — though floating-point representation in bases other than 10 can produce repeating fractions.
What about two's complement?: The converter displays signed values with a minus sign. For bit-level two's complement representation (e.g. 8-bit), enable the 'show binary as two's complement' option.
Why are file permissions in Linux written as 755 or 644?: Octal (base 8) representation of the 9 permission bits (rwx for owner, group, other). Each digit represents 3 bits: 7 = 111 (read+write+execute), 6 = 110 (read+write), 5 = 101 (read+execute), 4 = 100 (read), 0 = 000 (none). 755 means owner has all permissions, group and others can read+execute (typical for executables and directories). 644 means owner can read+write, others can read (typical for files). 600 means owner-only access (sensitive files). Octal is just easier to type than 'rwxr-xr-x' or 'rw-r--r--' — same information, fewer keystrokes.
Why are colors in CSS / web written in hex?: Hex (base 16) compactly represents 8-bit color channels. Each pair of hex digits is one byte (0-255 in decimal, 00-FF in hex). #FF0000 = R=255, G=0, B=0 = pure red. The format matches how memory stores 24-bit colors (3 bytes). Decimal would be 'rgb(255, 0, 0)' — same color, more verbose. Hex is also easier to glance at and identify (FF = max, 00 = min, 80 = mid). Modern CSS supports both; designers prefer hex for compactness, programmers sometimes prefer rgb()/hsl() for arithmetic.

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