Number Base Converter

Convert numbers between decimal, binary, octal, and hexadecimal. Instant results as you type.

Free to use. Runs in your browser.

Enter a number in decimal, binary, octal, or hexadecimal to see it converted to all other bases simultaneously. Results are best for integers within JavaScript's safe integer range.

Use it for byte values, colour channels, file permissions, subnet masks, and other everyday developer conversions. Very large integers need a BigInt-based converter.

Input Number

From Base

Good to know before converting bases

Each base has its own valid digit set. A value that is valid in one base can be invalid in another, such as 8 in octal or G in hexadecimal.

Binary groups bits

Eight binary digits make one byte. Four binary digits map neatly to one hexadecimal digit.

Octal is strict

Octal only accepts 0 to 7. It is mainly useful for Unix file permission values such as 755.

Hex is case-insensitive

ff and FF represent the same value, 255.

Watch the safe limit

JavaScript numbers lose precision past 9,007,199,254,740,991, so do not use this page for huge cryptographic integers.

Prefixes are not required

Enter FF for hex rather than 0xFF; choose the base from the dropdown.

Leading zeros are display choices

The converter returns the numeric value, so padding such as 00001111 may be removed.

Negative values keep the sign

The minus sign is preserved while the magnitude is converted between bases.

Colour work uses bytes

Each RGB colour channel is a decimal byte from 0 to 255, or hex from 00 to FF.

Output is uppercase for hex

Uppercase A to F keeps hexadecimal output easy to scan beside colour and memory values.

Number Bases: How Computers Count

Humans count in base 10 (decimal) because we have 10 fingers. Computers count in base 2 (binary) because transistors have two states: on and off. But binary is tedious for humans, 11111111 is easier to read as FF (hexadecimal, base 16) or 255 (decimal).

Hexadecimal (base 16) is everywhere in computing: colour codes (#FF5733), memory addresses, MAC addresses, and Unicode code points. Octal (base 8) appears in Unix file permissions (chmod 755). Binary shows up when working with bitwise operations, network masks, and low-level protocols.

This converter works with the four bases developers reach for most: binary, octal, decimal, and hexadecimal. Enter a number in any of those bases, select which one it is, and see it expressed in all four simultaneously. Negative values are supported; for very large integers, precision is limited to JavaScript's safe integer ceiling of 2^53 minus 1 (9,007,199,254,740,991).

Common Number Bases

Base	Name	Digits Used	Where You See It
2	Binary	0, 1	Low-level computing, network masks, flags
8	Octal	0 to 7	Unix file permissions (chmod 755)
10	Decimal	0 to 9	Everyday numbers, most user interfaces
16	Hexadecimal	0 to 9, A to F	Colours (#FF5733), addresses, UUIDs
32	Base32	A to Z, 2 to 7	TOTP secrets (2FA authenticator apps)
36	Base36	0 to 9, A to Z	URL shorteners, compact IDs

What this means for you: Most developers only need decimal, hexadecimal, and binary. Octal matters for Unix permissions. Base36 is useful for short URL-safe identifiers (toString(36) in JavaScript).

Practical Base Conversion Examples

Decimal	Binary	Hex	Octal	Context
255	11111111	FF	377	Max byte value, RGB channel max
420	110100100	1A4	644	Unix file permission (rw-r--r--)
493	111101101	1ED	755	Unix file permission (rwxr-xr-x)
65535	1111111111111111	FFFF	177777	Max 16-bit unsigned integer
16777215	111111111111111111111111	FFFFFF	77777777	White colour (#FFFFFF)

Quick Conversion Tricks

Hex → Binary (by hand)

Each hex digit maps to exactly 4 binary digits. F = 1111, A = 1010, 0 = 0000. So FF = 11111111, and A3 = 10100011. This is why hex and binary are so closely related.

Powers of 2 to memorise

2⁸ = 256, 2¹⁰ = 1024 (1K), 2¹⁶ = 65536, 2³² = ~4.3 billion. These come up constantly in byte limits, colour depth, integer ranges, and memory addressing.

JavaScript shortcuts

0xFF (hex), 0b11111111 (binary), 0o377 (octal), all equal 255 in JS. Use parseInt("FF", 16) and (255).toString(16) for conversions in code.

Subnet masks

255.255.255.0 in binary is 11111111.11111111.11111111.00000000, that's /24 in CIDR notation. Understanding binary makes network masks intuitive.

Worked Base Conversion Example

A common developer example is the Unix permission value 755. In octal, each digit maps to a permission group.

Octal

755

Owner, group, others

Binary groups

111 101 101

Read, write, execute flags

Decimal

493

Same numeric value

In permission notation, 7 means read, write, and execute. 5 means read and execute. Seeing the binary groups makes the flag pattern easier to remember.

Common Base Conversion Mistakes

Entering prefixes in the wrong field

Choose the base from the selector, then enter the raw digits. Prefixes such as 0x are useful in code but are not needed here.

Expecting padding to stay

Leading zeros can be meaningful in fixed-width binary displays, but they do not change the numeric value.

Using invalid digits

Binary accepts only 0 and 1. Octal accepts 0 to 7. Hexadecimal accepts 0 to 9 and A to F.

Ignoring precision limits

JavaScript numbers are precise for integers up to 2^53 - 1. Large identifiers may need BigInt tooling.

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How to use this tool

Enter a number in the input field

Select the base your number is in (decimal, binary, octal, or hex)

See instant conversions to all four bases

Common uses

Converting hex colour codes to RGB decimal values
Understanding Unix file permissions in octal
Working with binary subnet masks and IP addresses
Debugging memory addresses and byte values in hex

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Frequently Asked Questions

What is a number base?

A number base (or radix) defines how many unique digits a counting system uses. Decimal uses 10 digits (0-9) because humans have 10 fingers. Binary uses 2 (0 and 1) because transistors have two states. Hexadecimal uses 16 (0-9 plus A-F) because it maps neatly to 4-bit groups.

Why do developers use hexadecimal?

Hex is compact and maps perfectly to binary. One hex digit represents exactly 4 binary bits, so a byte (8 bits) is always 2 hex digits. FF is easier to read than 11111111. That's why colour codes (#FF5733), memory addresses, and byte values all use hex.

What is octal?

Octal (base 8) uses digits 0 through 7. Each octal digit represents exactly 3 binary bits. It's primarily used in Unix/Linux file permissions, chmod 755 means rwxr-xr-x. Outside of permissions, octal is rarely used in modern development.

How do I convert binary to decimal manually?

Multiply each binary digit by its positional power of 2, then add the results. For 1011: (1×8) + (0×4) + (1×2) + (1×1) = 11 in decimal. The rightmost digit is 2⁰, then 2¹, 2², and so on moving left.

What does 0x mean in code?

0x is the prefix for hexadecimal numbers in most programming languages (JavaScript, Python, C, Java). So 0xFF means 255 in decimal. Similarly, 0b means binary (0b1010 = 10) and 0o means octal (0o755 = 493).

Why are colours written in hexadecimal?

Each colour channel (red, green, blue) ranges from 0-255, which is exactly one byte. In hex, that's 00-FF, two digits per channel. So #FF5733 means red=255, green=87, blue=51. It's compact, widely understood, and maps directly to how computers store colour data.

What's the largest number this tool can convert?

JavaScript safely handles integers up to 2^53 - 1 (9,007,199,254,740,991). Beyond that, precision is lost. For larger numbers, you'd need a BigInt-based converter. For most practical use cases, colours, permissions, byte values, this range is more than sufficient.

How is base 36 useful?

Base 36 uses all 10 digits plus 26 letters (A-Z), producing the shortest possible alphanumeric representation of a number. URL shorteners like bit.ly use it to create compact IDs. In JavaScript, (1234567890).toString(36) gives 'kf12oi', much shorter than the decimal version.

What's the connection between binary and file sizes?

File sizes use powers of 2 because computers think in binary. 1 KB = 1024 bytes (2^10), 1 MB = 1,048,576 bytes (2^20). The 'kilo = 1000' vs 'kibi = 1024' debate exists because humans prefer powers of 10, but hardware uses powers of 2.

Why do MAC addresses use hexadecimal?

MAC addresses are 48 bits (6 bytes), written as 6 pairs of hex digits separated by colons: AA:BB:CC:DD:EE:FF. Hex is the natural choice because each pair represents one byte cleanly. Writing 48 binary digits would be unreadable.

Is the conversion done on a server?

No. All conversions happen in your browser using JavaScript's built-in parseInt() and toString() methods. Nothing is transmitted by the converter after the page loads.

How do subnet masks relate to binary?

Subnet masks like 255.255.255.0 are really about binary. In binary, that's 11111111.11111111.11111111.00000000, twenty-four 1s followed by eight 0s. That's why it's written as /24 in CIDR notation. Understanding binary makes networking click.

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