Free Number Base Converter — Binary, Hex, Octal, Decimal Online

Every number you use daily is in base 10 (decimal). Computers think in base 2 (binary). Programmers read memory addresses in base 16 (hexadecimal). Unix file permissions use base 8 (octal). Converting between these bases is a fundamental operation in computer science, programming, and IT.

Our free number base converter converts between binary, decimal, hexadecimal, and octal instantly. Enter a number in any base and see the equivalent in all others. No signup, no ads, everything runs locally.

What Are Number Bases?

A number base (or radix) is the number of unique digits used to represent numbers. Decimal (base 10) uses digits 0-9. Binary (base 2) uses 0 and 1. Hexadecimal (base 16) uses 0-9 and A-F. Octal (base 8) uses 0-7. The same value can be represented in any base — only the notation changes.

For example, the number forty-two is written as 42 in decimal, 101010 in binary, 2A in hexadecimal, and 52 in octal. Same value, different representations.

The Four Common Number Bases

Binary (Base 2) — The language of computers. Every piece of data in a computer is ultimately stored as binary. Understanding binary helps with bit manipulation, network masks, and low-level programming.

Decimal (Base 10) — The system humans use daily. Ten digits (0-9), positional notation. This is your default when someone says "the number 255."

Hexadecimal (Base 16) — Compact representation of binary data. One hex digit represents four binary digits (bits), so a byte (8 bits) is exactly two hex digits. Used in: CSS colors (#FF5733), memory addresses (0x7FFF), MAC addresses, and error codes.

Octal (Base 8) — Each octal digit represents three binary digits. Primarily used for Unix file permissions (chmod 755) and some legacy systems. Less common than hex but still essential for Linux/Unix administration.

When You Need Base Conversion

• CSS color codes. Converting between hex colors (#FF0000) and RGB values (255, 0, 0) requires hex-to-decimal conversion.
• Network engineering. Subnet masks, IP addresses, and network calculations often require binary representation.
• Unix permissions. chmod 755 means rwxr-xr-x — each octal digit maps to three permission bits.
• Debugging. Memory dumps and hex editors display data in hexadecimal. Understanding what those values mean requires conversion.
• Computer science coursework. Number base conversion is a core topic in CS fundamentals and is frequently tested in exams and interviews.

How Base Conversion Works

To convert from any base to decimal, multiply each digit by its positional value and sum the results. Binary 101010 = 1×32 + 0×16 + 1×8 + 0×4 + 1×2 + 0×1 = 42.

To convert from decimal to any base, repeatedly divide by the target base and collect remainders. 42 ÷ 16 = 2 remainder 10 (A), so 42 in hex is 2A.

Our converter does all of this instantly. Type a number in any field and the other three bases update in real-time.

Sell Custom Apparel — We Handle Printing & Free Shipping

Frequently Asked Questions

What is the largest number this can convert?

The converter handles numbers up to JavaScript safe integer limits (2^53 - 1, or about 9 quadrillion). This covers virtually all practical use cases including 64-bit addresses and large color values.

Can I convert between bases other than 2, 8, 10, and 16?

The tool focuses on the four most common bases. For arbitrary base conversion (base 3, base 36, etc.), you would need a specialized mathematical tool or a programming language.

Why do programmers use hexadecimal instead of binary?

Compactness. A 32-bit binary number like 11111111000000001111111100000000 is 32 characters. The hex equivalent FF00FF00 is 8 characters. Each hex digit maps to exactly 4 binary digits, making mental conversion easy.

What is chmod 755 in binary?

755 octal = 111 101 101 binary. Each group of three bits maps to read (4), write (2), execute (1) permissions. 7=rwx, 5=r-x, 5=r-x. Owner can read/write/execute, group and others can read/execute.

Is my data private?

Yes. All conversion happens locally in your browser.