Binary Converter

Convert between binary, decimal, hexadecimal, and octal — plus text to binary

Input base

BIN Binary (Base 2)

—

DEC Decimal (Base 10)

—

HEX Hexadecimal (Base 16)

—

OCT Octal (Base 8)

—

Understanding Number Bases

Computers work exclusively with binary — 0s and 1s — because electronic circuits have two states: on and off. But representing large numbers in pure binary gets unwieldy fast. That's why developers use other bases as shortcuts:

Base	Name	Digits used	Why it's used
2	Binary	0, 1	Native machine language
8	Octal	0–7	Unix file permissions (e.g., chmod 755)
10	Decimal	0–9	Human everyday counting
16	Hexadecimal	0–9, A–F	Compact binary — 1 hex digit = 4 bits

How Binary Works

In binary (base 2), each digit position represents a power of 2. Reading right to left: 1, 2, 4, 8, 16, 32, 64, 128...

Example: 1011 in binary = 1×8 + 0×4 + 1×2 + 1×1 = 11 in decimal.

Computers group binary digits into bytes (8 bits). One byte can represent 256 values (0–255). That's why IP addresses have four numbers each capped at 255, and why ASCII characters fit within one byte.

Hexadecimal in Practice

Hexadecimal is everywhere in programming. CSS colors use it — #FF5733 is three hex pairs (FF=red, 57=green, 33=blue), each mapping to a decimal 0–255 value. Memory addresses, SHA hashes, MAC addresses, and HTML color codes all use hex because one hex character represents exactly 4 binary digits, making it a clean shorthand.

Octal and Unix Permissions

Octal shows up most often in Unix file permissions. chmod 755 means owner gets 7 (rwx = 4+2+1), group gets 5 (r-x = 4+0+1), and others get 5. Each octal digit represents exactly 3 binary digits, making permission bits readable at a glance.

Frequently Asked Questions

What is 0x before a number?

0x is a prefix indicating hexadecimal in most programming languages. So 0xFF means 255 in decimal. Similarly, 0b prefixes binary (0b1010 = 10) and 0o or 0 prefixes octal in many languages.

What is the maximum number this tool can convert?

JavaScript's safe integer range is ±2⁵³ − 1 (about 9 quadrillion). For numbers beyond this range, use a language like Python that supports arbitrary-precision integers natively.

Why is hex used for colors?

Each color channel (red, green, blue) ranges from 0 to 255 — exactly one byte. Two hex digits can represent any byte value (00 to FF), so a 6-character hex code compactly encodes three 0–255 values. It's shorter than rgb(255, 87, 51) once you're used to it.