What are number bases and why do they matter?

A number base (or radix) defines how many unique digits a positional number system uses. Decimal (base 10) uses digits 0–9. Binary (base 2) uses 0–1. Octal (base 8) uses 0–7. Hexadecimal (base 16) uses 0–9 and A–F. Different bases are used in computing because binary maps directly to hardware logic gates, hex provides a compact representation of binary data, and octal is used in Unix file permissions.

How do I read hexadecimal numbers?

Hex uses digits 0–9 for values 0–9 and letters A–F for values 10–15. Each hex digit represents exactly 4 bits (a "nibble"). Two hex digits represent one byte (8 bits). For example, the byte 0xFF = 11111111 in binary = 255 in decimal. This is why colors in CSS are written as #RRGGBB - each channel is one byte.

What is the prefix convention for each base?

Standard programming prefixes: binary uses 0b (e.g., 0b1010), octal uses 0o (e.g., 0o12), decimal has no prefix, and hexadecimal uses 0x (e.g., 0xFF). This tool displays these prefixes in output but does not require them in input - just enter the raw digits.

What is the largest number I can convert?

JavaScript's safe integer limit is 2^53 − 1 (9,007,199,254,740,991), which covers most practical use cases. For very large binary or hex values (such as cryptographic keys or hash values), you would need a BigInt-capable tool.

How do I convert between bases by hand?

To go from any base to decimal, multiply each digit by the base raised to its position index (counting from 0 on the right) and sum the results: binary 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11. To go from decimal to another base, divide repeatedly by the target base and read the remainders bottom to top: 11 ÷ 2 = 5 r1, 5 ÷ 2 = 2 r1, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1, giving 1011. Binary to hex needs no arithmetic at all - group the bits into fours from the right and translate each group.

How is octal used in practice?

Octal is most commonly seen in Unix/Linux file permissions. The chmod command uses octal: chmod 755 sets owner=rwx (7), group=r-x (5), other=r-x (5). Each octal digit represents 3 bits - read (4), write (2), execute (1). Octal was also historically used in early computer systems but has largely been replaced by hex.

Number Base Converter - Binary, Octal, Decimal, Hex

Convert numbers between binary, octal, decimal, and hexadecimal instantly. Free number base converter online, no signup needed.

🔒 Your text stays in your browser - nothing is sent to our servers

Input base:

Decimal (base 10) Input

How to Use

Three steps to get started

Select input base

Choose Binary, Octal, Decimal, or Hexadecimal as the base of the number you will enter.

Enter a number

Type your number using digits valid for the selected base. Binary accepts 0 and 1; hex accepts 0–9 and A–F.

Copy any result

All four base representations appear instantly. Click Copy next to any result to use it in your code.

About This Tool

Number bases in computing

A number base (or radix) is the count of distinct digits a positional numeral system uses, and it determines the weight of each digit position: in base b, the digit at position n counting from the right contributes its value multiplied by bⁿ. Every integer can be written in every base - the quantity is identical, only its notation changes. The decimal 255, binary 11111111, octal 377, and hex FF are four spellings of one number.

Computers are binary at the hardware level because a transistor has two stable states, so bases that are powers of two convert to and from binary with no arithmetic at all: hexadecimal groups bits four at a time, octal three at a time. Decimal, being a power of neither, always requires real division - which is why floating-point decimals like 0.1 cannot be represented exactly in binary and why currency should be stored in integer cents rather than floats.

Why hexadecimal dominates programming

Hex is popular because each hex digit maps perfectly to 4 bits, making it a compact way to write binary data. A 32-bit integer that takes 32 binary digits can be written with just 8 hex digits. This is why:

Memory addresses look like 0x7fff5fbff8b0
Colors in HTML/CSS are written as #1A5CFF
SHA-256 hashes are 64 hex characters (256 bits)
UUID/GUIDs use hex digits separated by hyphens
Byte values in debugging are shown as two hex digits each

Quick reference

Decimal 255 = Binary 11111111 = Octal 377 = Hex FF. Decimal 16 = Binary 10000 = Octal 20 = Hex 10. Decimal 1024 = Binary 10000000000 = Octal 2000 = Hex 400. Decimal 4095 = Binary 111111111111 = Octal 7777 = Hex FFF.

Literal syntax across languages

Most modern languages inherited C's prefixes but not all of them agree. C, C++, Java, JavaScript, Python 3, Rust, and Go all accept 0x for hex and 0b for binary. Octal is the divergence: C and Java use a bare leading zero, so 012 means 10, a classic source of bugs in code that pads numbers with zeros. Python 3, Rust, Go, and modern JavaScript require the unambiguous 0o prefix instead, and Python 3 rejects 012 outright. Rust and Java also allow underscores as digit separators - 0b1010_1010 - which JavaScript adopted in ES2021.

Two boundaries to keep in mind. JavaScript numbers are IEEE 754 doubles, so integers stay exact only up to Number.MAX_SAFE_INTEGER, 2⁵³ − 1 = 9,007,199,254,740,991; beyond that you need BigInt or a dedicated arbitrary-precision tool. And every base representation of a negative number depends on the signing convention - two's complement means the 8-bit pattern 11111111 is 255 unsigned but −1 signed.

Every conversion on this page is computed locally in your browser; no values are sent to a server or logged.

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