Binary / Hex Converter

Number Base Conversion

A number base controls which digits can represent a value. Decimal (base 10) is used for everyday arithmetic, while binary (base 2), octal (base 8), and hexadecimal (base 16) are common in computing. This converter validates a value in one base and shows its equivalent representation in the other three.

Supported bases

Base	Valid digits	Common use	Display prefix
2	0–1	Bits, masks, and digital logic	0b
8	0–7	Unix permissions and legacy systems	0o
10	0–9	Human-readable arithmetic	None
16	0–9, A–F	Memory addresses, colors, and debugging	0x

Prefixes identify a representation in source code. They are shown beside results, but input fields expect digits without 0b, 0o, or 0x.

How positional conversion works

Every digit is multiplied by a power of its base. For example, binary 1010 means:

1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰ = 10

Hexadecimal is compact because one digit represents four binary bits. Therefore, FF is decimal 255 and binary 11111111. Octal digits represent groups of three bits, so octal 10 is binary 1000.

Common uses

• Inspecting bit flags and binary masks
• Converting Unix permission values such as 755
• Reading hexadecimal color or memory values
• Checking protocol fields and packed integers
• Explaining positional notation in programming lessons

Signed values and precision

Decimal input may include a leading minus sign. Results use a leading minus sign as well; they are not two's-complement bit patterns. The converter accepts JavaScript safe integers through 2^53 - 1 in magnitude. Use a big-integer implementation for larger identifiers, hashes, or cryptographic values.

Bit length counts digits in the binary representation, excluding a leading minus sign. Bytes round that length up to the next eight-bit boundary.

Code examples

JavaScript

const decimal = Number.parseInt("1010", 2);
const hexadecimal = decimal.toString(16).toUpperCase();

console.log(decimal);      // 10
console.log(hexadecimal);  // A

Python

value = int("FF", 16)

print(value)       # 255
print(bin(value))  # 0b11111111
print(oct(value))  # 0o377

MySQL

SELECT CONV('1010', 2, 10) AS decimal_value,
       CONV('10', 10, 16) AS hexadecimal_value;

Choosing a representation

Representation	Strength	Trade-off
Binary	Shows individual bits clearly	Long for large values
Octal	Compact three-bit grouping	Less common in modern application code
Decimal	Easy for people to read and calculate	Hides bit-level structure
Hexadecimal	Compact four-bit grouping	Requires remembering A–F values

All conversion happens locally in your browser. Input is not uploaded, and each result can be copied independently.