Number Base Converter

Convert any integer between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) simultaneously. Type your number, pick its source base, and instantly see all four representations at once.

Number to Convert

From Base

Binary (Base 2)

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Octal (Base 8)

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Decimal (Base 10)
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Hexadecimal (Base 16)

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What is a Number Base Converter?

A number base converter is a tool that translates an integer from one positional numeral system to another. While humans almost universally use the decimal system (base 10) for everyday counting, computers operate on binary (base 2), and programmers routinely encounter octal (base 8) and hexadecimal (base 16) when working with low-level data, memory addresses, color values, and encoded instructions. This converter lets you move seamlessly among all four bases.

Each base determines how many unique symbols are used to represent a value. In binary there are just two digits, 0 and 1, reflecting the on/off state of a transistor. Octal groups binary digits in threes and was popular on early mainframes. Hexadecimal groups binary digits in fours and uses the letters A through F to extend the ten decimal digits, giving a compact and readable way to express long binary sequences.

Understanding multiple bases is fundamental to computer science. Whether you are studying for an exam, debugging a memory dump, designing a network subnet, picking a color in CSS, or reading assembly code, you will encounter numbers expressed in bases other than ten. Having a reliable converter saves time and reduces errors caused by mental arithmetic on long digit strings.

This converter is designed for both beginners and professionals. Type any valid integer in your chosen base, and the tool instantly computes the equivalent representations in the other three bases. Validation prevents invalid digits (such as a 9 in a binary number) and gives immediate feedback, so you always know whether the input was correctly interpreted.

How Base Conversion Works

Every positional numeral system represents a number as a sum of digits multiplied by powers of the base. Converting between bases involves two complementary operations: expanding the source number to its decimal value, then re-encoding that value in the target base.

Formula Value = Σ (digit × base^position), positions counted right to left starting at 0

Example

Convert hexadecimal 2F to decimal:

2 × 16¹ + F(15) × 16⁰ = 32 + 15 = 47

Convert decimal 47 to binary:

47 ÷ 2 = 23 rem 1
23 ÷ 2 = 11 rem 1
11 ÷ 2 = 5 rem 1
5 ÷ 2 = 2 rem 1
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1

Reading remainders upward: 101111

How to Use This Number Base Converter

Enter your number: Type the number you want to convert. Use only digits valid for the source base (0–1 for binary, 0–7 for octal, 0–9 for decimal, 0–9 and A–F for hex).
Choose the source base: Select the base your input is currently written in from the dropdown.
Review all four outputs: The converter instantly displays your value in binary, octal, decimal, and hexadecimal simultaneously.
Check for errors: If you typed an invalid digit for the chosen base, an error message appears and the invalid outputs reset.
Copy results: Use the Copy All Results button to place all four representations on your clipboard for use in code or documentation.

Base Reference & Programming Tips

Binary (Base 2)

Uses digits 0 and 1. Each position represents a power of two. In code, binary literals are written with a 0b prefix (e.g. 0b1010 in JavaScript and Python). Eight binary digits form one byte, the basic unit of memory.

Octal (Base 8)

Uses digits 0–7. One octal digit maps to exactly three binary digits. In JavaScript, a leading zero historically indicated octal, while modern code uses the 0o prefix (e.g. 0o17) to avoid ambiguity with decimal.

Decimal (Base 10)

Uses digits 0–9 and is the system humans use daily. Decimal is the natural reference point for conversion: any number is first expanded to its decimal value, then re-encoded into the target base for output.

Hexadecimal (Base 16)

Uses digits 0–9 and letters A–F (or a–f) for values 10–15. One hex digit equals four binary digits, making it ideal for color codes like #FF5733, memory addresses, and byte-level data inspection. Use a 0x prefix.

Frequently Asked Questions About Number Bases

What is a number base (radix)?

A number base, also called a radix, is the number of unique digits used to represent values in a positional numeral system. Base 10 uses digits 0 through 9, base 2 uses 0 and 1, base 8 uses 0 to 7, and base 16 uses 0 to 9 plus letters A to F. The base determines how each digit position contributes to the overall value.

Why are binary, octal, and hexadecimal important?

Computers store and process data using binary because their circuits have two states. Octal and hexadecimal serve as compact human-friendly representations of binary, since one octal digit equals three bits and one hexadecimal digit equals four bits. Programmers use these bases daily for memory addresses, color codes, machine code, and bitwise operations.

How does positional notation work?

In positional notation, each digit is multiplied by the base raised to the power of its position, counted from right to left starting at zero. For example, the decimal number 245 means 2×10² + 4×10¹ + 5×10⁰. Summing these products yields the numeric value, which can then be re-expressed in any other base.

What is the maximum number this converter supports?

This converter supports integers up to 2⁶³ (9,007,199,254,740,992), which is the maximum safe integer in JavaScript. Beyond this value, floating-point precision issues may cause inaccurate results. For most programming, networking, and educational tasks, this range is more than sufficient and covers the full 32-bit and 48-bit address spaces.

How do I convert between bases manually?

To convert from any base to decimal, multiply each digit by its base raised to its position and sum the results. To convert from decimal to another base, repeatedly divide the number by the target base, recording each remainder. Reading the remainders from last to first gives the digits of the converted number in the new base.

Can negative numbers or fractions be converted?

This tool focuses on non-negative integer values, which is the standard use case for binary, octal, and hexadecimal in computing. Negative integers are usually represented using two’s complement notation in fixed-width formats, and fractions require a separate radix-point approach. For most programming tasks, working with positive integers is sufficient.