Base Converter

Number Base Converter

This online tool converts numbers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) in real time.

1. Enter a number in any base's input field
2. The other three bases update automatically
3. Switch to a different input field at any time — everything stays in sync

The tool also displays step-by-step conversion details, helping you understand the underlying math.

What Is Base Conversion?

Base conversion is a fundamental concept in computer science and mathematics — transforming a number from one numeral system to another. The four most common systems are:

• Binary — the native language of computers
• Octal and hexadecimal — compact shorthands for binary
• Decimal — the everyday number system

How Conversion Works

1. Parse the input number in its original base
2. Convert it to decimal (if it isn't already)
3. Convert from decimal to the target base

For the integer part, this uses repeated division:

• Divide by the target base
• Record the remainder at each step
• Read the remainders in reverse order to get the result

How to Use

Input & Conversion

The page provides four input fields, one for each base: binary, octal, decimal, and hexadecimal. Type a number into any field and the other three will update instantly.

Input format rules:

• Binary — only 0 and 1, e.g. 11010110
• Octal — only 0–7, e.g. 326
• Decimal — standard digits, e.g. 214
• Hexadecimal — 0–9 and A–F (case-insensitive), e.g. D6

View Conversion Steps

The tool shows a step-by-step breakdown of how the conversion is performed:

1. First, the input is converted to decimal (if it isn't already)
2. Then, decimal is converted to the target base via repeated division and remainder collection

This makes the tool useful for learning, not just calculating.

Common Use Cases

Hex color values — CSS colors like #FF5733 are hexadecimal. Enter FF, 57, or 33 in the hex field to see their decimal RGB equivalents (255, 87, 51).

File permissions — Linux permissions use octal. For example, 755 in binary is 111 101 101, representing rwx r-x r-x.

IP addresses & subnet masks — Network debugging often requires converting between binary and decimal, e.g. the subnet mask 255.255.255.0 is 11111111.11111111.11111111.00000000 in binary.

Memory addresses — Program memory addresses are typically displayed in hex. Use this tool to quickly convert them to decimal or binary.

API

function convertBase(num, fromBase, toBase) {
  const decimal = parseInt(num.toString(), fromBase);
  return decimal.toString(toBase);
}

// Examples
console.log(convertBase('1010', 2, 10)); // Output: 10
console.log(convertBase('A', 16, 2));    // Output: 1010

Related Resources

• Number.prototype.toString()
• parseInt()

These built-in JavaScript functions handle conversion between arbitrary bases (2–36).

FAQ

Q: Why do programmers need to understand base conversion?

Base conversion is foundational to understanding how computers work at a low level. Binary is the native format for storage and computation. Hexadecimal is used for memory addresses, color values (e.g. #FF5733), and byte-level data. Octal appears in Unix file permissions (chmod 755). A solid grasp of base conversion helps with debugging, reading protocol specifications, and performing bitwise optimizations.

Q: Does letter case matter in hexadecimal?

No — uppercase (A–F) and lowercase (a–f) represent the same values. 0xFF and 0xff both equal 255. That said, conventions vary: CSS colors typically use lowercase (#ff5733), while memory addresses and assembly code tend to use uppercase (0x7FFF). This tool accepts both formats.

Q: How can I quickly convert between binary and hexadecimal?

Remember that one hex digit maps to exactly four binary digits (4 bits). Memorize the 16 mappings — 0 = 0000, 1 = 0001, …, 9 = 1001, A = 1010, B = 1011, C = 1100, D = 1101, E = 1110, F = 1111 — and you can expand any hex number to binary digit by digit, or group binary digits into nibbles of four for the reverse conversion.