Number Base Converter — Free Online Base Conversion Tool

Converting numbers between different bases is a core skill in computer science, digital electronics, and systems programming. Our free Number Base Converter instantly translates any number between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — just enter a value in any field and all others update simultaneously.

What Are Number Bases?

A number base (or radix) defines how many unique digits a number system uses. Each digit position in the number represents a power of the base:

• Binary (Base 2) — Uses only 0 and 1. Each position is a power of 2 (1, 2, 4, 8, 16…). The native language of digital hardware.
• Octal (Base 8) — Uses digits 0–7. Each position is a power of 8. Groups 3 binary bits. Common in Unix file permissions and legacy systems.
• Decimal (Base 10) — Uses digits 0–9. The human-default number system.
• Hexadecimal (Base 16) — Uses 0–9 and A–F. Each position is a power of 16. Groups 4 binary bits. Universal in computing for representing byte values.

How to Use the Number Base Converter

1. Select your input base (binary, octal, decimal, or hexadecimal)
2. Enter your number in the input field
3. The equivalent values in all other bases are displayed instantly
4. Click Copy on any output to grab it

All conversion happens in your browser — no network requests.

Number System Quick Reference

How Each Conversion Works

Binary ↔ Hexadecimal (Direct 4-Bit Grouping)

This is the most useful conversion in practice. Since 16 = 2⁴, every hex digit represents exactly 4 binary bits:

Binary:  1010 1111 0011 0101
Hex:       A    F    3    5  = AF35

You can convert in your head by splitting binary into 4-bit groups from right to left, then looking up each group in the nibble table:

0000=0, 0001=1, 0010=2, 0011=3, 0100=4, 0101=5, 0110=6, 0111=7 1000=8, 1001=9, 1010=A, 1011=B, 1100=C, 1101=D, 1110=E, 1111=F

Binary ↔ Octal (Direct 3-Bit Grouping)

Octal similarly groups 3 binary bits per digit (since 8 = 2³):

Binary: 101 011 110 001
Octal:   5   3   6   1  = 5361

Decimal ↔ Any Base (Division Method)

To convert decimal to another base, divide by the target base repeatedly:

• To binary: divide by 2
• To octal: divide by 8
• To hex: divide by 16

Track remainders bottom-to-top for the result.

Example: 75 to binary:

• 75 ÷ 2 = 37 R 1
• 37 ÷ 2 = 18 R 1
• 18 ÷ 2 = 9 R 0
• 9 ÷ 2 = 4 R 1
• 4 ÷ 2 = 2 R 0
• 2 ÷ 2 = 1 R 0
• 1 ÷ 2 = 0 R 1

Reading remainders bottom to top: 1001011 = 75 in binary ✓

Real-World Applications

Unix File Permissions — chmod 755 uses octal. 7 = 111 (rwx), 5 = 101 (r-x). Understanding octal = understanding Unix permissions.

CSS Colors — #FF6B6B is three hex bytes: R=255, G=107, B=107. Hex-to-decimal is daily work in web design.

Bitmask Operations — Low-level code uses hex bitmasks: flags & 0x0F isolates the lower nibble. Seeing 0x0F = binary 0000 1111 instantly reveals what’s being masked.

IPv4 Addressing — Each IP octet (0–255) is one byte. Understanding its binary and hex representation helps with subnetting, CIDR calculations, and protocol analysis.

x86/ARM Assembly — Instructions, registers, and offsets are all expressed in hex in disassembly output.

Color Theory — #RGB hex triplets map directly to 8-bit decimal values per channel, used across CSS, SVG, and image processing libraries.

Frequently Asked Questions

Can I convert numbers with letters like “AF3” in the input?

Yes — hexadecimal inputs can contain digits 0–9 and letters A–F (case-insensitive). Enter AF3 or af3 and the tool will convert it correctly.

Does this support floating-point numbers?

This tool converts integers. Floating-point numbers in different bases require special handling (IEEE 754 encoding or converting the fractional part separately using multiplication by the base). Use integer inputs for reliable conversion.

What’s the maximum number I can convert?

JavaScript safely handles integers up to 2^53−1 (9 quadrillion). Values above this threshold may lose precision. For very large numbers (cryptographic keys, etc.), use a BigInt-capable library.

Why does octal start causing confusion?

In JavaScript and C, a leading zero can indicate an octal literal in some contexts: 010 in JavaScript’s old eval mode was 8 (octal), not 10 (decimal). This has caused subtle bugs. Always be explicit: 0o10 (octal in modern JS), 0x10 (hex), or 0b10 (binary).

What is the relationship between binary and hexadecimal?

They are directly related: hex is a compact shorthand for binary. One hex digit = 4 binary bits. This makes hex the preferred format for humans working with raw binary data — it’s 4× shorter than binary while being mechanically convertible.