What number bases are supported?

We support binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) conversions.

How do I convert between bases?

Enter a number in any base and the tool automatically shows its equivalent in all other bases in real-time.

What format should I use for hex numbers?

You can enter hex numbers with or without the 0x prefix. Both "FF" and "0xFF" are valid inputs.

Can I convert negative numbers?

Yes! The tool supports negative numbers in all bases. Just use the minus sign (-) prefix.

What are common use cases?

Number base conversion is essential for programming, debugging, working with colors (hex), file permissions (octal), and low-level computing (binary).

Number Base Converter

Convert numbers between binary, octal, decimal, hexadecimal, and more.

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Enter a number to see conversions

A number base (or radix) is the number of unique digits used to represent numbers in a positional numeral system. Each position in a number represents a power of the base, making it possible to represent any value using a limited set of symbols.

The most common bases in computing are:

Binary (Base 2): Uses 0 and 1. The fundamental number system for computers, as digital circuits have two states: on (1) and off (0).
Octal (Base 8): Uses 0-7. Historically used in computing, still common in Unix file permissions (chmod 755).
Decimal (Base 10): Uses 0-9. The standard human-readable number system we use daily.
Hexadecimal (Base 16): Uses 0-9 and A-F. Compact representation for binary data, commonly used for colors (#FF5733), memory addresses, and MAC addresses.

💡 Fun fact: The Babylonians used base 60 (sexagesimal), which is why we have 60 seconds in a minute and 60 minutes in an hour!

Enter your number: Type or paste any number in the input field. The tool accepts numbers in any of the supported bases.
Select source base: Choose the base of your input number (Binary, Octal, Decimal, or Hexadecimal).
Instant conversion: The tool automatically converts your number to all other bases in real-time.
Copy results: Click the copy button next to any result to quickly copy it to your clipboard.
Large numbers: The tool supports very large numbers, limited only by JavaScript's number precision.

Web Development: Convert RGB color values to hexadecimal codes. For example, rgb(255, 87, 51) = #FF5733.
Unix/Linux: File permissions use octal notation. Understanding that chmod 755 = rwxr-xr-x = 0b111101101 helps debugging permission issues.
Network Engineering: Convert IP subnet masks between decimal and binary for CIDR calculations. 255.255.255.0 = 0xFFFFFF00 = /24.
Low-level Programming: Work with bitwise operations, memory addresses, and hardware registers that are typically represented in hexadecimal.
Data Encoding: Understand how data is represented in different formats for compression or transmission.
Debugging: Interpret memory dumps, packet captures, or binary file formats that display data in hexadecimal.
Computer Science Education: Learn number systems and understand how computers represent and process data.

How Binary Works:

In binary (base 2), each position represents a power of 2. Reading from right to left: 1, 2, 4, 8, 16, 32, 64, 128, and so on.

Binary: 1011

= (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)
= 8 + 0 + 2 + 1
= 11 in decimal

Common Binary Operations:

AND (&): Both bits must be 1 → Result is 1
OR (|): At least one bit is 1 → Result is 1
XOR (^): Bits are different → Result is 1
Left shift (<<): Multiply by 2 for each shift
Right shift (>>): Divide by 2 for each shift

🎨 RGB Color Conversion

Converting RGB values to hexadecimal for CSS:

Red: 255 = FF
Green: 87 = 57
Blue: 51 = 33
Result: #FF5733

🔐 File Permissions (chmod)

Understanding Unix file permissions:

chmod 755 (octal)
= 7 (owner: rwx) | 5 (group: r-x) | 5 (others: r-x)
= 111 101 101 (binary)
= Read, Write, Execute for owner

🌐 IP Subnet Masks

Network calculations:

255.255.255.0 (decimal)
= 11111111.11111111.11111111.00000000 (binary)
= 0xFFFFFF00 (hexadecimal)
= /24 CIDR notation

Hexadecimal (base 16) is widely used because each hex digit represents exactly 4 binary digits (bits).

Hex to Decimal:

0=0, 1=1, 2=2, 3=3
4=4, 5=5, 6=6, 7=7
8=8, 9=9, A=10, B=11
C=12, D=13, E=14, F=15

Hex to Binary:

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

💡 Quick tip: To convert hex to binary, replace each hex digit with its 4-bit binary equivalent. FF = 11111111, A3 = 10100011

Different number bases aren't just academic curiosities—they serve practical purposes:

Binary mirrors how computers actually work at the hardware level (transistors on/off).
Hexadecimal provides a compact, human-readable representation of binary data. Two hex digits = one byte.
Octal was popular when computers used 12-bit, 24-bit, or 36-bit words (all divisible by 3).
Decimal is what humans are comfortable with for everyday calculations.

Understanding these conversions is essential for low-level programming, debugging, networking, cryptography, and understanding how computers represent data internally.

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Number Base Converter

What are Number Bases?

How to Use This Tool

Common Use Cases

Understanding Binary Arithmetic

Real-World Examples