Sync Conversions

Type in any format to instantly decode the others.

⚠️ Invalid formatting detected for this base type.
Decimal (Base 10)
0-9
Binary (Base 2)
0-1
Hexadecimal (Base 16)
0-9, A-F
Octal (Base 8)
0-7
Formatting Reference
Common Notations
  • Dec: Standard numbers (e.g. 42)
  • Bin: Prefixed with 0b in code (e.g. 0b101)
  • Hex: Prefixed with 0x in code (e.g. 0xFF)
  • Oct: Prefixed with 0o in code (e.g. 0o52)
Quick Table
Dec
Hex
0
0
10
A
15
F
16
10
255
FF

Number Base Converter: Decimal, Binary, Hex, and Octal

Human beings naturally count in Base-10 (Decimal) because we have ten fingers. However, computers process information using transistors that can only exist in two states: on or off. Because of this, computer science relies entirely on Base-2 (Binary) and its more compact mathematical derivatives: Hexadecimal (Base-16) and Octal (Base-8).

Our free online Number Base Converter acts as an instant Rosetta Stone for programmers and computer engineering students. By typing a value into any of the input fields, the engine simultaneously translates that exact integer into all other major numeral systems, saving you from tedious manual division and remainder calculations.

The Four Primary Numeral Systems

  • Decimal (Base-10): The standard system used in everyday life, utilizing ten symbols: 0-9. In programming, if you don't prefix a number with a special character, the compiler assumes it is a decimal.
  • Binary (Base-2): The absolute lowest level of machine code, utilizing only two symbols: 0 and 1. Every digit in a binary number represents a power of 2. In modern programming languages, binary literals are usually prefixed with 0b.
  • Hexadecimal (Base-16): Because binary strings get extremely long and unreadable, developers use Hexadecimal to compress them. It utilizes sixteen symbols: 0-9 followed by A-F (where A=10 and F=15). Exactly four binary bits map perfectly to one hex digit. It is heavily used for memory addresses and web color codes (e.g., #FF0000). In code, hex is prefixed with 0x.
  • Octal (Base-8): Utilizing eight symbols: 0-7. While less common today than Hex, Octal is still widely used in Unix/Linux systems for setting file permissions (e.g., chmod 755). Exactly three binary bits map to one octal digit. It is typically prefixed with 0o.

How Manual Conversion Works

To manually convert a Decimal number to Binary, you use the "Divide by 2" method. You divide the decimal by 2, write down the remainder (which will always be 0 or 1), and continue dividing the quotient by 2 until you reach zero. The binary string is then read by writing the remainders from the bottom up.

Our tool automates this entire process using optimized JavaScript bitwise operators, ensuring instant, error-free translations even for massive integer values.

Frequently Asked Questions (FAQs)

Why is my input showing an error?
You have likely typed an invalid character for the specific base. For example, typing a "2" into the Binary field or an "8" into the Octal field will trigger a strict syntax error, as those systems do not contain those digits.
Can this convert floating-point numbers (decimals)?
No. This specific calculator is designed strictly for integer (whole number) conversions. Converting fractional values into binary requires implementing the IEEE 754 floating-point standard, which goes beyond standard base translation.
Does Hexadecimal care about uppercase letters?
No. In mathematics and programming, 0xff is mathematically identical to 0xFF. Our tool auto-capitalizes hex inputs for better visual readability.

Translate Your Code

Stop dividing by two on a piece of scratch paper. Scroll up, type your number, and extract the bits instantly.