The Utility Base

Number Base Converter

Free Online Binary/Octal/Decimal/Hex Converter

Convert between binary, octal, decimal, and hexadecimal in real time with step-by-step explanations.

🔢 What is Base Conversion?

Number bases (radix) are systems for representing numbers. Computers use binary (base 2), daily life uses decimal (base 10), and programming often uses hexadecimal (base 16). A base converter makes it easy to translate between them.

Conversion Results

Binary (Base 2)0b1111 1111
Octal (Base 8)0o377
Decimal (Base 10)255
Hexadecimal (Base 16)0xFF

Conversion Steps: Decimal (Base 10) → Binary (Base 2)

Divide decimal 255 by 2 repeatedly:

255 ÷ 2 = 127 ... remainder 1

127 ÷ 2 = 63 ... remainder 1

63 ÷ 2 = 31 ... remainder 1

31 ÷ 2 = 15 ... remainder 1

15 ÷ 2 = 7 ... remainder 1

7 ÷ 2 = 3 ... remainder 1

3 ÷ 2 = 1 ... remainder 1

1 ÷ 2 = 0 ... remainder 1

Result: 0b11111111

Conversion Steps: Decimal (Base 10) → Octal (Base 8)

Divide decimal 255 by 8 repeatedly:

255 ÷ 8 = 31 ... remainder 7

31 ÷ 8 = 3 ... remainder 7

3 ÷ 8 = 0 ... remainder 3

Result: 0o377

Conversion Steps: Decimal (Base 10) → Hexadecimal (Base 16)

Divide decimal 255 by 16 repeatedly:

255 ÷ 16 = 15 ... remainder F

15 ÷ 16 = 0 ... remainder F

Result: 0xFF

📝 How to Use

  1. Select the base of your input number
  2. Enter the number
  3. All conversions appear instantly
  4. Review the step-by-step explanation

💡 Base Conversion Tips

  • Binary: Foundation of all computer data
  • Octal: Unix file permissions (chmod 755)
  • Hex: Color codes, memory addresses, MAC addresses
  • Bit ops: Understand AND, OR, XOR in binary
  • IP addresses: Subnet masks calculated in binary