Binary Calculator

Convert between binary, decimal, octal, and hexadecimal. Perform binary arithmetic.

Result

Fill in the fields above, then press Calculate.

A binary calculator converts numbers between binary, octal, decimal, and hexadecimal bases and performs arithmetic in any base.

Select an operation (convert or arithmetic). Enter values in the chosen base. For conversion, select source and target bases. For arithmetic, both values must be in the same base.

Examples

Binary to Decimal

1010₂ = 1×8 + 0×4 + 1×2 + 0×1 = 10₁₀

Binary addition

1010₂ + 1100₂ = 10110₂ (10 + 12 = 22)

Hex to Binary

FF₁₆ = 11111111₂ = 255₁₀

Frequently Asked Questions

Why is binary important?
Computers use binary (base 2) because digital circuits have two states: on (1) and off (0). All computer data is stored and processed in binary.
What is hexadecimal used for?
Hexadecimal (base 16) is a compact way to represent binary data. Each hex digit represents exactly 4 binary digits. It is used for colors (#FF0000), memory addresses, and more.
How do I convert decimal to binary?
Divide by 2 repeatedly and record the remainders. Read the remainders from bottom to top. For example: 13 = 1101₂.
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Quick Tips

  • •Double-check your inputs — small errors lead to incorrect results.
  • •When converting, ensure the input digits are valid for the selected source base.
  • •Use the conversion mode to quickly translate between number systems.