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Binary Converter

Convert numbers from binary to decimal, hexadecimal, etc.

Math
Binary, Hex, & Decimal Converter
Convert between binary, hexadecimal, and decimal number systems.

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Understanding Number Systems

This Binary Converter is an essential tool for computer science students, programmers, and engineers. It allows for seamless, real-time conversion between the three most common number systems used in computing:

  • Decimal (Base-10): The standard number system we use every day.
  • Binary (Base-2): The fundamental language of computers, using only 0s and 1s.
  • Hexadecimal (Base-16): A more compact way to represent binary data, using digits 0-9 and letters A-F.

The Conversion Formulas

The conversions are based on the positional value of digits in each number system.

  • Binary to Decimal: Each digit is multiplied by 2 raised to the power of its position. 1011₂ = 1*2³ + 0*2² + 1*2¹ + 1*2⁰ = 8 + 0 + 2 + 1 = 11₁₀
  • Decimal to Binary: Repeatedly divide the decimal number by 2 and record the remainders in reverse order.
  • Hexadecimal to Decimal: Each digit is multiplied by 16 raised to the power of its position. 1A₃₁₆ = 1*16² + 10*16¹ + 3*16⁰ = 256 + 160 + 3 = 419₁₀

How to Use the Calculator

Simply type a valid number into any of the three fields (Decimal, Binary, or Hexadecimal). The other two fields will update instantly with the converted values.

Real-World Example

Enter the decimal number 255.

  • The Binary field will instantly update to 11111111.
  • The Hexadecimal field will instantly update to FF.

Now, try clearing the fields and entering 1010 in the Binary field.

  • The Decimal field will update to 10.
  • The Hexadecimal field will update to A.

Frequently Asked Questions (FAQ)

  • Why is hexadecimal used in computing? Hexadecimal is used because it's a more human-friendly way to represent binary-coded values. Each hexadecimal digit corresponds to exactly four binary digits (a nibble), making conversions straightforward and less error-prone than reading long binary strings.
  • What are the letters A-F in hexadecimal? Since base-16 needs 16 unique symbols, it uses 0-9 for the first ten values, and then A, B, C, D, E, F to represent the decimal values 10, 11, 12, 13, 14, and 15, respectively.
  • What is this used for in the real world? These conversions are fundamental in low-level programming, network engineering (IP addresses, MAC addresses), and digital color representation (hex color codes).