Math & Numbers

Binary Calculator

Convert between binary, decimal, and hexadecimal.

Enter a number in any base to instantly see its binary, decimal, and hexadecimal equivalents.

Enter a valid number for the selected base.

Binary

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Decimal

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Hexadecimal

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How to Use This Tool

  1. Select the input base of your number (decimal, binary, or hexadecimal).
  2. Enter the value.
  3. Click Convert to see it in all three bases.

Understanding Number Bases

Decimal (base 10) is the standard number system humans use daily, with digits 0-9. Binary (base 2), using only 0 and 1, is the fundamental language of computers, since digital circuits represent two states (on/off, high/low voltage). Hexadecimal (base 16), using digits 0-9 and letters A-F, is a compact way to represent binary data, since each hex digit maps exactly to 4 binary digits.

Why Computers Use Binary

Computer hardware is built from transistors that are most reliably operated as simple on/off switches, making base-2 (binary) the natural representation for all data processing, memory, and storage at the hardware level.

Why Programmers Use Hexadecimal

Since 4 binary digits (bits) map exactly to 1 hexadecimal digit, hex provides a much more compact and human-readable way to represent binary data — commonly used for memory addresses, color codes (like #FF5733), and low-level programming.

Frequently Asked Questions

Why do computers use binary instead of decimal?

Computer hardware is built from transistors that reliably operate as simple two-state (on/off) switches, making binary the natural fit for digital circuits, memory, and data processing at the hardware level.

Why is hexadecimal used in programming?

Each hexadecimal digit corresponds exactly to 4 binary digits, making hex a much more compact and readable way to represent binary data — commonly used for memory addresses, color codes, and byte-level programming.

This calculator is provided for general informational and estimation purposes only. Results should not be treated as professional financial, tax, legal, medical, or engineering advice. Always verify critical calculations with a qualified professional or official source before making decisions.