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Binary to Decimal

Convert binary (base 2) numbers to decimal (base 10) instantly online.

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About this tool

Binary (base 2) is the fundamental number system used by all digital computers. Every value stored in memory, every pixel in a display, and every character in a text file is ultimately represented as a sequence of 0s and 1s. Converting binary to decimal is a core skill in computer science, programming, and digital electronics, and is frequently tested in exams and interview questions.

  • ✅ Free to use, no sign-up required
  • ✅ Files never leave your device
  • ✅ Instant conversion
  • ✅ Works on any browser and device

How it works

To convert binary to decimal, each digit is multiplied by 2 raised to the power of its position (counting from right, starting at 0). For example, binary 1101 = (1×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 8 + 4 + 0 + 1 = 13 in decimal. This tool performs that calculation instantly for any binary input.

Frequently Asked Questions

What is the binary number system?
Binary is a base-2 number system that uses only two digits: 0 and 1. It is the native language of digital computers because electronic circuits can easily represent two states — off (0) and on (1).
What is binary 1111 in decimal?
Binary 1111 equals decimal 15. It is calculated as: (1×8) + (1×4) + (1×2) + (1×1) = 15.
What is binary 1000 in decimal?
Binary 1000 equals decimal 8. It is calculated as: (1×8) + (0×4) + (0×2) + (0×1) = 8.
Why do computers use binary instead of decimal?
Computers use binary because digital circuits have two reliable states: high voltage (1) and low voltage (0). It is far simpler and more reliable to detect two states than ten, making binary the practical foundation of all digital systems.

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