Binary Decimal

Professional real-time number system converter with step-by-step mathematical breakdowns.

Logic Breakdown

Start typing in either box to see the math

Understanding the Conversion

What is Binary?

Binary is a base-2 number system used by almost all modern computers. It consists of only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from 20 on the far right.

How to Convert manually

To convert binary to decimal, multiply each digit by 2 raised to the power of its position index (starting from 0 on the right) and sum the results.

Example: 1011
= (1 2?) + (0 2?) + (1 2?) + (1 2?)
= 8 + 0 + 2 + 1 = 11

Common Use Cases

  • Programming: Understanding bitwise operations and data storage.
  • Networking: IP address subnetting and MAC address calculations.
  • Digital Logic: Designing circuits and understanding gate behaviors.

Frequently Asked Questions

Is there a limit to the number size?

Our converter handles large integers up to the JavaScript MAX_SAFE_INTEGER (9,007,199,254,740,991).

Can I convert decimals to binary too?

Yes! The tool is bi-directional. Type in the decimal box to get the binary equivalent instantly.